Microwave photonics: devices and applications

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Microwave Photonics

Microwave Photonics: Devices and Applications Edited by Stavros Iezekiel © 2009 John Wiley & Sons, Ltd. ISBN: 978-0-470-84854-8

Microwave Photonics Devices and Applications Edited by

Stavros Iezekiel Department of Electrical and Computer Engineering, University of Cyprus, Cyprus

This edition first published 2009 # 2009 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Microwave photonics : devices and applications / edited by Stavros Iezekiel. p. cm. Includes bibliographical references and index. ISBN 978-0-470-84854-8 (cloth) 1. Microwave devices. 2. Photonics. 3. Electrooptics. 4. Optoelectronics. I. Iezekiel, Stavros. TK7876.M265 2009 621.3810 3–dc22 2008052215 A catalogue record for this book is available from the British Library. ISBN: 978-0-470-84854-8 Set in 10/12pt Times New Roman by Thomson Digital, Noida, India. Printed in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire.

Contents List of Contributors

vii

Preface

xi

List of Acronyms

xv

Part I 1

Introduction to Microwave Photonics

Microwave Photonics – an Introductory Overview Stavros Iezekiel

1 3

Part II Component Technologies

39

2

Direct Modulation for Microwave Photonics Rajeev Ram and Harry Lee

41

3

High-power Distributed Photodetectors for RF Photonic Applications Sagi Mathai and Ming C. Wu

67

4

Photonic Oscillators for THz Signal Generation Andreas St€ ohr and Dieter J€ ager

85

5

Terahertz Sources R. E. Miles and M. Naftaly

111

Part III Systems Applications

131

6

Analogue Microwave Fibre-optic Link Design Edward I. Ackerman and Charles H. Cox, III

133

7

Fibre Radio Technology Dalma Novak, Ampalavanapillai Nirmalathas, Christina Lim, and Rod Waterhouse

169

vi

Contents

8

Microwave Photonic Signal Processing Jos e Capmany, Jos e Mora, Daniel Pastor, Beatriz Ortega, and Salvador Sales

191

9

RF and Microwave Photonics in Biomedical Applications Afshin S. Daryoush

239

10 Characterization of Microwave Photonic Components Stavros Iezekiel

291

Index

333

List of Contributors Edward I. Ackerman Photonics Systems, Inc., 900 Middlesex Turnpike, Building #5, Billerica, MA 01821, USA. Email: [email protected] Jose Capmany Optical and Quantum Communications Group, ITEAM Research Institute, Polytechnic University of Valencia, Camino de Vera, s/n 46022 Valencia, Valencia, Spain. Email: [email protected] Charles H. Cox, III Photonics Systems, Inc., 900 Middlesex Turnpike, Building #5, Billerica, MA 01821, USA. Email: [email protected] Afshin S. Daryoush Department of Electrical and Computer Engineering, Drexel University, Bossone 312, 3141 Chestnut Street, Philadelphia, PA 19104-2875, USA. Email: [email protected] Stavros Iezekiel Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Avenue, P.O. Box 20537, 1678 Nicosia, Cyprus. Email: [email protected] Dieter J€ ager Universit€at Duisburg-Essen, ZHO/Optoelektronik, Lotharstr. 55, 47057 Duisburg, Germany. Email: [email protected] Harry Lee Physical Optics and Electronics Group, Research Laboratory of Electronics, Room 26-459, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA. Email: [email protected] Christina Lim ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia. Email: [email protected]

viii

List of Contributors

Sagi Mathai Electrical Engineering and Computer Sciences and Berkeley Sensors and Actuators Center, 261M Cory Hall, 3-0808, University of California, Berkeley, CA 94720-1770, USA. Email: [email protected] Bob Miles Professor of Semiconductor Electronics, Institute of Microwaves and Photonics, School of Electronic Electrical Engineering, University of Leeds, Leeds LS2 9JT, UK. Email: [email protected] Jose Mora Optical and Quantum Communications Group, ITEAM Research Institute, Polytechnic University of Valencia, Camino de Vera, s/n 46022 Valencia, Valencia, Spain. Email: [email protected] Mira Naftaly National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, UK. Email: [email protected] Ampalavanapillai Nirmalathas ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia; and National ICT Australia, Victoria Research Laboratory. Email: [email protected] Dalma Novak Pharad, LLC, 797 Cromwell Park Drive, Suite V, Glen Burnie, MD 21061, USA; and ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia. E-mail: [email protected] Beatriz Ortega Optical and Quantum Communications Group, ITEAM Research Institute, Polytechnic University of Valencia, Camino de Vera, s/n 46022 Valencia, Valencia, Spain. Email: [email protected] Daniel Pastor Optical and Quantum Communications Group, ITEAM Research Institute, Polytechnic University of Valencia, Camino de Vera, s/n 46022 Valencia, Valencia, Spain. Email: [email protected] Rajeev Ram Research Laboratory of Electronics and Professor of Electrical Engineering, Department of Electrical Engineering and Computer Science, Room 36-491, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA. Email: [email protected]

List of Contributors

ix

Salvador Sales Optical and Quantum Communications Group, ITEAM Research Institute, Polytechnic University of Valencia, Camino de Vera, s/n 46022 Valencia, Valencia, Spain. Email: [email protected] Andreas St€ ohr Universit€at Duisburg-Essen, ZHO/Optoelektronik, Lotharstr. 55, 47057 Duisburg, Germany. Email: [email protected] Rod Waterhouse Pharad, LLC, 797 Cromwell Park Drive, Suite V, Glen Burnie, MD 21061, USA; and ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia. Email: [email protected] Ming C. Wu Electrical Engineering and Computer Sciences and Berkeley Sensors and Actuators Center, 261M Cory Hall, 3-0808, University of California, Berkeley, CA 94720-1770, USA. Email: [email protected]; [email protected]

Preface Microwave engineering and photonics technology are two areas of electrical engineering that have had a dramatic impact on everyday life, in particular in the fields of communication and sensing. The last few decades have seen optical techniques dominating long haul communications, and optical-fibre-to-the-home deployment is being actively pursued in some regions. The huge bandwidth of optical fibres has acted as the spur to develop techniques such as wavelength division multiplexing and to design optoelectronic components, driver electronics and receiver electronics operating at ever higher speeds. This means that the designers of optical-fibre systems have to now consider microwave design issues when dealing with optoelectronic components and their associated electronics. We have also witnessed phenomenal growth in wireless communications in order to support an increasingly mobile and nomadic lifestyle, and this has been driven by advances not only in signal processing but also microwave components and systems. Whilst early generations of wireless systems have operated at a few GHz, there is substantial research and development activity in mm-wave wireless technology and this has been supported by the development of radio-over-fibre in which optical networks are used for signal distribution and also mm-wave signal generation. Whatever form future generations of communications networks take, it is clear that the physical layer will continue to be dominated by photonics technology (for wired) and microwave technology (for wireless). The ‘interface’ between microwave and photonics technologies will therefore also be of major importance and this ‘interface’ has created a new interdisciplinary field known as microwave photonics. In order to gain a clearer definition of microwave photonics, it is perhaps best to refer to applications and examples. Whenever one has to consider bit rates of several Gb/s in an optical fibre communication system, then microwave design techniques must be applied to components such as modulators and photodiodes. Thus the application of microwave engineering to the design of high-speed optoelectronic components and optical fibre systems is an example of microwave photonics. However, it is the availability of high-speed optoelectronics and optical fibres that has also opened up the possibility of using optical fibre links to transport microwave signals in applications such as phased array antennas, radio astronomy arrays and distributed antenna arrays for in-building wireless communications. Hence the application of photonics technology and techniques to microwave systems is another example of microwave photonics. As microwave photonics has matured, however, we have seen the emergence of more advanced applications of photonics to microwave engineering, leading to enhanced ‘functionality’. Light modulated at microwave frequencies is now being investigated for medical imaging, and we are also seeing the emergence of ‘microwave photonic signal generation and processing’. The

xii

Preface

primary motivation here is to take advantage of the large time-bandwidth product available from optical fibres. A good example of this is the use of optical fibres (in the form of recirculating loops, and more recently through the use of Bragg grating structures and optical amplifiers) to perform filtering of microwave signals. This area of microwave photonics has since expanded to include the development of microwave oscillators using fibre loops (socalled optoelectronic oscillators) and the implementation of analogue-to-digital converters, photonic ‘time stretch’ and arbitrary waveform generation. In addition, we have seen the use of photonics techniques to generate microwave and mm-wave signals through the realization of optical comb generators and optical phase-locked loops in addition to optical heterodyning. This last technique also forms the basis of THz signal generation, where the primary interest is in using the THz spectrum to explore sensing and imaging applications. (The advantage here is that the wavelengths in the THz part of the spectrum enable spectroscopy of molecules.) In fact the THz spectrum has now begun to enter the domain of microwave photonics, since it occupies the ‘gap’ between microwaves and optics. As such, techniques for THz signal generation from both microwave engineering (e.g. Gunn diodes) and from photonics (e.g. heterodyning) are being explored, and the field uses concepts and component designs originating from both microwaves and optics. From an educational perspective, the fields of microwave engineering and photonics are often taught in separate courses (this being yet another symptom of the modularization of many modern degree courses). It is quite rare to find textbooks let alone courses which treat both in a unified way, and as a consequence the field of microwave photonics tends to be populated by practitioners with a mix of backgrounds – physicists and electrical engineers mostly. Some have come to the topic as microwave engineers, optical engineers or semiconductor optoelectronics specialists, each having to learn something of the others fields. This is challenging, since microwave photonics encompasses physical concepts, devices and systems in two different parts of the spectrum. A microwave photonics engineer needs to be well-versed in electromagnetism, semiconductor electronics and optoelectronics, circuit and optics design and communications theory and systems to name but a few topics. Over time a small community of microwave photonics engineers has developed, as evidenced for example by special joint issues of the IEEE Transactions on Microwave Theory and Techniques/OSA Journal of Lightwave Technology and the development of conferences such as the IEEE Topical Meeting on Microwave Photonics. The time is now appropriate for the publication of books in this field, and some texts have already been published on the topics of analogue links and component technology. The aim of this book is to provide some flavour of the work being carried out in this field, and as such it is more an ‘anthology’ rather than an exhaustive compendium of knowledge. To do full justice to the breadth of work being done under the umbrella of microwave photonics would result in an unwieldy tome and the fast pace of innovation and the generation of new applications would soon require the inclusion of new topics in a future edition. Instead I have sought to provide a snapshot of selected work at both the device level and the application level that gives an indication of how microwave photonics can be applied to the design of highspeed optoelectronics and how such high-speed optoelectronics can be exploited for applications in areas such as wireless communications, medical imaging and measurements. Each of the chapters has been written by experts in these particular areas, and it is hoped that both existing practitioners and researchers new to the field will find something that whets their appetite for future work in this exciting area.

Preface

xiii

My sincere thanks and appreciation go to the contributing authors who took time out of their busy schedules to write and revise their chapters. In addition, I thank all my students and colleagues (past and present) who have indirectly contributed to the book via discussions on various parts of microwave photonics technology. On the publishing side, I am particularly indebted to Juliet Booker for helping me through the final stages of production. Finally, I must thank my family (and especially Kalina) for their constant support and understanding. Stavros Iezekiel Nicosia, Cyprus October 2008

List of Acronyms ADC AGC ALMA APD AR ASE AWG BCL BDT BEON BER BLNA BS BSCCO BWC BWO CATV CDMA CMOS CMRR CNR CO CPS CPW CTB CW DAS DAST DBR DD/IM DE-MZM DFB DFG DHBT

analogue to digital converter automatic gain control Atacama Large Millimetre Array avalanche photodiode anti-reflection amplified spontaneous emission arrayed waveguide grating bipolar cascade laser ballistic deflection transistor bilateral electro-optic network bit-error rate bilateral lightwave network analyzer base station Bi2Sr2CaCu2O8 backward wave cancellation backward wave oscillator cable television code division multiple access complementary metal oxide semiconductor common mode rejection ratio carrier-to-noise ratio central office coplanar strip coplanar waveguide composite triple beat continuous wave distributed antenna system 4-(4-Dimethylaminostyryl)-1-methylpyridinium tosylate distributed Bragg reflector direct detection/intensity modulation dual-electrode Mach–Zehnder modulator distributed feedback difference frequency generation double heterojunction bipolar transistor

xvi

DS DUT EAM EDFA EM EMI EML EO E/O ESA FBG FC/APC FDA FDLF FDPM FEL FEM FET FGDLF FIR FO FP FSR FTTH FWM HBV HD HEMT HFC HIC HiperLAN HR IF IIR IM IM/DD IMD IMD3 IMPATT IP LAN LCA LCFBG LMDS LO LT LTI

List of Acronyms

dual sources device under test electro-absorption modulator erbium-doped fibre amplifier external modulation electromagnetic interference electro-absorption-modulated laser electro-optic electrical to optical European Space Agency fibre Bragg grating fibre connector/angled physical contact Food and Drug Administration fibre delay line filter frequency-domain photon migration free-electron laser finite element model field effect transistor fibre grating delay line filter finite impulse response fibre optic Fabry–Perot free spectral range fibre-to-the-home four-wave mixing heterostructure barrier varactor harmonic distortion high electron mobility transistor hybrid fibre coax hybrid integrated circuit high-performance radio LAN high-reflection intermediate frequency infinite impulse response intensity modulation intensity modulation/direct detection intermodulation distortion third-order intermodulation distortion impact avalanche transit time internet protocol local area network lightwave component analyser linearly chirped fibre Bragg gratings local multipoint distribution system local oscillator low-temperature grown linear time invariant

List of Acronyms

MAN MASER MBE MIC MLLD MMF MMI MMIC MQW MSLR MSM MS-TWDP MTI MWP MWPSP MZI MZM NDR NEP NF NIR OA O/E OEL OFCG OFDM OMD OP OPO OPPL OSSB OSSBþC OTDR PAN PCS PD PDW PF-VMDP PIN PIIN PLL PM PMD PMT PO PRF PRI

metropolitan area network microwave amplification by stimulated emission molecular beam epitaxy monolithic integrated circuit mode-locked laser diode multimode fibre multimode interference microwave monolithic integrated circuit multiple quantum well main-to-secondary lobe ratio metal–semiconductor–metal multisection travelling wave distributed photodetector moving target identification microwave photonic microwave photonic signal processing Mach–Zehnder interferometer Mach–Zehnder modulator negative differential resistance noise equivalent power noise figure near infrared optical amplifier optical to electrical optoelectronic optical frequency comb generators orthogonal frequency division multiplexing optical modulation depth optical prefiltering optical parametric oscillator optical phase locked loop optical single sideband optical single sideband with carrier optical time domain reflectometry personal area network personal communication system photodetector photon density waves parallel fed VMDP a junction diode with an intrinsic layer between doped p and n layers phase induced intensity noise phase locked loop polarization-maintaining polarization mode dispersion photomultiplier tube photonic oscillator pulse repetition frequency inter-pulse period

xvii

xviii

PVDF QB Q-BER QCSE QCL RF RIN RN RoF RTD SBS SCH SCM SCML SDE SEM SFDR SI SIS SKA SLED SLM SNR SOA SPM SRS SS SSB TAR TFBG TO TRS TUNNETT TWPD UMTS USB UTC UTC-PD VCSEL VMDP VNA VOA WDM WI-MUX WI-OADM XPM

List of Acronyms

polyvinylidenfluorid quadrature bias point quasi-ballistic electron reflection quantum confined Stark effect quantum cascade laser radio frequency relative intensity noise remote node radio over fibre resonant tunnelling diodes stimulated Brillouin scattering separate confinement heterostructure subcarrier multiplexing subcarrier multiplexed label standard diffusion equation scanning electron micrograph spur-free dynamic range semi-insulating superconductor–insulator–superconductor Square Kilometre Array superlattice electron device spatial light modulator signal-to-noise ratio semiconductor optical amplifier self-phase modulation stimulated Raman scattering signal source single sideband thru-attenuate-reflect tapered fibre Bragg grating transistor outline time-resolved reflectance spectroscopy tunnel injection transit time travelling wave photodetector universal mobile telecommunications system upper sideband uni-travelling carrier uni-travelling-carrier photodiode vertical cavity surface emitting laser velocity match distributed photodetector vector network analyser variable optical attenuator wavelength division multiplexed wavelength-interleaved multiplexer wavelength-interleaved optical add-drop multiplexer cross-phase modulation

Part I Introduction to Microwave Photonics


1 Microwave Photonics – an Introductory Overview Stavros Iezekiel In the 1960s, photonics was seen by some visionaries as a possible alternative to microwaves for future high-speed communications. Towards the end of that decade it was not clear which one of these two technologies would eventually prevail for terrestrial telecommunications; indeed, there were trials of a long-distance ‘Millimetric Waveguide’ system by the UK Post Office [1] (which would eventually be abandoned in favour of optical fibre). It was always clear, however, that the two technologies are complementary to one another in many ways, and it is not surprising that they should overlap and merge to form a new interdisciplinary topic – microwave photonics. In this chapter we aim to: (i) define what is meant by the term ‘microwave photonics’, (ii) describe its evolution, (iii) discuss its advantages and limitations and (iv) describe its applications.

1.1 The Roots of Microwave Photonics Microwave photonics combines technology developed for both the microwave and optical parts of the spectrum (Figure 1.1) [2]. From a historical basis, examples of simple optical communications have existed since ancient times; these relied on human vision to observe signals, such as those generated using semaphore codes by Chappe’s optical telegraph in revolutionary France [3]. The subsequent appearance of the electrical telegraph [4], however, suppressed optical communications for over a century. The first commercially successful transatlantic telegraph cable was installed in 1866 and it would take another century before the publication by Kao and Hockham [5] of a paper outlining how, with suitable reductions of losses in silica, dielectric waveguides in the form of optical fibres could be used for signal transmission. In addition to the telegraph, researchers in the 19th century also began to examine wireless communications. Despite the demonstration of the photophone in 1880 [6] – the first example of a free-space link in which modulation of a light beam’s intensity and photodetection of it


4

RF & Microwaves

30 MHz

X-ray

Ultraviolet

Visible

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10-8 10-9

Optics

Electronic techniques

30 kHz

1 nm

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Extremely ultrashortwave

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Wavelength (m)

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Microwave Photonics: Devices and Applications

3 GHz 30 GHz

THz Gap

Photonics

3 THz

3 PHz

Frequency

Figure 1.1

The electromagnetic spectrum

was employed for telephone transmission – radio techniques eventually took over and have dominated wireless transmission ever since. The advantages of higher frequencies were recognized early on, and mm-wave transmission was pioneered by Chandra Bose [7] in the 1890s. It was the Second World War and the need for radar, however, that provided the impetus for increased research activity in microwave engineering. Vacuum tubes were the workhorse of microwave electronics for radar systems and then satellite communications, but compound semiconductor technology has since dominated the field of active microwave circuits. In particular, GaAs microwave monolithic integrated circuits (MMICs) have enabled compact and complex circuits of the type needed in applications such as mobile communications and satellite navigation receivers, and the evolving technologies of SiGe and RF CMOS contribute to the continued development of low-cost transceiver technology. A key component in a communication system is a sinusoidal oscillator. One method of producing coherent oscillations is through stimulated emission, and in the early 1950s the first maser (microwave amplification by stimulated emission) was demonstrated. It was to be the optical maser [8], however, – better known as the laser – that would eventually revolutionize communications (and also many other areas of science and technology). The first solid-state laser was developed by Maiman in 1960 [9] and was soon followed by the first gas laser [10]. Lasing was to be demonstrated subsequently in many other material systems, including semiconductors. If one considers the free-space wavelength of the first laser (ruby), which is 694.3 nm, the corresponding frequency is 432 THz. Even 1% modulation of this frequency still results in a bandwidth far in excess of microwave systems and it was simple calculations such as these that caught the attention of communication engineers in the early 1960s [11]. In spite of the obvious attractions of an optical oscillator, it was still some years away from commercial success and significant progress would have to be made in the many other components needed for an optical communications link. Aside from the practical difficulties of modulating an

Microwave Photonics – an Introductory Overview

5

optical carrier at high frequencies and then detecting it, there remained the significant problem of guiding it between transmitter and receiver. Proposals for hollow waveguides with periodically located lenses were at one point under serious consideration, but were eventually discarded as impractical. Looking back at a review of the field from 1970 [12] gives some indication of how there was scepticism as to whether optical communications would supplant microwave and mm-wave communications: Whether or not there will be a real need for the potentially large bandwidth possibilities in the optical and near-optical region remains something of a question. Even some of the warmest adherents of optical communications laugh at questions about ‘payoff’. Some of them assert that they are working with optical devices and systems out of scientific curiosity, because it is fun, because it is intriguing, and other such reasons. Nilo Lindgren, Optical Communications – A Decade of Preparations, 1970 [12]

The above statement was made only four years after the feasibility of optical fibre was reported in Kao and Hockham’s seminal paper [5], and barely a decade after semiconductor laser diodes were demonstrated [13]. Despite the rather cautious nature of Lindgren’s analysis, the communications industry viewed the large potential bandwidth of optical communications as being sufficient incentive to pursue the continued development of both optical fibre and semiconductor optoelectronic components. Breakthroughs such as Corning’s demonstration of relatively low attenuation in silica fibre [14] and room-temperature operation of laser diodes [15] provided some of the ingredients needed for commercially viable optical links. Since then, the success of optical fibre communications has more than surpassed what many of its earliest developers would have dared hoped for. Field trials of first-generation systems in the late 1970s using multimode fibre operating at 850 nm had bit-rate distance products of approximately 1 Gb/s-km. This figure-of-merit would go on to double approximately every two years due to the development of a further four generations of optical communications [16]; techniques such as wavelength division multiplexing [17] and soliton transmission [18], both of which were enabled by optical amplifiers [19], meant that long-distance optical fibre links had broken the 1 Tb/s barrier by 2000 (Figure 1.2). Long-awaited developments in fibre-to-thehome (FTTH) are also starting to bear fruit, with a steady evolution from 10 Gb/s Ethernet (10 GbE) through to recent interest in 40 Gb/s and 100 Gb/s Ethernet (IEEE 802.3). Most optical fibre links are used for digital communications, but due to the high bit rates that are often involved, one must apply analogue microwave techniques to the design of components such as high-speed lasers, optical modulators and photodetectors. In a Mach–Zehnder modulator, for example, it is important to design the electrodes correctly in order to match the phase velocities of the microwave and optical signals. This is a problem in transmission line design. Travelling wave effects must also be considered in certain photodetector designs, while impedance matching techniques play an important part in microwave fibre-optic link design. The study of the interaction of optoelectronic devices with microwave signals is a cornerstone of microwave photonics, but the topic is much wider than this as we shall see in the following sections. Before proceeding to define exactly what ‘microwave photonics’ means, some mention should be made of the root words. The term ‘microwaves’ [20] refers to signals in the frequency

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1 10 100 Data rate per channel (Gb/s)

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Figure 1.2 Improvements in optical fibre link bit rates and link distance; data points prior to 2004 taken from H. Kogelnik, ECOC’04 (Paper Mo1.1.1)

range between 300 MHz and 300 GHz (while the term ‘mm-waves’ refers to signals with wavelengths of the order of millimetres). ‘Photonics’ [21] is a term that is analogous to electronics, in that it implies control of photons (as opposed to electrons) in either free-space or matter. The photon energies of interest are in the range 0.5 eV to 2 eV, corresponding to freespace wavelengths spanning the visible spectrum as well as the infrared and ultraviolet on either side. One may argue that the term optics could be applied instead, given that we are dealing with the optical part of the spectrum. The fact that multiple terms are available in this field – including optoelectronics, electro-optics and lightwaves – can be confusing, especially given the lack of complete agreement over the precise meaning of these terms. The fields of electronics and photonics are, at the fundamental physical level, intertwined in any case, since accelerating electrons generate light and light propagating through optical media interacts with dipoles. Whilst electron–electron interaction is strong (with the result that devices such as transistors are feasible), light–light interaction is weak and devices such as lasers and photodiodes rely on electron–photon interaction. In the former electrons control the flow of photons, while in the latter the roles are reversed. According to Saleh and Teich [21], electro-optics is used to refer to optical devices in which electrical effects play a key role (examples include lasers and modulators); optoelectronics refers to devices that are essentially electronic (e.g. diodes) in which optical effects are important (examples include photodiodes). In recent years the term ‘lightwave’ has also proved popular, and the term is to ‘microwave’ as photonics is to electronics. Lightwave technology is commonly used to refer to systems that combine electro-optic and optoelectronic devices with an optical transmission medium (usually optical fibre) in order to transmit and/or process optical signals. Here we will largely use the word photonics to deal with devices and systems in which photons may be generated, transmitted, controlled or detected. As such, the photons are likely to interact with matter and electrons at various points in the system.

7


1.2 What is Microwave Photonics? Microwave photonics has been defined by Seeds and Williams [22] as having two aspects: (i) the study of photonic devices which are capable of processing microwave signals, and (ii) the application of photonic components and techniques to microwave systems. The first definition will be familiar to those who have worked with high-speed fibre-optic links. This line of research parallels the general field of optical fibre communications, in which significant progress has been made with devices such as lasers, modulators and photodetectors that are capable of handling digital signals up to several Gb/s (or analogue signals up to several GHz). The second definition is a consequence of high-speed optoelectronic components (that were originally developed for the telecommunications industry) being available ‘off-theshelf’. This has allowed them to be used not only for transmission of analogue microwave signals over optical fibre, but also for the processing of microwave signals in the optical domain. This includes tasks such as filtering and analogue-to-digital conversion, and a major advantage of using photonics in a microwave system is the huge bandwidth potential of optical fibre coupled with low optical loss.

1.3 Why Use Microwave Photonics? Microwave and photonic components process electromagnetic waves, albeit in different parts of the spectrum. When combined together in an appropriate sequence, we have a microwave photonic system, and a simple example illustrating the basic concepts is shown in Figure 1.3. This diagram uses terminology borrowed from the lightwave measurements community (see Chapter 10 and also [23]), in which analogue electrical signals in the microwave frequency range are denoted by ‘E’ and optical signals modulated by these same electrical signals are denoted by ‘O’. Conversion between the two domains is carried out by an E/O (electrical-tooptical) transducer at the input and an O/E (optical-to-electrical) transducer at the output end. Between the E/O and O/E stages is the O/O component, which in many examples is optical fibre. It is the exceptional qualities of optical fibre as a transmission medium which are behind the success of optical communications in general, and which provided one of the primary motivations for microwave photonics research. These include low cost, low weight (typically 1.7 kg/km for fibre as opposed to 567 kg/km for coaxial cable [2]), low cross-sectional area, high degree of physical flexibility, immunity to electromagnetic interference and relatively low dispersion (especially at 1310 nm for silica single-mode fibre) and very low loss (as low as 0.2 dB/km at 1550 nm in terms of optical loss, which is equivalent to just 0.4 dB/km of electrical loss). This last quality of optical fibre is compared with other transmission media in Figure 1.4;

Input

Drive circuit

E/E Figure 1.3

Modulated optical source

E/O

Optical fibre

O/O

Photoreceiver

O/E

Output

Amplifier

E/E

Block diagram of a basic microwave photonics link. Reproduced from [23] ( 2008 IEEE)

8

Figure 1.4

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100

Propagation loss characteristics of various delay media (after [102])

the figure shows that an additional advantage of optical fibre is that the loss is flat as a function of microwave frequency. This is because the fractional (i.e. modulation) bandwidth is so small compared to the optical carrier, that is only a minute part of the 1550 nm wavelength window is being used. From a communications perspective, it is the fibre attenuation and dispersion (along with noise and nonlinearity due to E/O and O/E conversion) which are most crucial in determining signal degradation, but their impact differs according to the application of the link. If digital signals are applied at baseband to the link in Figure 1.3, our primary concern is to recover them at the output at an acceptable BER (bit-error rate – typically 109) assuming that the E/O and O/E transducers can handle sufficiently high bit rates. By using Poisson statistics it is possible to arrive at the required O/E receiver sensitivity [24] for a given bit rate, which can then be used (along with knowledge of the E/O source power and fibre loss) to determine the maximum repeaterless transmission distance. The figure-of-merit that is of most interest for digital links, therefore, is the maximum bit rate – distance (BL) product for a specified BER. In addition to attenuation, however, we must also consider dispersion since this will be more deleterious as bit rates increase beyond the so-called attenuation limit (Figure 1.5). In a digital link, we can tolerate a certain amount of signal degradation as long as the pulse distortion does not result in excessive bit errors at the receiver. We can use optical amplification and regeneration at regular intervals along an optical fibre in order to increase the transmission distance. Moreover, in the electronic domain advanced pulse shaping and error recovery techniques are available. From the point of view of a digital link, therefore, our main aim is to maximize the distance between repeaters and the fact that optical fibre is a superior medium (in terms of attenuation) when compared with free-space, say, is the key factor in the uptake of optical communications over long distances. When one considers analogue links one must now also factor in the effect of the E/O and O/E transducers. This is because the function of an analogue microwave photonic link is to convey a microwave signal from the input to the output with as little signal degradation as possible, and so we compare it with conventional microwave transmission media. Ideally the link should act as a ‘transparent tube’, in which the output is a delayed replica of the input signal. Looking at

9


Distance (km)

1000

Standard single-mode at 1550 nm Standard single-mode at 1310 nm

100 Step-index multimode

10 Graded-index multimode

1 0.1

1

10 100 Bit rate (Mb/s)

1000

10000

Figure 1.5 Attenuation- and dispersion-limited distance for various optical fibres; the fibres are dispersion-limited at the high bit rate end and attenuation-limited at the low bit rate end

the effect of the optical fibre alone, it certainly outperforms something like microstrip by a substantial margin (Figure 1.4). Not only is its loss lower, but it has a flat frequency response. These two qualities of low transmission loss and large bandwidth capability are the main factors which first persuaded researchers to investigate the use of photonic techniques in microwave systems. In order for a microwave signal to encounter this low fibre loss, it must first be converted to microwave modulation of an optical carrier and then recovered through photodetection. The E/O and O/E conversion processes introduce a penalty, typically anywhere between 20 dB and 40 dB. When this is included into the link loss calculations, then microwave fibre-optic links only yield lower loss than coaxial cables once they exceed a crossover point, as shown in Figure 1.6. A major goal of microwave photonic link design is the reduction of overall link loss, and to this end improvements can be obtained either through improved O/E conversion [25, 26] or transformer-based matching techniques [27]. In addition to affecting link loss, the inclusion of active E/O and O/E components will also have an impact on three other important performance parameters. The first of these is the overall frequency response of the link, which in turn is affected by the small-signal frequency response (also termed the modulation response when looking at E/O conversion) of the E/O and O/E components. The second is the noise figure; noise is introduced into the link by both the E/O and O/E conversion processes. Finally, E/O (and to a lesser extent O/E) components are inherently nonlinear, and thus they will act to limit the dynamic range of the microwave photonic link. The above discussion highlights the importance of improving the design and fabrication of E/O and O/E components, along with the development of link design techniques (such as impedance matching) in order to derive the most out of the excellent properties of optical fibre. Later in this book we will discuss the different technologies that are available to achieve these goals, but first we will look at how microwave signals are ‘processed’ by a microwave photonic system.

10

Microwave Photonics: Devices and Applications 100

Link loss (dB) at 1 GHz

90

3/8” Coax

80 70

E/O and O/E transducer losses

60 50

Upper bound 40 dB

40 30

Fibre link loss Lower bound 20 dB

20 10 0 0.001

0.01

0.1 Distance (km)

1

10

Figure 1.6 Comparison of typical coaxial cable loss compared to standard single-mode fibre; between 20 dB and 40 dB of E/O and O/E transducer losses are included for the fibre

1.4 Anatomy of a Basic Microwave Photonic System We now examine the E/O and O/E conversion processes in more detail, as shown in Figure 1.7. Many microwave photonic systems use laser diodes for the E/O source module. The laser diode is basically an oscillator, which upon application of a bias current will produce lightwaves with an optical frequency (vo) of about 200 THz (assuming we choose a typical emission wavelength such as 1550 nm). If we assume the existence of a perfectly monochromatic laser and also neglect noise, the electric field at a fixed point can be represented by a time-varying complex quantity: EðtÞ ¼ E0 exp jðv0 t þ f0 Þ. In principle, the amplitude (|Eo|), frequency (vo) or phase (fo) of the lightwave may be modulated; this is analogous to the situation found in microwave communications. Once modulation has been applied to the lightwave, it will be guided by the optical fibre and be subjected to attenuation, dispersion and possible changes in polarization. At the fibre output, a photodetector is used to recover the original modulation signal. The first stage in a photodetector is a photodiode; this is a square-law device that produces a photocurrent that is directly proportional to the square of the electric field magnitude. This quantity is proportional to the intensity (W/m2), which in turn is proportional to the optical power. A photodiode can therefore only directly detect intensity modulation (i.e. modulation of |Eo|2), hence the term direct detection. Most fibre link designs are based on intensity modulation/direct detection (IM/DD) partly to have simple receiver architectures. This is in a loose sense the optical equivalent of the amplitude modulation/envelope detection scheme in radio communications, a scheme which is relatively primitive when compared to the more advanced techniques commonly used in wireless systems, such as those based on phase shift keying. The word ‘loose’ is used in the previous sentence, because if we apply a sinusoidal microwave signal of frequency vm to an E/O component, the resulting optical field will contain a central optical frequency vo and multiple sidebands at vo nvm. The exact

11


ωO RF input

Microwave signals reside as sidebands on an optical carrier

Modulated optical source Single-mode optical fibre

[E/O modulation]

ωm Direct modulation (intensity modulation)

External modulator

CW laser

RF input

RF output

Modulated optical input

Photo -diode

Or

Or External modulation

ωm

Direct detection

Intensity modulated optical signal (“AM”)

Directly modulated laser diode

[O/E demodulation]

Receiver options:

Source options:

RF input

RF output

Photoreceiver

Modulated optical signal Intensity, phase, or frequency modulation

Coherent detection

Modulated optical input CW laser (LO)

Optical coupler

RF output

Photodiode

+ Square-law detection and LPF

Figure 1.7 Microwave photonic link architectures for direct and external modulation, and for direct and coherent detection. Reproduced from [23] ( 2008 IEEE)

form of the spectrum depends on the E/O device and bias conditions. This is in contrast to the amplitude modulation of radio signals, which normally produces no more than two sidebands. Intensity modulation can be achieved either directly or externally. Direct modulation of a laser simply means adding a time-varying current which results in the intensity (i.e. optical power) tracking changes in the current. Direct modulation up to about 30 GHz is possible, but one disadvantage of this scheme is chirp, that is the optical frequency is inadvertently modulated. This can be overcome by operating the laser in CW (continuous wave) mode and using an external modulator instead; these are voltage-driven devices and have larger modulation bandwidths (beyond 100 GHz for polymer-based devices). An added advantage of these devices is that in addition to intensity modulation, they can also provide phase and frequency modulation. However, detection of phase and frequency modulation requires coherent photoreceivers using local oscillator lasers. Whilst coherent detection offers improved sensitivity (through the use of high-power local oscillator lasers which effectively amplify the incoming signal), it is more complex to implement than direct detection and places stringent requirements on the linewidth of the source and local oscillator lasers. Moreover, the use of optical amplifiers as pre-amplifiers for photoreceivers means that the sensitivity of direct detection has been improved relative to that of coherent receivers.

12


1.5 Device Technology In this section we describe some of the devices which are available to provide the basic functions of E/O and O/E conversion in a microwave photonic system and we briefly discuss O/O components.

1.5.1 E/O Conversion As mentioned previously, intensity modulation of light can be achieved either through direct modulation of a laser diode or by using a modulator to externally modulate light from a CW laser [28]. External modulation is preferred in ‘high-performance’ applications whereas the advantage of direct modulation is low cost, especially when uncooled laser diodes are used. 1.5.1.1 Directly Modulated Laser Diodes The advantage of laser diodes is that they are compact and only require a few mA of drive current in order to operate; they also offer a potential route to monolithic integration with a variety of other electronic and photonic structures on the same chip. If we confine our discussion to single frequency signals, then in a directly modulated laser diode (Figure 1.8), the drive current IL is given by IB[1 þ mcos(vmt þ wm)], where IB is the bias current and m is the modulation index. We can show that the electric field emitted by the device (if we neglect chirp) has the form: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1:1Þ EðtÞ ¼ E0 1 þ m cos vm t expðj½vo t þ fo Þ For small-signal modulation m 1 so we can use Bessel functions to expand the electric field expression. We can show that this contains multiple frequency components of the form vo nvm. In effect the E/O transducer is an up-converter, mixing vm onto an optical carrier. However, the optical intensity will be given by the square of the electric field magnitude. If we square the magnitude of Equation (1.1), we find that the optical output power is of the form P0 ð1 þ mðcos vm t þ um ÞÞ where Po is the average power, vm is the microwave modulation

Figure 1.8

Typical light–current characteristic for a laser diode. Reproduced from [23] ( 2008 IEEE)

13


frequency and um the phase. If we consider the light–current characteristic of a laser diode, the above result makes sense. The light–current (L–I) characteristic is a plot of optical output power versus drive current as shown in Figure 1.8. This resembles the DC piecewise-linear I–V characteristic of a diode. Above threshold and below saturation, the L–I characteristic can be approximated very well by a straight line segment with a slope given by sL ¼ dPL/dIL, where sL is the slope efficiency in W/A. Ideally we want the slope efficiency to be as high as possible but it is fundamentally limited by the quantum efficiency of the laser. Hence, if we ensure that the drive current does not go below threshold or into saturation, the optical power will follow the drive current (Figure 1.8). The ‘DC’ components are related via Po ¼ sLIB, where Po is the average optical power. Although it is not obvious from the L–I curve, the slope efficiency is frequency-dependent. At a given frequency, the sinusoidal components of the current and optical power can be described using phasors, and they are related via: sL ðjvm Þ ¼

pL ðjvm Þ iL ðjvm Þ

ð1:2Þ

where iL(jvm) is the modulation current phasor and pL(jvm) is the corresponding output optical power phasor. sL(jvm) is referred to as the intensity modulation response and is an important parameter. Directly modulated laser diodes have a low-pass second-order response which places a limit on the bandwidth they can support, as shown in Figure 1.9. The second-order response is a consequence of the interaction between carrier recombination and photon emission, which in the simplest case is described by a pair of nonlinear ordinary differential equations (the rate equations, as described in greater detail in Chapter 2). These can be solved to determine both the damping factor and the resonance frequency, which in turn influences the small-signal intensity modulation bandwidth. It should also be borne in mind that the bond wire and package parasitics will influence the overall response (usually in an adverse way), so optimization of these is required in high-speed laser diodes. When considering direct modulation for microwave photonics systems, we therefore have to be aware of a number of performance parameters and device limitations. Two important parameters are the slope efficiency (which will impact the overall link gain as discussed in Chapter 6) and also the bandwidth (which given the fact the O/E transducers generally have very high bandwidths will often be the limiting factor in overall link bandwidth). Limitations of the direct modulation approach include: (i) the inadvertent modulation of wavelength Parasitics can degrade the response (parasitic roll-off)

p L ( jω m ) i L ( jω m )

Resonance peak: The laser is modulated at frequencies below this point

Roll-off = 40 dB/dec (Due to second-order response)

ωm Figure 1.9

Typical intensity modulation response for a laser diode

14


(the chirp referred to earlier), which when combined with fibre dispersion will lead to signal degradation; (ii) nonlinearity, which can be significant at the resonance frequency (and in severe cases can lead to chaos); (iii) multiple-sideband modulation, which when combined with fibre dispersion can lead to power fading (this depends on the fibre length and the laser wavelength); (iv) relative intensity noise (RIN), which will affect the overall noise figure performance of a microwave photonic system; (v) a differential quantum efficiency which is less than unity, which results in E/O conversion loss; and (vi) perhaps most important of all, lower bandwidth compared to external modulation. In spite of the above limitations, the simplicity and relatively low cost of direct modulation are very attractive for many applications, and this continues to drive forward research in highspeed laser diodes. We can categorize laser diodes according to device structure, three main types being Fabry–Perot, distributed feedback (DFB) and vertical cavity surface emitting lasers (VCSELs); these are compared in Figure 1.10. We can also classify the laser material according to whether it is bulk, quantum well or quantum dot. Over the years a large body of research has aimed to engineer both the device structure and materials in order to increase bandwidth, improve slope efficiency and also yield other improvements (such as reduced threshold current and temperature sensitivity). The use of multiple quantum wells for DFB lasers has proved particularly successful, leading to increased differential gain and reductions in threshold current compared to bulk devices. Bandwidths in excess of 30 GHz have been demonstrated for InGaAsP quantum well lasers operating at 1550 nm [29] and for distributed Bragg reflector devices [30]. In recent years much effort has been put into quantum dot devices [31], since these lasers promise near zero threshold currents and reduced sensitivity of threshold current to temperature fluctuations. This last feature is important, since it dispenses with the need for temperature control circuits, thereby leading to reduced cost. Devices for 10 Gb/s applications have been reported [32]. The theme of low cost also crops up in the development of VCSELs; here the vertical emission opens up the possibility of on-wafer test and the circular beam profile also simplifies the laser-to-fibre coupling problem. Given the renewed interest of multimode fibre for microwave photonics applications, as discussed later, the VCSEL takes on added significance for the implementation of in-building fibre radio networks for example. Modulation bandwidths of the order of 10 GHz have been obtained at 1550 nm [33]. Significant work has also been carried out with more complex structures to improve slope efficiency (e.g. the gain lever laser [34] and bipolar cascade laser [25,35]). The use of multiple junction laser transmitters [36] is discussed in more detail in Chapter 2. Recently, much work has also been done to extend the modulation frequency performance of laser diodes. Some techniques are narrowband and rely on using external optical cavities with frequency selective feedback in order to enhance the resonant response [37], while an alternative method is based on optical injection locking [38] and this has been used to demonstrate an enhanced resonance frequency of 72 GHz [39]. In this last technique, the free running lasers typically have modulation bandwidths of no more than 10 GHz. By using high optical injection ratios, it is possible not only to achieve resonant enhancement but also to enhance the 3 dB bandwidth, improve the modulation efficiency (by a factor of 10) and reduce the relative intensity noise (to 140 dB/Hz) [38]. Optical injection locking also reduces distortion, leading to enhanced spur-free dynamic range (SFDR). Recent work has focused on cascaded optical injection locking, in which an additional slave laser is introduced [40]. This enables 1.55 mm VCSELs with a free running 10 GHz bandwidth to exhibit up to 66 GHz bandwidth, thus opening up their use in mm-wave fibre radio systems.

Figure 1.10 Example structures for Fabry–Perot, DFB and VCSEL lasers

Microwave Photonics – an Introductory Overview 15

16


1.5.1.2 External Modulation As implied by the name, external modulation entails the use of an external device (i.e. the modulator) to vary either the intensity or phase of the light emitted by a laser diode emitting a constant power level (CW mode). The obvious disadvantages are the added cost, complexity and increase in the size of the E/O module, but these are accepted in many instances because of the greater bandwidth on offer (especially important for mm-wave applications) and the greater control over which the modulation is carried out, which opens up possibilities such as singlesideband operation. Furthermore, unlike direct modulation, external modulation does not suffer from the problem of chirp. Many of the performance requirements that were discussed for direct modulation also apply in the case of external modulation, namely the need for high modulation efficiency, large bandwidth and good linearity. There are also some differences, however, the most evident being that external modulators are voltage driven rather than current driven. In addition, they have an optical input (connected to the CW laser) as well as an optical output, and so low optical insertion loss is required. Since the basic effect in an external intensity modulator is varying absorption of the optical input from the CW laser, it is desirable to have high optical power handling capability. As with direct modulation, a number of material systems and device structures are available. The most successful from a commercial perspective is the Mach–Zehnder structure implemented in lithium niobate, but there are also many examples of electro-absorption modulators (fabricated from III-V semiconductors) and polymer-based devices. A particular advantage of electro-absorption modulators is the possibility of monolithic integration with the CW laser. The underlying mechanism in lithium niobate modulators is the Pockels (or linear electrooptic) effect in which an electric field (originating from an external drive voltage) induces change in the refractive index, which in turn will lead to a change in phase. When an interferometric structure is used, the phase modulation is converted to intensity modulation. The electro-optic effect is found in crystals such as lithium niobate and gallium arsenide as well as poled polymers. Figure 1.11 shows the basic structure of a lithium niobate Mach–Zehnder modulator. The basic idea is that an applied voltage can be used to vary the phase shift between the two optical waveguide arms, such that when light is combined from these arms at the output it can vary between a minimum level (corresponding to destructive interference) and a maximum (due to constructive interference). The simplest Mach–Zehnder design is one in which phase modulation is applied to only one of the arms, but it is also possible to have dual electrode designs and these have been used for optical single sideband generation (OSSB) in order to overcome the dispersion penalty which occurs in mm-wave fibre radio systems. In a similar vein to the analysis carried out for the directly modulated laser diode, we can consider the static transfer characteristic (Figure 1.12) of an external modulator in order to deduce parameters such as the slope efficiency. The approach has several important differences though. (i) The actual optical power level (Po) depends not only on the modulator but also on the power supplied by the CW laser source (Pi); the y-axis is a ratio of powers rather than being absolute power. (ii) The x-axis is also a ratio, of the drive voltage Vm to Vp (this being defined as the voltage required for a phase shift of p between the two modulator arms).

17

Microwave Photonics – an Introductory Overview Ti-diffused optical waveguide

CW light

Lithium niobate substrate

Figure 1.11

Electrodes

Modulated light

Simplified diagram of Mach–Zehnder modulator

(iii) The transfer characteristic is periodic, in principle allowing more choice in terms of choosing the bias point. One suitable bias point is located at 3 Vp/2 as shown in Figure 1.12, and if we apply small-signal modulation then excursions in voltage will occur over a quasi-linear part of the characteristic. (It can be shown quite easily that the optimum bias point for maximum modulation efficiency can be located at any odd multiple of Vp/2.)

Figure 1.12

Mach–Zehnder modulator transfer characteristic

18


As for the case of the directly modulated laser diode, we are interested in the slope of the characteristic in the vicinity of the bias point. The important difference here is that the points (i) and (ii) above indicate that the slope will depend on both Vp (which crudely speaking can be thought of as analogous to the threshold current in a laser diode, in that it is a property of the device) and Pi (which is in effect an external control parameter). For directly modulated laser diodes, the slope efficiency is essentially dictated by the device’s differential quantum efficiency alone. The transfer characteristic for the Mach–Zehnder modulator is given by: Po Tff pVm 1 þ cos ¼ Pi 2 Vp

ð1:3Þ

where Tff is the optical insertion loss of the modulator when it is biased for maximum transmission (e.g. at zero volts). If we now apply a bias voltage of VB ¼ nVp/2 (where n is odd) and a small-signal modulation component given by vm(t), then linearization of Equation (1.3) around the bias point will yield: Po Tff pðVB þ vm ðtÞÞ Tff pvm ðtÞ 1 þ cos ¼ 1 ð1:4Þ Vp Pi Vp 2 2 from which the slope efficiency (in W/V) is obtained as: sM ¼

dPo Tff p ¼ Pi : dvm 2Vp

ð1:5Þ

Equation (1.5) shows one advantage of using an external modulator, namely that by increasing the CW laser power Pi we can increase the slope efficiency of the external modulation process. In other words the external laser acts as a ‘bias’ which can be used to control modulator efficiency, and in turn the gain of the microwave photonic link. Indeed, this approach has been used to demonstrate link gain without any other optical or electronic amplification being used. The above equation also illustrates one of the key issues of modulator design, namely the desire to reduce the drive voltage Vp so as to bring it within the range available from drive electronics (ideally below 3.5 V). One technique for doing so is to increase the microwave-optical interaction length (i.e. the electrode length), but this demands reductions in electrode and optical waveguide loss, and wafer size will ultimately place a limit on length. This can be overcome by using folded structures [41]. A further issue in modulator design is that of velocity matching, and as such this represents an excellent case study of classical microwave engineering techniques being used to optimize the performance of a microwave photonic device. In travelling-wave modulators, the electrodes are designed to act as microwave transmission lines, with the microwave signals propagating in the same direction as the optical signals (the optical waveguides being parallel with the electrodes). One advantage is that these devices are not capacitance limited in terms of their frequency response, thus enabling relatively long electrode designs (typically thousands of wavelengths [28]). It then becomes imperative that the phase velocities of the microwave signals and optical signals are matched to one another, and this should be done over a range of frequencies. In lithium niobate, the microwave signal has a lower velocity than the optical signal and so it must be speeded up – usually by appropriate modification of the transmission line capacitance per unit length, this being achieved with a silicon dioxide buffer layer. Conversely,


19

in GaAs and InP devices this situation is reversed and the microwave signal needs to be slowed down; this can be achieved through periodic capacitive loading of the electrodes. The other transmission line issue for Mach–Zehnder modulators relates to having to avoid standing wave formation on the electrode structure due to reflections from impedance mismatches. Ideally the characteristic impedance of the electrodes should match that of the driver electronics. As was the case for directly modulated laser diodes, a Mach–Zehnder modulator will in general produce multiple optical sidebands when modulated by a microwave sinusoid, leading to terms in vo nvm. This is a consequence of the nonlinearity of the E/O conversion process. However, through appropriate bias and modulation conditions, it is possible to suppress higher order sidebands, leaving a carrier plus an upper and lower sideband, namely vo and vo vm. It is also possible to generate a single sideband as mentioned above, and this has uses in optical filter measurements (Chapter 10) and mm-wave fibre radio (Chapter 7). Extensive work has been done on linearization schemes for lithium niobate Mach–Zehnder modulators. One of the motivations for this is to improve the dynamic range of microwave photonic links. The general approach is to connect two modulators together (either in a cascade or in a ‘dual signal’ arrangement) and select appropriate bias points such that the composite device behaves more linearly than either one of the individual modulators [42]. One of the difficulties of these approaches is the susceptibility to tight tolerance requirements and the increased optical losses due to the use of two modulators rather than one. A comparison of different schemes in terms of their bandwidth is available in [43]. Recently a new design of Mach–Zehnder has been proposed in which linearization is performed by using phase control and a resonator on one of the modulator arms, leading to reduced optical losses compared to earlier techniques [44]. The one disadvantage of lithium niobate as a material is that it cannot be integrated with the laser diode source, a fact which has motivated the investigation of III-V semiconductors, including both GaAs and InP. Semiconductor-based modulators are also more compact, but the linear electro-optic (Pockels) effect is weaker than that in lithium niobate and there tends to be a poor overlap between the optical mode and the applied electric field. Furthermore the refractive index of InP, for example, is relatively higher (3.5) than that for silica optical fibres, all of which leads to increased fibre-to-fibre insertion loss for these modulators (typically 10 dB). Nevertheless, some impressive results have been achieved, including demonstrations of low drive voltage (0.45 V for a GaAs Mach–Zehnder modulator for an estimated bandwidth of 50 GHz [45]) and demonstrations of 80 Gb/s modulation (for an InP modulator with capacitively loaded electrodes [46]). Another material system that has attracted much interest is organic polymers, the primary motivation being the potential for low-cost manufacturing [47]. These materials can be endowed with an electro-optic effect via high-temperature poling, resulting in a Pockels coefficient (r33) as high as 320 pm/V at 1550 nm [48], as opposed to 31 pm/V for lithium niobate. Another parameter that works in favour of electro-optic materials is the fact that the dielectric constant for the microwave signals is approximately equal to the square root of the refractive index in the optical range, meaning excellent velocity matching between microwave and optical signals on the same substrate. This removes the need for techniques such as capacitive loading of electrodes and also results in extremely wideband performance. Bandwidths in excess of 100 GHz were demonstrated some time ago [49], while drive voltages in the sub-volt region have recently been demonstrated at 1550 nm [50]. A further benefit of the polymer approach is that it lends itself to hybrid packaging of both microwave and optical

20


components on the same platform [51]. In spite of all these advantages, polymer modulators have been beset by a number of difficulties, including optical power handling capability and long-term bias point stability. Research work continues on refining the technology [52]. In addition to be being able to exploit the electro-optic effect in semiconductor materials in order to form Mach–Zehnder modulators, it is also possible to use the electro-absorption effect. Electro-absorption can occur in both bulk semiconductors and quantum well structures; for the former it is referred to as the Franz–Keldysh effect while in the latter it is called the quantum confined Stark effect (QCSE) [53]. Several examples of multiple quantum well (MQW) electro-absorption modulators (EAMs) have been reported. A typical EAM structure is one in which MQWs are embedded within the intrinsic region of a reverse-biased PIN diode, which being relatively thin (of the order of 0.1 mm) means that only a few volts will result in very large electric fields. QCSE is based on the concept of excitonic absorption, which in a MQW is stronger than in bulk materials and has a sharp spectrum at wavelengths corresponding to the bandgap energy. Application of reverse bias, however, will lead to a reduction of excitonic absorption and broadening of the spectrum, as the exciton absorption line shifts to longer wavelengths [54]. The end result of these physical effects is the set of absorption spectra shown in Figure 1.13. Because the shift of absorption spectra with varying bias occurs over a relatively narrow window of wavelengths, precise alignment between the wavelength of the CW source laser and the EAM is required. EAMs have been successfully demonstrated at frequencies as high as 60 GHz [55], and the envisioned application here would be 60 GHz fibre radio picocells. The fact that EAMs can be monolithically integrated with lasers points toward the possibility of low cost, although it should be pointed out that packaging issues still need to be resolved as does sensitivity to changes in temperature and/or bias voltage.

1.5.2 O/E Conversion An O/E transducer performs the reverse of E/O conversion, that is it converts incoming modulated light into corresponding variations of current. The term photodetection is commonly used. However, incident modulated light can also interact with electronic devices such

Absorption

Wavelength of CW source

Increasing reverse bias

Wavelength

Figure 1.13 Absorption spectra for EAM; as the bias is adjusted the absorption will vary for a given wavelength as shown


21

as diodes and transistors, a field known as optical control of microwaves; an excellent review can be found in [56]. Optical control can be used to perform functions such as amplifier gain control, oscillator tuning and optoelectronic mixing [57]. Although a large body of work exists on the modelling, characterization and use of optically controlled microwave devices, it is a niche area and we will concentrate on discussing high-speed photodetection instead. 1.5.2.1 Photodetection Just as the requirement of high bandwidth and conversion efficiency is demanded of E/O components for microwave photonics, the same is true for photodiodes although in this case we refer to responsivity (in A/W) as opposed to slope efficiency (in W/A or W/V) when considering conversion efficiency. The DC responsivity is given by the slope of the characteristic shown in Figure 1.14, and is defined as: R¼

IP ql ¼h hc PI

ð1:6Þ

where IP is the photocurrent generated in response to the incident optical power PI, h is the quantum efficiency, which is limited to a theoretical maximum of unity, h is Planck’s constant, c is the speed of light, q is the electron charge and l is the operating wavelength. The incremental responsivity, which will be frequency-dependent, is given by R(jv) ¼ iP(jv)/pI(jv). Here we are dealing with the modulation component of both the current and optical power. In a high-quality photodiode the responsivity will have a fairly flat frequency response. Often there is also a need for high-power handling capability, which originates from the fact that externally modulated systems have increased link gain if higher powers are used for the CW laser driving the modulator. In addition, it is required to avoid optical reflection from the device input in order to maximize the optical power entering the active region, so antireflection coatings are often used for this purpose. Two main classes of photodiode exist – lumped element designs (which include vertically illuminated photodiodes and edge coupled waveguide photodiodes) and distributed designs (such as travelling wave photodiodes and periodically loaded travelling wave photodiodes). These are illustrated in Figure 1.15.

Figure 1.14

Photodiode transfer characteristic. Reproduced from [23] ( 2008 IEEE)

22


Figure 1.15

Examples of lumped (on the left) and distributed (on the right) photodiodes

Before discussing these various device types, brief mention should be made of the avalanche photodiode (APD), which unlike the structures in Figure 1.15 offers internal gain and hence improved receiver sensitivity without the need for external amplification. In addition, for high enough multiplication factors (i.e. gain) there is an improvement in the signal-to-noise ratio (SNR) that becomes shot-noise limited provided there is little excess noise [24]. One limitation of APDs is that there is a fixed gain–bandwidth product resulting from the fact that for higher multiplication factors there is an increased time required in order for the avalanche to build up within the photodiode structure [58]. This means there is a trade-off between bandwidth and gain. Gain–bandwidth products in excess of 300 GHz have been demonstrated in waveguide APDs [59], hence such devices are restricted to a few tens of GHz at most if even modest gains of the order of 10 are required. Moreover, the APD structure is notorious for temperature sensitivity and the avalanche gain process requires higher operating voltages compared to photodiodes without internal gain. The device that is most commonly used in microwave photonic applications is the PIN, which has a simple structure – it is a junction diode with an intrinsic layer between doped p and n layers, hence the name PIN [60]. The simplest PIN is a vertically illuminated structure in which light enters the upper layers of the device and is absorbed as it travels through the structure, generating electron-hole pairs in the depletion region. The depletion region extends mostly over the intrinsic region, being formed by a reverse bias voltage. The generated electron-hole pairs are then swept by the bias electric field to the device contacts to produce a photocurrent. One advantage of the vertical illumination scheme (also known as surface illumination) is the ease with which light can be coupled into the device. A disadvantage is the trade-off between conversion efficiency and transit-time limited microwave performance. The transit time is defined as the time taken for the photogenerated carriers to reach the device contacts and it is determined by both the width of the active absorption region and the saturation velocity in the semiconductor material. The thickness of the active region will also determine how much optical power is absorbed, with this being given by: PðdÞ ¼ P0 ð1 e aðlÞd Þ

ð1:7Þ


23

where Po is the incident optical power, P(d) is the optical power absorbed in a distance d and a(l) is the optical absorption coefficient. It is assumed here that there is no optical reflection off the device surface. Equation (1.7) clearly indicates that for improved responsivity the device must be thick enough to absorb a large fraction of the incident optical power, but this then leads to increased transit time and hence reduced bandwidth. The maximum bandwidth–efficiency product for single-pass surface illuminated PIN photodiodes is of the order of 30 GHz [61]. It should also be remembered that device parasitics will affect the frequency response and must therefore be minimized, and the lumped nature of the PIN device leads to an RC time constant which can become an issue if the area of the active region is relatively much bigger than the thickness, leading to increased capacitance. In addition to bandwidth, it was mentioned earlier that power handling capability is important. The space charge effect [62] limits the extent to which optical input power can be increased before saturation, and therefore increased nonlinearity occurs. One technique for overcoming the bandwidth–efficiency limitations of the vertically illuminated PIN is to try to increase the distance over which photons travel through the absorption region in order to maximize optical absorption, whilst keeping the distance that the electron-hole pairs travel as small as possible to minimize the transit time. This may be achieved through creating a resonant optical cavity in order to set up multiple passes of the optical signal through the active region [63], but the resonance leads to wavelength selectivity thus making these devices of more interest for use in wavelength division multiplexed (WDM) systems. An alternative way of increasing optical absorption and reducing the transit time impact is to use edge-coupling, thus allowing the optical input to enter the intrinsic region directly and to propagate orthogonally to the electric field. In effect the structure becomes an optical waveguide, allowing the design of long but narrow absorption regions which ensure that a large fraction of the input power is absorbed whilst maintaining low transit times [64]. Waveguide photodiodes with bandwidths in excess of 100 GHz have been demonstrated [65], and typical bandwidth–efficiency products for these devices are about 55 GHz [66]. The waveguide photodiode has two disadvantages. First, the thickness of the active layer is often less than 1 mm, leading to a significant reduction in coupling efficiency between the photodiode and single-mode fibre. This can be mitigated to some extent by using tapered fibre or by fabricating devices that have doped optical guiding layers around the absorption region [60]. Secondly, the ‘long and narrow’ topology creates a capacitive region with a large area-to-thickness ratio, resulting in increased capacitance which causes an RC time limitation once device contact and load resistances are taken into account. The PIN structures discussed above are lumped element approaches. In order to eliminate the limitation of the RC time constant and to improve impedance matching, distributed designs were proposed in the early 1990s [67–69]. These are commonly known as travelling-wave photodetectors [70–72] and they are a natural evolution of the edge coupled waveguide PIN structure discussed above. In this case, in addition to the optical waveguiding mechanism, the device contacts are engineered to support microwave travelling waves; the approach is similar to Mach–Zehnder travelling wave modulators in that it is another example of transmission line effects in microwave photonics. Coplanar waveguide is typically chosen which supports a quasi-TEM mode; the transmission line parameters are determined by the device capacitance and the contact strip inductance. Absorption of optical power occurs in a distributed manner along the length of the device, setting up a travelling wave on the electrodes as it does so (Figure 1.16). Such a device is no longer limited by RC effects but by the velocity mismatch

24

Microwave Photonics: Devices and Applications Contacts (Transmission line) Electrical signal Optical input

Optical signal

Absorption region and optical waveguide

Figure 1.16

Distributed effects in a travelling wave photodetector

between the optical group velocity and electrical phase velocity [60]. When velocity matching is achieved, then long device lengths compared to waveguide photodiodes are possible in principle. The fact that the absorption volume is increased also means that these devices will saturate at a higher power level [73]. A large variety of travelling-wave photodiodes have been demonstrated and exhibit excellent performance. Bandwidths in excess of 500 GHz have been reported for PIN based devices [66], but structures based on metal–semiconductor–metal (MSM) [74], Schottky [75] and phototransistor structures [76] have also been published. In contrast to the other structures, the phototransistor-based travelling wave photodetector provides electrical gain as high as 35 at DC [76]. Recent work [77], however, indicates that the carrier spreading occurring in the base layer of a heterojunction phototransistor travelling-wave structure prevents independent longitudinal operation of the device in response to a position-dependent signal. The extent of the spreading leads to an effective minimum area over which a lumped capacitance limitation still remains. One method for overcoming this problem is to move away from a fully distributed topology to one which is analogous to a microwave travelling-wave amplifier, that is to use a periodically distributed photodetector. The theory of these structures is well known [69] and a variety of approaches to its implementation have been reported, including the use of multimode interference (MMI) couplers [78]. An added advantage of the periodically distributed photodetector is that it can handle higher optical powers. An alternative approach to handling high optical powers, that also offers high electrical output power is the uni-travelling-carrier (UTC) photodiode [79,80]. Applications of InPbased UTC photodiodes include optical generation of high-power mm-wave signals via heterodyning [81]. The basis of the UTC structure is that of a travelling-wave photodiode, but here the optical waveguide and absorption functions are physically separated. Optical waveguiding occurs in the n layer whilst absorption occurs in the p layer. In this way, the optical power absorption still occurs over an extended region, but the photogenerated current consists solely of electrons –hence the term uni-travelling-carrier. The major advantage is that electrons are faster than holes in materials such as InP, leading to potentially high bandwidths as well as high saturation powers.

1.5.3 O/O Components The broad bandwidth of optical media is a major driver for microwave photonics, and so we will briefly discuss some O/O components suitable for microwave photonics. The main one is

25


Dispersion-induced power penalty (dB)

optical fibre, and many of the microwave photonic systems reported in the literature use standard single-mode fibre and associated components (such as Bragg gratings, circulators, couplers, optical amplifiers and WDM multiplexers). A major advantage of single-mode fibre is the low loss of 0.2 dB/km at 1550 nm, but one also needs to be aware that signal degradation due to chromatic dispersion, polarization-mode dispersion and nonlinearity may need to be considered. If one considers intensity modulated light then, as argued earlier, this can be considered analogous to amplitude modulation. As the optical carrier and its upper and lower sideband propagate through the fibre, dispersion will introduce a phase shift between these components [82], leading to periodic power fading [83] with distance as shown in Figure 1.17. Optical single-sideband modulation can mitigate against this fading, and this can be used to implement WDM-based fibre-radio systems as described in Chapter 7. However, one must then be wary of cross-phase modulation due to optical nonlinearities, which leads to crosstalk between WDM channels [84]. In recent years, multimode fibre has begun to be considered for microwave photonics [85], despite it having a relatively low bandwidth–distance product of 500 MHz.km. This interest is due to the potential low cost of multimode fibre systems, the fact that most installed in-building fibre is multimode and the use of lasers rather than LEDs, with the subsequent demonstration of links operating up to 20 GHz [86]. Given that multimode dispersion can be thought of as equivalent to a transversal optical filter, its transfer function exhibits fading that is reminiscent of multipath fading in wireless systems. Hence orthogonal frequency division multiplexing (OFDM) techniques developed to combat multipath fading for wireless systems have been investigated for multimode fibre radio [87]. Although many microwave photonic systems use passive fibre components, mention should also be made of active O/O components, namely the erbium-doped fibre amplifier (EDFA) and the semiconductor optical amplifier (SOA). The latter is of interest because of the potential to integrate it with E/O and O/E devices, while the former is better suited for splicing into fibre

0

20 GHz

-5

30 GHz

-10 -15

60 GHz

-20 -25 -30 0

1

2

3

4

5

Distance (km)

Figure 1.17 Dispersion-induced power fading for standard single-mode fibre at 1550 nm; curves obtained using method described in [83]

26


systems. A number of microwave photonic filters make use of EDFAs, while both EDFAs and SOAs have been proposed for relatively short fibre links as a means of compensating for E/O and O/E conversion losses. In this second case, optical power levels are relatively high, forcing the amplifier to operate in the gain saturation region. It has been shown theoretically and experimentally that the small-signal microwave frequency response for this mode of operation in an SOA is quasi-high-pass [88].

1.6 Applications of Microwave Photonics There are a large number of systems and devices that can be said to involve microwave photonics. The main system functions can be divided into: (i) transport of microwave and mmwave signals over optical fibre (discussed in Chapter 6); (ii) filtering and processing of microwave signals in the optical domain (discussed in Chapter 7); (iii) generation of microwave, mm-wave and THz signals using photonic techniques (discussed in Chapters 4 and 5). These three areas in turn can be subdivided into specific applications including: radio over fibre (Chapter 7), antenna remoting for radar systems, antenna beam forming, local oscillator generation for radio astronomy arrays, and THz spectroscopy. Since Chapters 4 to 10 deal with many of the above applications in detail, we will simply provide a brief overview here.

1.6.1 Signal Transport The use of optical fibre for transmission of microwave signals is often advocated due to the advantageous properties of the optical fibre itself [89]. These include low losses, good dispersion management (over the relatively short distances used in some applications), flexibility and immunity to electromagnetic interference. Moreover, the ability to first modulate and then detect modulated light for microwave modulation frequencies up to a few tens of GHz means that such links find applications in the remote location of antennas and radar signal processing, for example. The basic architecture follows the scheme in Figure 1.3. Key parameters of interest are: link gain, noise factor and spur-free dynamic range. A recent review of analogue links by Cox et al. [89] points to a number of requirements for E/O and O/E devices in order to enable higher link gain, lower noise and a wider SFDR. These include (i) directly modulated laser diodes with greater slope efficiency, bandwidth and lower relative intensity noise, (ii) CW lasers with higher output power and lower RIN, (iii) external modulators with lower Vp and higher power handling ability, and (iv) photodetectors with higher responsivity, bandwidth and saturation power. When a microwave signal is transported over fibre, the resulting link is often termed as being analogue in order to distinguish it from the digital links used in telecommunications. It is possible, however, to digitally modulate a microwave signal before transmission over an ‘analogue’ link and so Cox et al. distinguish between an analogue and digital optical link as follows. An analogue link involves small optical modulation depths, thus ensuring small-signal operation of the E/O and O/E devices, whereas a digital link relies on on–off keying that may involve modulation depths close to 100 %. Perhaps the simplest signal that can be transmitted over an analogue link is a sinusoid, and there are several applications for distribution of RF, microwave and mm-wave carriers. A high


27

profile example is the development of fibre networks for radio astronomy facilities [90] such as SKA (the Square Kilometre Array based in Australia) and ALMA (the Atacama Large Millimetre Array based in Chile). ALMA will consist of over 60 12-metre parabolic antennas which can interferometrically detect signals between 27 GHz and 938 GHz [91]. This large frequency range is spanned by 10 bands, and the low noise heterodyne receivers at each antenna each require a local oscillator which is generated optically. The local oscillator signals are then distributed via a fibre network, which must accommodate a maximum antenna separation of 25 km. In this particular application, an optical fibre distribution network offers numerous advantages. Apart from the low loss and large bandwidth provision, the use of fibre also allows a single LO reference to be located at a central office, removing the need for individual LO units at each antenna. This is a feature that also appears in the radio-over-fibre networks (Figure 1.18) discussed below. In addition to the distribution of local oscillator signals, both fibre radio and radio astronomy arrays have a requirement for data transmission over fibre, and the different schemes for sending data over analogue fibre-optic links will be outlined in Section1.6.4.

1.6.2 Signal Generation The ALMA project represents but one example of the need for ever higher oscillator frequencies. Other examples include mm-waves for multi-Gb/s wireless communication, where there is much work at 60 GHz, and even demonstrations of 10 Gb/s transmission using a carrier frequency of 120 GHz [92]. Generation of microwave and mm-wave signals has

Figure 1.18

Architecture of a mm-wave fibre radio system

28


traditionally been the realm of electronic oscillators using III-V devices [93], although recent work has also proved the feasibility of using cheaper SiGe CMOS technology [94]. Nevertheless, as one goes beyond 100 GHz the power available from electronic oscillators declines. There is then a so-called ‘gap’ in the THz region before one reaches optical frequencies, where laser sources are available. The THz region itself is of growing importance in sensing and biomedical applications [95]. It is possible to use photonic techniques to generate mm-wave and THz signals, and one immediate advantage is that the signals can then be transported immediately over optical fibre. The availability of high-speed photodiodes and photomixers then ensures relatively efficient conversion into the wireless domain. The two obvious techniques for optical generation of microwaves are direct and external modulation as discussed above, but the former is limited to about 30 GHz while the latter can suffer from dispersion-induced fading at mm-wave frequencies. One can generate microwave and mm-wave frequencies by a number of other methods as discussed below: (a) Heterodyning of two laser sources, in which the wavelength difference corresponds to the subsequent microwave signal’s frequency. One advantage is that very high optical singlesideband frequencies can be generated. This is discussed in detail in Chapters 4, 5 and 10. (b) Actively and passively mode locked lasers. Of particular interest here is work at Drexel [96] on the use of microchip lasers. A microchip laser is a solid-state laser (based on erbiumdoped lithium niobate for example) of short length onto which dielectric mirrors are deposited directly. It is a potentially low cost solution which is very suitable for mode locking at mm-wave frequencies. Performance-wise, the microchip laser is inherently more stable than a semiconductor laser, has higher output power and lower relative intensity noise. (c) Optical phase locked loops (OPPLs) [97] and optical frequency comb generators (OFCGs) [98]. The OPLL architecture is similar to a conventional phase locked loop, but in this case a master and slave laser produce a heterodyne signal. After photodetection this is mixed with a mm-wave reference from an oscillator, and the resulting phase error signal is used to tune the slave laser so that the heterodyne signal frequency equals the reference frequency. The OFCG is an amplified recirculating optical delay line into which a phase modulator is inserted. By applying microwave modulation to the modulator, and through the process of continued recirculation (and hence ‘remodulation’), an optical comb spectrum is generated in which the spacing between combs corresponds to the modulation frequency. One can then select two of the combs using injection-locked slave lasers and then subsequently photodetect the heterodyned signal. This technique can potentially produce frequencies well over 100 GHz. (d) Optoelectronic oscillators (OEL) [99]. The basic configuration of an OEO (Figure 1.19) is based on the loop oscillator principle, in which the open loop gain must balance out losses. In this structure the oscillation frequency is inversely proportional to the fibre group delay. An OEO is a hybrid oscillator in the sense that it uses both microwave and photonic components, and the oscillation can be extracted either from the electronic part of the loop or the optical part. One of its perceived advantages is the potential to offer better phase noise performance than electronic oscillators at microwave frequencies [99] in addition to higher Q. A disadvantage of the scheme in Figure 1.19, however, is the thermal dependence of the fibre delay (although this does make it possible to use an OEO for sensing applications).

29

Microwave Photonics – an Introductory Overview Low noise “pump” laser

Fibre coupler

Mach–Zehnder modulator

Optical output

Fibre loop Electrical loop

Microwave output Microwave directional coupler

Microwave amplifier

Photodiode

Bandpass Filter

Figure 1.19

A single-loop optoelectronic oscillator

1.6.3 Signal Processing

RF input

Mach–Zehnder modulator

a0

1 × N optical splitter

CW optical source

Commensurate optical delays

a1 a2

T 2T

NT

1 × N optical combiner

Weights

As shown in Figure 1.4, optical fibre has a much lower loss than alternative technologies such as surface acoustic wave devices for a given delay. Put another way, this means that at a given microwave frequency an optical fibre can provide longer delays than competing media, which translates into a large time–bandwidth product. Single-mode fibre offers a time–bandwidth product in excess of 106, thus making it suitable for the processing of wideband signals. An early application of microwave photonic signal processing was in optical fibre recirculating delay lines designed for the storage of microwave signals [100]. This was then followed in the early 1980s with implementations of microwave photonic filters at Stanford using delay line structures [101]. Since then the field has expanded significantly and a very large body of published work exists. Excellent review [102] and tutorial papers [103] provide a comprehensive discussion of much of this work. An example of a very simple microwave photonic filter is shown in Figure 1.20. This architecture is an extension of the Mach–Zehnder interferometer, and can be shown to be

Photodetector RF output

aN-1

Figure 1.20 Example of a microwave photonic filter (for more details, see Figure 8.4 of Chapter 8)

30


functionally equivalent to a tapped delay line filter. Since the various fibre delays are commensurate, it is possible to use z-domain techniques from the field of digital filtering for analysis and synthesis purposes. (This is done for mathematical convenience, since microwave photonic filters are analogue.) Borrowing from digital filter terminology, the structure in Figure 1.20 is termed FIR (finite impulse response). It is also possible to have IIR (infinite impulse response) transfer functions by using recirculating loops. Just as one might compare an analogue fibre link with a coaxial cable, one may compare a microwave photonic filter with a conventional microwave filter using lumped components, transmission lines or waveguides. The need for E/O and O/E conversion raises the question of whether the added complexity is worthwhile. However, given the increased interest in systems such as fibre radio, in which microwave signals are already being generated and transported optically, it seems reasonable to filter them in the optical domain as well. Moreover, as pointed out by Minasian [102], photonic signal processing offers numerous advantages, including highspeed, parallel processing and high sampling frequencies (in excess of 100 GHz as opposed to a few GHz for electronics). These advantages, coupled with advances in photonic technology such as fibre Bragg gratings (both uniform and chirped), optical amplifiers, high-speed modulators and detectors, WDM multiplexers and demultiplexers, and tuneable lasers, have created new opportunities not only for advanced microwave photonic filter structures but also other functions. Microwave photonics technology has been used to implement analogue to digital converters (ADC) [104], arbitrary waveform generators [105] and beamformers for phased array radars [106]. An example of a photonic ADC is shown in Figure 1.21; a good review of the field is given in [104].

1.6.4 Radio Over Fibre Radio over fibre (RoF) is one of the major applications of microwave photonics and there is some significant commercial activity in this field. The main concept is shown in Figure 1.18 and

v

Analogue input

λ1

t Electro-optic modulator

Mode-locked laser

λ1λ2

λN

t

t

ADC 1

Photodiode 2

ADC 2

λ2

Optical demultiplexer

λN

Photodiode 1

Photodiode 1

Multiple sample digital interleaving

ADC 1

Modulated pulse train

Figure 1.21 Example of a photonic analogue-to-digital converter. The analogue signal is sampled by a pulse train by using external modulation. The output of the external modulator is then demultiplexed according to wavelength prior to photodetection and electronic quantization. (There are examples of purely photonic ADCs, in which both sampling and quantization are performed in the photonic domain)


31

it involves the merging of wireless networks (indoor and also outdoor) with a fibre backbone (which is often WDM-based). Motivation for using RoF includes providing a solution to the ‘last mile’ problem and the improvement of wireless coverage (for example in buildings and ‘dark zones’ such as tunnels). Indoor distributed antenna systems (DAS) currently have a large share of the RoF market [107]. They are designed to transport cellular and WLAN signals to remote antenna units distributed throughout a building, and the key driver here is to reduce costs. This is facilitated by the fact that the frequencies are low enough (in the range 800 MHz to 2.5 GHz) to allow the use of directly modulated laser diodes, even though device linearity is an issue. Since there is already a large amount of installed multimode fibre, significant efforts have been made to develop multimode RoF for DAS [108]. As the demand for higher data rates (for applications such as HDTV) continues to increase, more use will be made of mm-wave carrier frequencies. Of particular interest is the availability of several GHz of spectrum centred on 60 GHz, which will ease some of the spectrum congestion of cellular systems. The sizeable atmospheric losses at this frequency lead to relatively small cell sizes (known as picocells), thus allowing greater frequency reuse which enhances network capacity. The small size of picocells means that a large number of remote antenna units must be produced, implying that their architecture must be suitably simple. In this manner the complexity moves to the central office, in which the functions of data modulation and multiplexing are housed. There are trade-offs between complexity of the picocells and the central office, leading to different schools of thought as to which is the best overall approach. These can be broadly defined as: (i) optical generation and transport of mm-wave signals at 60 GHz, and (ii) optical transport of data signals with remote upconversion to 60 GHz at the picocell site. The former approach is known as RF over fibre. It results in simple picocell architectures, which at their bare minimum use electro-absorption transceivers [109] plus an antenna and associated circuits – this passive picocell approach removes the need for electronic amplification. It does, however, require use of the techniques described in Section1.6.2 in order to generate the mm-wave carrier. The second approach is known as baseband over fibre and it removes the need for high-speed components, but in its place it requires local oscillators to be generated locally at each picocell unit. A third approach, known as IF over fibre is also possible, and this technique is illustrated in Figure 1.22 along with the other two signal transport approaches.

1.7 Conclusions Microwave photonics is a field in which many advances have been made since the 1960s, and the high level of research activity continues unabated. In this introductory chapter we have sought to give a brief flavour of the topic from the perspective of devices and their various system applications. Later chapters will report on advances in some of these devices (e.g. direct modulation of lasers, photodiodes and THz generation with O/E and E/O devices) and will focus on how microwave photonic functionality can be used to implement microwave signal processing (e.g. microwave filters and analogue links) and to implement advanced communication systems (e.g. fibre radio).

32

Microwave Photonics: Devices and Applications • Potentially very simple RAP. • Could, in theory, use only passive mmwave components.

Optical carrier

ωRF OLSB

Antenna

OUSB

O/E Coupler

ω Central office

RF over fibre

Diplexer

E/O RAP

• Need to generate 60 GHz by optical means at central office. For optical double sideband signals, fibre dispersion leads to a “beating” effect (see Figure 1.17). This can be overcome with single-sideband methods.

•60 GHz carrier recovered at RAP. •Need high bandwidth O/E and E/O components.

•Relaxed bandwidth requirements on O/E and E/O components. •More tolerant of chromatic dispersion.

O/E

ω

Central office

Coupler

ωIF

Diplexer

Local Oscillator E/O

Mixer

IF over fibre

RAP

•60 GHz carrier generated at RAP. •Need mm-wave components such as mixers and oscillators; phase noise can be an issue. •However, modified architectures (including remote LO delivery) are possible.

Optical carrier O/E

Central office

LO

Diplexer

Baseband over fibre

E/O

•Digital fibre optic link •Mature technology, relatively cheap •Tolerant of fibre link impairments (e.g. nonlinearity, dispersion)

Figure 1.22

IF

Coupler

ω

RAP •Similar comments as for the RF over fibre case apply to the RAP

The three main classes of signal transport for radio over fibre compared and contrasted

It is highly likely that microwave photonics will continue to flourish as a research field, given that the demand for ever increasing bit rates in both wireless and optical communications shows no signs of stopping yet. There are also a number of growing applications in areas such as THz technology for sensing. To date, much of the progress in microwave photonics has been driven by impressive advances in optical fibre components. However, a number of key challenges remain (including the issue of producing low-cost components in high volumes) and there are also new opportunities on the horizon. These include: (i) the demonstration of high-speed modulators on silicon [110], which opens up a route to cheaper components that can be integrated with silicon drive electronics,


33

(ii) ‘new physics’, such as the use of slow light to perform phase shifting for use in microwave filters [111], and (iii) the development of new structures such as micro-ring resonators that promise more compact optical filters designed with techniques that are well established in the area of microwave filters [112].

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Part II Component Technologies


2 Direct Modulation for Microwave Photonics Rajeev Ram and Harry Lee

2.1 Introduction to Direct Modulation for Microwave Photonics Today, nearly 100 companies are involved in the transport of RF or microwave signals over fibre optics – primarily a modulated RF carrier residing on the optical signal. The applications for such systems range from in-building distribution of wireless signals (for example in shopping malls and tunnels), wireline interconnections between base stations and microcellular antennas, antenna remoting for various commercial (wing-tip antennas in aircraft) and military radar systems and broadcasting of cable television signals in both hybrid fibre coax (HFC) and triplexer based fibre-to-the-home (FTTH) systems. The simplest, lowest cost and hence most widely deployed system consists of a directly modulated laser, a length of optical fibre and a detector. This simple link is referred to as an intensity modulation/direct detection (IM/DD) system in contrast to externally modulated systems. While direct modulation links tend to be simpler and cheaper, generating and modulating the photons in a single device – the laser – clearly entails compromises in overall performance that can be avoided by separating these functions as in an externally modulated link. In particular, the effect of nonlinearity and noise must be considered (Figure 2.1). However, as we shall show here, the performance gap between externally modulated and directly modulated links can be narrowed with judicious design of the semiconductor laser. As in all optical systems, the performance requirements for the individual components are set by the overall system specifications. For analogue IM/DD links, the three most important system parameters for specifying optical components are unamplified link gain (typically 25 dB, best case þ 6 dB), unamplified link noise figure (typically 40 dB, best case 17 dB) and spurious free dynamic range (typically 100 dB-Hz2/3, best case 127 dB-Hz2/3). The link gain is a simple function of the efficiency with which the laser can convert an electrical signal to a modulated optical waveform, the optical transmission loss and the efficiency for a detector to



42 Second-order distortion

Intensity noise

Figure 2.1 Schematic showing sinusoidal modulation of a laser and the results of second-order distortion and noise

convert the modulated optical waveform back to the electrical domain. The noise figure depends on the link gain as well as the noise added at each O/E (optical to electrical) and E/O (electrical to optical) conversion step. The dynamic range depends on the link gain and noise figure as well as the linearity of the E/O and O/E conversion processes. All of these concepts are conveniently summarized in Figure 2.2. The fundamental has a slope of one and the third-order intermodulation distortion (IMD3) has a slope of three. The input noise is shown as thermal noise with the corresponding output noise floor. The output and input signal-to-noise ratio is shown along with the noise figure (NF). The spur-free dynamic range (SFDR) is also shown.

N in = kT

0

P in = Pout

IP3

-20

-40

-60

G

Pout (dBm)

-80

Fundamental

IMD3

-100 SNRout

-120

-140

SFDR

N out = GkT + N las

-160 NF

-180

GNin = GkT

-200

-220

SNRin

-200

-150

-100

-50

0

Pin (dBm)

Figure 2.2 Received (electrical) signal power versus transmitted (electrical) signal power; the plot indicates the thermal noise level at the transmitter and receiver as well as the level of third-order distortion

Direct Modulation for Microwave Photonics

43

In this chapter, we will describe the detailed physical processes that contribute to both the typical and best case link performance for IMDD. Section 2.2 offers a quick tutorial on the physical processes within a laser which in later sections will be shown to set the important limits on the signal strength, noise and linearity. Section 2.3 discusses the physics behind link gain, Section 2.4 discusses the physics behind signal bandwidth and Section 2.5 discusses distortion in an IMDD system. The final sections of the chapter present specific case studies that are important for the future development of IMDD systems. Section 2.6 discusses low-cost VCSEL based links and Section 2.7 discusses cascade based lasers for positive link gain and low noise figure.

2.2 Review of Semiconductor Laser Devices The semiconductor laser is more intrinsically linear than any other active semiconductor device. Diodes and LEDs obey the highly nonlinear diode law and therefore exhibit very poor linearity. However, beyond threshold, a semiconductor laser has a light output versus electrical current input curve that is extremely linear (Figure 2.3(a)). Semiconductor lasers – although utilizing p–n junctions – exploit optical feedback to effectively suppress the diode nonlinearity. In fact, a semiconductor laser moderately above threshold has essentially the same I–V characteristics as a resistor (Figure 2.3(b))! In order to explain how a laser is able to achieve such a highly linear response it is useful to compare the laser diode with an LED. From this discussion, not only will we clarify the origin of the semiconductor lasers linearity but also gain an insight into the distortion that can be generated when the laser is modulated at high speeds (relaxation oscillation nonlinearity) or biased with high injection currents (spatial hole burning and optical gain compression nonlinearities).

2.2.1 Laser Structures Any description of the physical processes that give rise to lasing action in a semiconductor must begin with a careful look at the structure within which electrons, holes and photons interact.

Figure 2.3 (a) Measured light output power versus injected electrical current for a single mode DFB laser. (b) Measured voltage versus injected electrical current for the same laser


44

Leakage

Electron injection

Electron density

SCH

Recombination

SCH Quantum wells

Hole density Hole injection

Figure 2.4 Schematic of a separate confinement heterostructure (SCH) quantum well laser showing the key transport process for electrons and holes

The vast majority of modern semiconductor lasers rely on quantum wells that trap electrons and holes. The quantum wells are located at a p–n junction so that both electrons and holes can be supplied from the doped regions (Figure 2.4). Stimulated emission relies on accumulating sufficient numbers of electrons and holes within the quantum wells so that population inversion is established. From Figure 2.4, it is clear that different bandgap materials are employed to make the carrier confining quantum wells, the separate confinement heterostructure (SCH) and highly doped carrier reservoirs. In order to foster stimulated emission by photons trapped in the vicinity of the quantum wells, additional materials are used to form a waveguide cladding around the active region of the laser. The arrangement of quantum wells in conventional multiple quantum well lasers offers injected electrons the option of recombining in any one of the quantum wells. As such, there can be at most one photon emitted for every electron injected from the doped regions. One approach to circumvent this limit is the bipolar cascade laser structure that will be presented in Section 2.7. In addition towaveguideconfinement in the transverse direction, photonsmustalso be confined by resonator structures. Without high quality resonators the escape rate of photons is so large that the average number of photons near the quantum wells would always be less than one and stimulated emission would always remain negligible. The resonator and the quantum well materials together determine the wavelength of the light emerging from the laser. There are three common resonator geometries that arewidely used today; these are the Fabry–Perot resonator, the distributed Bragg reflector (DBR) laser and the distributed feedback (DFB) laser. Figure 2.5 shows schematics of the backward and forward propagating photons within the optical resonator. The simplest resonator for providing optical feedback is the cleaved facet Fabry–Perot laser. Here the light is amplified by stimulated emission on its trajectory across the laser resonator (Figure 2.5(a)). Once it reaches the facet it is reflected by the semiconductor-to-air boundary – typical reflectivities for most uncoated facets are 56%. An extension of the basic Fabry–Perot resonator is to rely on multilayer coatings to increase the mirror feedback (as in a vertical cavity


45

Figure 2.5 Schematics of the backward and forward propagating photons within the optical resonator for (a) the Fabry–Perot resonator, (b) the DBR or VCSEL resonator, (c) the weak grating DFB and (d) the strong grating DFB

surface emitting laser– VCSEL) or to rely on wavelength selectivegratings in place of the cleaved facets; both geometries are referred to as DBR lasers (Figure 2.5(b)). In DBR lasers, the grating reflector is passive and does not provide gain to the propagating light beam. However, it is possible to co-locate the gain and the wavelength selective grating to make a single mode laser; these structures are referred to as DFB lasers. Figures 2.5(c) and 2.5(d) show two DFB laser schematics for weak ((c)) and strong ((d)) grating feedback. The strength of the grating is quantified by the parameter kLg – for weak gratings this is simply the reflectivity of the total grating [1]. In the weak grating case, the optical field has a spatial distribution similar to the Fabry–Perot laser (Figure 2.5(a)). In the strong grating case, the grating tightly confines the photons within the laser resonator. A typical laser emission spectrum for a DFB semiconductor laser is shown in Figure 2.6 – the grating preferentially provides optical feedback that favours a single lasing mode; here, the lasing mode is approximately 40 dB more intense than the next strongest mode. It is important to note that in all of these laser structures the light distribution shown in Figure 2.5 is not spatially uniform. This nonuniformity in the distribution of photons plays an important role in the signal distortion that occurs when these structures are modulated. Even from this cursory view, it is clear that an intermediate strength grating in a DFB geometry will allow for a nearly uniform photon distribution. In fact, the highest dynamic range semiconductor lasers do, in fact, utilize such moderate strength gratings. The optimal grating strength for uniform photon distribution is kLg 0:7 for DFB lasers with one HR coated facet and one AR coated facet [2]. These spatially uniform DFB lasers are the workhorse of the CATV Hybrid Fibre Coax (HFC) distribution network.

2.2.2 Rate Equations When the photon distribution is uniform along the length of the laser cavity, it is possible to describe the dynamics of the device by considering only the spatially averaged


46

Figure 2.6

Optical spectrum of a single mode DFB laser with cleaved (uncoated) facets

photon density (S) and carrier density (N). Figure 2.7 shows the various processes that are involved in converting the stream of injected electrons into a stream of output photons. The dynamics of a semiconductor laser are most easily described by a rate equation model that accounts for the various electron and photon generation and recombination/loss processes. (All modes) (Lasing mode)

Spontaneous emission

Current injection

Carrier density, N

Stimulated emission

Photon number, S

Optical output

Leakage

Stimulated absorption Nonradiative recombination

Absorption (outside of active region), scattering loss

Figure 2.7 The various transport and recombination processes within a semiconductor laser resonator. The most important processes which contribute to inefficient conversion of injected current into output light are: (a) carrier leakage, (b) nonradiative recombination, (c) spontaneous emission into nonlasing modes and (d) parasitic absorption and scattering of photons within the laser resonator


47

Our development closely follows that of [1]. dN hi I ¼ Rnr ðNÞ Rsp ðNÞ vg gðN; SÞS dt qV Gvg gðN; SÞnsp dS S ¼ Gvg gðN; SÞS : dt tp Vp The rate equations are a system of coupled, nonlinear differential equations for the spatially averaged photon density (S) and carrier density (N). Within the above equations, I is the injected electrical current, hi is the injection efficiency into the active region, Rnr(N) is the rate of nonradiative recombination and Rsp(N) is the total rate of spontaneous emission into all colours and modes, gðN; SÞ is the optical gain per unit length for the lasing mode, G is the spatial overlap of the lasing mode with the active region (quantum wells), vgis the group velocity of photons in the lasing mode, tp is the lifetime of photons in the optical resonator, nsp measures the relative importance of stimulated emission and absorption in the net optical gain (it is typically between 2–5 for diode lasers above threshold), V is the volume of the active region (quantum wells) and Vp is the mode volume of the lasing mode. At low optical powers, the net optical gain is only a function of the carrier density. Figure 2.8 shows the optical gain versus wavelength and carrier density for a typical quantum well active material emitting at 1550 nm. The complex dependence of optical gain on carrier density and wavelength is often compressed into a simple analytic form. The peak optical gain increases with carrier density. However, the magnitude of this increase diminishes as the energy levels at a given optical transition fill with electrons. This band filling results in a logarithmic dependence on carrier density. Finally, at high optical densities, the low-energy carriers are quickly removed by stimulated emission and leave behind a hot electron distribution. These hot electrons do not

Figure 2.8

Calculated optical gain for typical quantum well material emitting at 1550 nm


48

efficiently populate the individual states thereby lowering the peak gain of the active material. This is the dominant physical mechanism for gain compression in semiconductors. All of these factors are often incorporated into a phenomenological model for the active region gain: g0 N gðN; SÞ ¼ ln : Ntr 1 þ «S Here, Ntr is the transparency carrier density – when stimulated emission balances active region absorption – and « is the gain compression factor which accounts for the effect of carrier heating on the net optical gain. In steady-state, the equations can be parameterized to give the current and photon density in terms of the carrier density: I¼

qV ðRnr ðNÞ þ Rsp ðNÞ þ vg gðN; SÞSÞ hi

S¼

Gvg gðN; SÞnsp : 1=tp Gvg gðN; SÞ

Furthermore, the intracavity photon density (S) can be related to the output optical power, Pout ¼ S hn Vp ðvg am Þ Fout ; where hv is the photon energy, am ¼ 1=2L lnð1=R2 Þ is the total mirror loss, and Fout is the fraction of the intracavity power that exits from a single facet. The above system of equations can easily be plotted by varying the carrier density from zero to the point where the net optical gain balances the total cavity loss: vg gth ðNth ; S ¼ 0Þ ¼ 1=Gtp ¼ vg ðam þ ai Þ=G: For reasons we will address shortly, this condition is often called the threshold condition – but in truth it is the upper limit to the steady-state carrier density that can be injected into the laser. The resulting optical power and current are shown in Figure 2.9. Note that the carrier density increases as the current in increased. However, when N Nth , the increase in carrier density becomes very small and we can consider the steady-state carrier density to be clamped. Also, at this point the output optical power rises rapidly. Every additional electron that is injected into the active region cannot increase the carrier density appreciably and must rapidly generate a photon via stimulated emission. In fact, the likelihood of stimulated emission for electrons injected above threshold is nearly unity – limited only by carrier leakage. Clamping the carrier density near threshold suppresses the intrinsic nonlinearity within the semiconductor device. It is for this simple reason that the semiconductor laser diode has a highly linear optical response (light versus current) and electrical response (I–V curve). Carrier density clamping due to optical feedback is the essential difference between a laser diode and an LED. Any process that prevents clamping of the carrier density will unleash the intrinsically nonlinear optical and electrical response of the diode. The key processes that prevent the carrier density from clamping are: . .

spatial-hole burning (no local carrier density clamping), current leakage,


49

Optical power (mW)

15

10

5

0 0 4

18

5

10

15

20

25

5

10

15

20

25

10 15 Current (mA)

20

25

x 10 N th

Carrier density (cm -3)

3

2

1

0 0

N th

0

5

Figure 2.9 Steady-state output optical power and carrier density versus current for a semiconductor laser diode; while the carrier density is always increasing with current, N Nth near the lasing threshold

. .

gain compression (carrier heating induced by stimulated emission), and current modulation.

Spatial hole-burning can be suppressed by judicious design of the laser cavity to ensure that the photon density is uniform. Current leakage can be suppressed by appropriate design of the quantum wells and SCH. However, gain compression («) and the effects of modulation are fundamental to the operation of a semiconductor laser and cannot be easily engineered away. Of particular concern for communications links is that modulation frustrates carrier density clamping and results in a nonlinear device response. This will be discussed in greater detail in Sections 2.4 and 2.5.

2.3 RF Signal Strength and Optical Link Gain Section 2.1 has alluded to some of the challenges in converting an electrical signal into an optical signal. The most important processes that result in the inefficient conversion of injected current into output light are (a) carrier leakage, (b) nonradiative recombination, (c) spontaneous emission into nonlasing modes and (d) parasitic absorption and scattering of photons within the laser resonator. However, in addition to these internal processes, there is the challenge of


50

delivering an electrical signal into the laser. Specifically, RF or microwave signals are usually delivered as power (PRF, in) travelling along a transmission line of known impedance (Z0). Because a semiconductor laser is typically a forward biased p–n junction diode, its electrical impedance is typically only a few ohms – a notable exception being single-mode VCSELs. The small load impedance presented by the laser results in large RF reflections if no impedance matching scheme – such as a transformer – is employed. A unique aspect of a directly modulated semiconductor laser is that only the RF current – not the RF voltage – generates an optical modulation. This means that it is more important to deliver RF current to the laser diode than to deliver RF power. A little analysis will clarify this often puzzling and misunderstood fact. The injection current can be related to the input electrical power by rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2PRF;in I¼ ð1 GRF Þ Z0 where GRF ¼

ZL Z0 ZL þ Z0

is the electrical reflection due to impedance mismatch. The optical signal generated by the laser travels through the link and generates an RF electrical current at the detector: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2PRF;in Idet ¼ hlas HðvÞhcp hdet ð1 GRF Þ; Z0 where hlas is the overall conversion efficiency from electrons to photons in the laser, H(v) is the modulation response of the laser, hcp is the optical link loss, and hdet is the quantum efficiency of the detector. The ratio of the received electrical signal power to the input electrical signal power is the link gain (G). Assuming that the detector drives a load Z0;det , the link gain is given by G ¼ ðhlas HðvÞhcp hdet Þ2 ð1 GRF Þ2

Z0;det : Z0

In order to isolate the inefficiency associated with electrical impedance mismatch we separate the terms in the link gain associated with impedance mismatch and define this to be the mismatch link gain (Gmismatch): Gmismatch ¼ ð1 GRF Þ2

Z0;det : Z0

The mismatch gain is plotted as a function of diode laser resistance in Figure 2.10. When the laser is impedance matched to the input electrical transmission line – here, assumed to be 50 W– the mismatch gain is unity. As the laser impedance rises above 50 W, the electrical reflections increase and most of the electrical power is delivered as a voltage across the laser. Both effects reduce the optical signal strengths. Surprisingly, reducing the laser impedance actually enhances the gain of the device. As the laser impedance drops, more of the electrical power is delivered as a load that can effectively modulate the light output. This more than compensates for the electrical reflections.


51

6 G mismatch(dB)

4

2

0

-2

-4

0

10

20

30

40

50

60

70

80

90 100

Figure 2.10 The contribution to link power gain due to impedance mismatch between the laser and the input electrical transmission line (with a 50 W impedance). The ‘mismatch’ gain is plotted as a function of laser (differential) resistance

If the electrical signal source can tolerate the impedance mismatch and reflections, it is often desirable to drive the small load of the laser diode directly. However, sensitive or complex signal sources require some effort to achieve impedance matching. In order to optimize the link gain while reducing reflections requires the use of transformers for reactive impedance matching. While such reactive loads are useful in RF applications such as CATV, they are of limited utility in microwave applications such as wideband radar. An alternative approach to improve the overall link gain is to increase the ‘internal’ conversion efficiency of semiconductor lasers by forcing each individual electron to emit multiple photons. This enables laser (differential) efficiencies greater than one and is a promising route to broadband positive link gain. This approach will be discussed in greater detail in Section 2.7.

2.4 Signal Bandwidth and High-speed Lasers In this section, we will continue with our discussion of optical link gain but now focus on the modulation response of the semiconductor laser, H(v). The goal of this section is to describe the optical signal that results from a modulation on the injection current. While most communication systems utilize large signal modulation of the optical signal, it is instructive to consider a linearized or small-signal analysis of the laser dynamics. Here we shall consider the current, electron density and photon density to be composed of steady-state terms plus terms that represent a modulation: I ¼ I0 þ DI, N ¼ N0 þ DN, and S ¼ S0 þ DS. For now, we will focus on the linear response of the system and therefore will not consider the influence of nonlinear terms in the rate equations, that is we will ignore any terms that involve products of the small signals: DNDS 0; DN 2 0; etc.. Similarly, the gain function can be expanded in a Taylor series to the first order since DN and DS are very small. Thus, we can substitute: gðN0 þ DN; S0 þ DSÞ gðN0 ; S0 Þ þ aN DN aP DS; where aN ¼ @g=@DN and aP ¼ @g=@DS. Inserting the current, carrier density and photon density (including modulation) into the rate equations of Section 2.2 gives the following: dDN hi DI ¼ vg aN S0 DN vg g0 DS þ vg aP S0 DS dt qV


52

and dDS G DS ¼ Gvg aN S0 DN þ vg g0 DS Gvg aP S0 DS : dt Vp tp Since we are typically considering a laser biased well above threshold, we only consider carrier recombination due to stimulated emission in the above rate equations. The solutions for these small-signal rate equations for sinusoidal modulation at v are: DN ¼

HðvÞ h ðGvg aP S0 þ jvÞ i DI 2 qV vR

DS ¼

HðvÞ h Gvg aN S0 i DI; 2 qV vR

where HðvÞ ¼ v2R

v g aN S0 v þ jvðvg aN S0 Þ þ tP

1

2

:

A characteristic frequency is evident in the form of the modulation response. This frequency is the relaxation oscillation frequency v2r ¼

v g aN S0 : VP

For moderate damping, the 3 dB modulation bandwidth is about 20–50% larger than the relaxation oscillation frequency so design for high relaxation oscillation frequency is equivalent to design for high bandwidth. Figure 2.11 shows the modulation response of a diode laser as a function of the steady-state optical power [3]. As the device is biased to higher powers, the increased rate of stimulated emission directly shows up as a higher modulation bandwidth.

Response (dB)

10 1.3

5

0.4

3.1

8.0 20.9

0

43.3 mW

-5

-10

0

5

10 15 Frequency (GHz)

20

Figure 2.11 Modulation response as a function of steady-state optical power for a 980 nm laser diode [3] ( 1992 IEEE)


Figure 2.12

53

Modulation response for a coplanar fed 1550 nm high-speed laser diode [4]

Designing for high relaxation oscillation frequency for a given amount of input current can be accomplished by designing the active material to have a high differential gain, increasing the confinement factor, decreasing the active volume, and heatsinking so that the device can be biased far above threshold. This can be seen by recasting the relaxation oscillation frequency as v2r ¼

vg aN Ghi ðI0 ITH Þ: qVP

The desire to bias the laser at the largest injection current and output power requires that adequate thermal management is employed to extract heat from the laser. In practice, state-ofthe-art multiquantum well diode lasers are limited by device heating and electrical parasitics. Figure 2.12 shows a 1550 nm diode laser with an integrated coplanar microwave transmission line to mitigate inductive and capacitive parasitics in the input electrical signal [4]. Finally, Figure 2.13 shows the evolution of high speed lasers. The record modulation bandwidth is still 45 GHz for a 980 nm diode laser. Today, several designs exist for 1550 nm diode lasers with bandwidths from 30–35 GHz. So far, we have only considered the small signal (linear) modulation response of the laser. In order to look at practical input modulation signals, it is useful to define the optical modulation depth (OMD): OMD ¼

DS HðvÞ h ¼ 2 Gvg aN i DI: S0 qV vR

The next section looks at the modulation response of the laser when the OMD is appreciable.

2.5 Signal Distortion and Spurious Free Dynamic Range In Section 2.2, we demonstrated that clamping the carrier density near threshold suppresses the intrinsic nonlinearity within the semiconductor device. This section describes the nonlinear response of semiconductor lasers given failure of gain clamping due to gain compression and current modulation.


54 50 InGaAs/GaAs

Modulation bandwidth [GHz]

GaAs/AlGaAs

40

1.3µm InGaAsP/InP 1.55µm InGaAsP/InP

30

GaAS VCSEL

20

10

0 1980

1985

1990 Time of publication

1995

2000

Figure 2.13 Historical data showing improvements in direct modulation bandwidth for various semiconductor lasers

A perfectly linear device will generate a purely sinusoidal intensity modulation in response to a sinusoidal current modulation. For linear devices, superposition guarantees that multiple electrical channels driving a single element will not suffer from crosstalk. However, the superposition principlefailswhenconsideringnonlineardevices.Twoperfectlysinusoidalinputswillgeneratea host of output signals of varying frequencies. Figure 2.14 shows the RF frequency spectrum for a laser that is driven by two large signal sinusoids. The fundamental (linear) response is clearly visible as are the second-order (quadratic) and third-order (cubic) distortion products. To analyse the nonlinear distortions, the small signal expansion performed in Section 2.5 is applied, except this time, higher-order terms are kept as driving terms to the linear

Power relative to fundamental (dBc)

10 Fundamentals

0

Third-order in-band intermodulation products

Second-order harmonic and intermodulation product

-10

-20

-30

Third-order harmonics and intermodulation products

Second-order harmonic and intermodulation product

-40

-50

-60

-70

-80

0

1

2

3

4

5

6

7

8

Frequency (GHz)

Figure 2.14 RF spectrum of an optical link driven by two channels with large signal sinusoids. The various second-order and third-order distortion products are labelled


55

equations. This is based on the assumption that the overriding response of the system is linear and that the nonlinear distortions serve only to generate harmonics and intermodulation products which are subsequently filtered by the linear system. This assumption was used when deriving the small signal frequency response. This method will not work in general for arbitrary inputs, but for two-tone modulation with predictable nonlinear distortion products we can assume a sum of complex exponentials for the variations in the photon and carrier densities and substitute into the equations. The resulting series of equations in distortion products is closed by assuming the higher-order distortion products are much smaller than the lower-order ones, which allows a closed form solution with higher-order distortions expressed in terms of lower-order distortions. This is a reasonable assumption based on the experimental results and also from power series expansions of the optical power versus current response at low frequencies. As in Sections 2.2 and 2.4, the spatially homogeneous, single mode equations will be used to derive the majority of the discussion for this introduction. Near resonance, this model provides an accurate representation of even multimode lasers if appropriate model parameters are used. The small signal equations, retaining only the dominant intrinsic nonlinear driving terms for illustrative purposes are given below. In general, solving the nonlinear rate equations analytically is very difficult. However, for a sum of sinusoids it is straightforward to develop a scheme that gives reasonably simple analytic expressions. The basic idea is to assume a form of the current modulation: DI ¼ DI1 ejv1 t þ DI2 ejv2 t þ cc and a resulting carrier density and photon density modulation containing distortions of all orders of interest. Here cc denotes the complex conjugate. For example, to calculate the intermodulation distortions requires assuming the following form for the photon density: DS ¼ s11 ejv1 t þ s12 ejv2 t þ cc s21 ej2v1 t þ s22 ej2v2 t þ s23 ejðv1 þ v2 Þt þ s24 ejðv2 v1 Þt þ cc s31 ej3v1 t þ s32 ej3v2 t þ s33 ejð2v2 v1 Þt þ s34 ejð2v1 v2 Þt þ cc and similarly for the carrier density (see Table 2.1). After substituting these expressions into the rate equations and multiplying out the nonlinear terms, we collect the terms that have the same frequency dependence as the distortion product of interest and solve the resulting linear system, only keeping the driving term contributions of lower order than the distortion product of interest. Using this hierarchy, closed form solutions for the intermodulation distortion products can be calculated. Table 2.2 lists the solutions for the various distortion terms in the optical response of the laser. The contributions from the various device nonlinearities for second harmonic distortion are shown in Figure 2.15. Table 2.1 Form for the nonlinear photon density response under two-tone modulation. Photon density Harmonic distortion Intermodulation distortion

2HD DS ¼ s1 ejvt þ s2 ej2vt 3HD DS ¼ s1 ejvt þ s2 ej2vt þ s3 ej3vt DS ¼ s11 ejv1 t þ s12 ejv2 t þ cc s21 ej2v1 t þ s22 ej2v2 t þ s23 ejðv1 þ v2 Þt þ s24 ejðv2 v1 Þt þ cc s31 ej3v1 t þ s32 ej3v2 t þ s33 ejð2v2 v1 Þt þ s34 ejð2v1 v2 Þt þ cc


56

Table 2.2

Definition of photon response terms used in Table 2.1.

Linear terms s1 ¼ S0 OMD Second-order harmonic terms Hð2vÞ 2 v ðOMDÞs1 v4R Third-order harmonic terms 3 Hð3vÞHð2vÞ 2 2 v2R 2 v v þ jvv þ s1 s3 ¼ OMD2 R 2 2 v4R

s2 ¼

Third-order intermodulation terms 1 HðvÞHð2vÞ 2 2 v2R 2 s1 v v þ jvv þ s33 ¼ OMD2 R 2 2 v4R

Figure 2.15 The second-order harmonic distortion in the optical modulation response of a laser diode. The heavy-line is the total distortion. Also shown are the various device nonlinearities that contribute to the harmonic distortion


57

Figure 2.16 The third-order intermodulation distortion in the optical response. Also, shown are the DC nonlinearities which also appear in the L-I curve. For reference, the analytic expressions obtained by [5] and [6] when there is no gain compression are also shown

The separate contributions from the nonlinearity due to stimulated emission (intrinsic) and the gain compression nonlinearity are shown. At low frequencies, the intrinsic and gain compression nonlinearities are equal and cancel as seen by the roll off in the total driving terms. This cancellation is the “local” cancellation of these two effects that comes from the feedback stabilization of the carrier and photon densities at their steady- state values. Figure 2.16 shows the third-order intermodulation distortion – often referred to as the inband distortion. The components of the third-order intermodulation driving terms are not shown because cancellation effects are not explicitly evident. However, since the third-order terms are generated by the second-order terms, a reduction in the second-order nonlinearities in general leads to a reduction in the third-order nonlinearities. Near resonance, the nonlinear driving terms are dominated by the intrinsic nonlinearity. The third-order intermodulation distortion is plotted in units of dBm/mA3 for different laser injection currents. The units are chosen per mA3 of modulation current because third-order distortions scale as the cube of the input modulation current. The intermodulation distortion spectrum contains two peaks: one at the relaxation oscillation peak and one at half of that frequency. The half frequency peak occurs because at that frequency, the second harmonic, which is a driving component for the third-order distortion, is resonant with the relaxation oscillation resonance. The main peak occurs because both the fundamental and the in-band third-order intermodulation distortion are resonant with the relaxation oscillation resonance.


58

Output power (mW)

60

3

Intermodulation distortion (dBm/mA )

40 20 0 –20

80 40 20 0

50 Blas (mA)

0

100

–40 –60 –80 –100

Increasing output power

–120 5 10

Figure 2.17

106

107

108 Frequency (Hz)

109

1010

1011

The third-order intermodulation distortion as a function of increasing DC bias on the laser

The intermodulation distortion decreases as the modulation frequency decreases below the relaxation oscillation frequency because the gain clamping improves, which damps the nonlinear response. The same effect also occurs as the injection current increases because the larger steady-state photon density provides stronger feedback against carrier and photon density variations (see Figure 2.17). From this figure, it appears that to minimize the distortion, at a given modulation frequency, it is desirable to bias the laser as high as possible. There is a limit, however, that depends on the gain compression factor and device heating. From the above discussions, we see that there are different dependencies on DC output power for the various distortion components. In general, spatial-hole burning nonlinearities increase with output power whereas the intrinsic or stimulated emission nonlinearity improves with bias. The gain compression nonlinearity can cancel either of the above in different frequency ranges. Figure 2.18 shows that there will generally be an optimal bias point for minimizing the overall distortion.

2.6 Low-cost VCSEL RF Photonic Links Vertical cavity surface emitting lasers (VCSELs) benefit from their small form factor and circular geometry. The form factor enables massive parallelism in semiconductor manufacture and the circular geometry simplifies device packaging; both contribute to the relatively low cost of high-speed VCSELs. As a result, these small, inexpensive devices are finding their way into a large array of applications from sensing to data communications. Historically, the major thrusts of VCSEL design have been to minimize the threshold current, reduce the resistance of the DBR mirrors, increase device modulation speed and increase the single mode output power. All of these factors contribute to the increased utility of VCSELs for microwave photonics applications. With the VCSELs favourable optical properties, it is no surprise that there is a wealth of work done to characterize VCSELs for use in communication applications.


59

Figure 2.18 The measured spur-free dynamic range for a Fujitsu CATV DFB laser. The dominant distortion considered was third-order intermodulation distortion

Early work with high-speed characterization was carried out by Choa et al. [7] in 1991, and Shtengel et al. [8] and Mahon et al. [9] in 1993. Choa et al. provided modulation response measurements of high efficiency ion implanted VCSELs and demonstrated intensity and frequency modulation bandwidths as high as 8 GHz with a differential quantum efficiency estimated to be 50% which corresponds to a maximum link gain of 6 dB. However, when including the impedance matching to the 450 W differential resistance, the maximum link gain drops to 20 dB. Shtengel et al. demonstrated modulation bandwidths as high as 14 GHz with a differential quantum efficiency of only 8.4% which corresponds to a maximum link gain of 21.5 dB. When factoring in the measured differential resistance of 95 W, the maximum link gain is 31.7 dB assuming perfect coupling and perfect detector quantum efficiency. The second harmonic distortion was also measured and shown to be 5 dB below the fundamental when the input modulation power was 0 dBm, corresponding to a current of 4 mA. This gives a second harmonic distortion of 36 dB/mA2. Mahon et al. studied the relative intensity noise and second- and third-order harmonic distortion in multimode VCSELs. The modulation bandwidth was approximately 5 GHz with differential quantum efficiency of 20 % (14 dB maximum link gain) with differential resistance of 663 W (31 dB maximum total link gain). The second harmonic distortion estimated from the published data is 24 dB/mA2. More recently, investigations into the modulation response and linearity in VCSELs were carried out by Hietala et al. [10] in 1997. In that work, the modulation response and distortion was measured for an oxide aperture VCSEL along with light emission from square wave excitation. The maximum modulation bandwidth measured was 19 GHz with 40 % differential quantum


60 10 5

Link Gain (dB)

0 –5 1996 [11] –10

1996 [11]

1995 1996

–15

1987 [18] 1991 [15]

–20 1991 –25

1993 [16]

–30 –35 0

1993 [17] 100

200

300

400 500 600 700 Differential Resistance (Ω)

800

900

1000

Figure 2.19 The calculated link gain based on historical data for VCSEL quantum efficiency and electrical differential resistance. The solid curve is the calculated mismatch gain based only on the electrical impedance

efficiency (7.8 dB maximum link gain) and differential resistance of 264 W (17.8 dB maximum total link gain). The input IP3 was 6.5dBm. Subsequent studies of analogue modulation properties of VCSELs were carried out by Wesselmann et al. [11], who measured the spurious free dynamic range in long wavelength 1.3 mm and 1.5 mm VCSELs of 69 dB in an unspecified bandwidth. The IP3 was approximately 10 dBm; however, this measurement included an erbium doped optical amplifier whose gain was not specified. Dalal et al. [12], measured the dynamic range in short wavelength 980 nm VCSELs with maximum dynamic range of 85 dB in 1 Hz bandwidth. Finally, recent work by Lee et al. [13] and Carlsson et al. [14] explores the dynamic range of links employing oxide aperture VCSELs. The historical data discussed above is summarized in Figure 2.19. It shows a steady trend during the 1990s that coupled the reduction in electrical series resistance and enhanced external quantum efficiency to the overall improvements in link gain. We have employed relatively large diameter VCSELs to both reduce the series resistance, and therefore improve the mismatch link gain, and increase the external differential efficiency, since the boundary scattering is minimized. Measured SFDR for a 27 m multimode optical link employing an 850 nm VCSEL link is plotted in Figure 2.20. As the bias current increases the bandwidth over which high dynamic range can be achieved also increases. At low frequencies, the multimode link suffers from mode partition noise and therefore has a reduced dynamic range. The highest dynamic range (approximately 110 dB-Hz2/3) occurs for a number of bias currents in a range of frequencies between 900 MHz and 2.5 GHz. The centre of mass of the dynamic range is 105 dB- Hz2/3. From these measurements, it is clear that the dynamic range


Figure 2.20 link [13]

61

The measured spur-free dynamic range for an 850 nm VCSEL in a 27 m multimode fibre

intrinsic to the VCSELs is comparable to edge emitting lasers [15] and opens the possibility for considering VCSELs in high fidelity RF photonic links.

2.7 Cascade Laser Optical Links Here, we present a new class of laser structures which can be directly modulated and do not have any of the conventional restrictions on loss of electrical signal strength or increased noise of conventional semiconductor lasers. A conventional semiconductor laser emitting photons with perfect quantum efficiency has a slope efficiency of one; for every electron injected into the laser one photon is emitted from the laser. Some fraction of the generated photons is coupled into single mode fibre and arrives at the detector. Cascade lasers can compensate for link losses by generating more than one photon for every electron injected into the laser. This is possible because each carrier injected into the laser can sequentially tunnel into each of the multiple active regions, stimulating photon emission in each. Because each carrier injected into an N-stage cascade laser can undergo N photoemission events, the slope efficiency can potentially see an N-fold increase as well. If the noise in each of the photon streams from the N stages is independent of the noise in the other photon streams, a concomitant improvement in the signalto-noise ratio of the link is expected. In order to better appreciate the difference between a conventional multiple quantum well laser and a bipolar cascade laser (BCL) the reader is referred to Figure 2.21. In the conventional laser an injected electron may go into any one of the multiple quantum wells, but never more than one. The quantum wells may therefore be viewed as being in parallel. Figure 2.21 shows a three quantum well (or, equivalently, three gain section) BCL. In this case the injected electron can participate in a recombination event in the first quantum well, quantum mechanically tunnel from the valence band of the first gain section to the conduction band of the second gain section, and on through to the third gain section. In this case the electron goes through all the quantum wells and they are seen as being connected in series.


62

Electron

Figure 2.21 In a conventional multiple quantum well laser an injected electron may go into any one of the quantum wells and recombine, but only one. A cascade laser contains three quantum wells which are electrically in series

Assuming that enough photons can be generated (by connecting a sufficiently large number of lasers in series) to compensate for any loss in transporting the photons to a photodetector, it is conceivable that more electrons will be generated at the receiver than were put in at the source. This results in the concept of radio frequency (RF) gain. It is important to realize that this is not ‘creating energy’. The voltage drop across the series connected diodes is equal to N times the voltage drop across a single diode, where N is the number of diodes in series. Gain only occurs in the ‘small signal’ sense. The promise of cascade lasers for high-performance microwave links was first understood by researchers at DRA Malvern [16] and MIT [15] in a set of experiments employing series connected laser arrays. The series connected lasers mimic the enhanced efficiency expected in a cascade laser array. Indeed, these experiments demonstrated that positive link as high as þ 4 dB in a fibre coupled 1550 nm optical link could be achieved [15]. More importantly the additional photons were only weakly correlated in terms of their noise so the overall noise figure improved with the number of elements in series. A 6 dB improvement in the overall link noise figure was realized in these laser arrays (Figure 2.22).

2.7.1 Bipolar Cascade Lasers It is worthwhile to consider the historical evolution of the BCL. While all the devices described below operate on the same principle each is different from the others in some critical way. Careful study of each of these devices indicated the design limitations that prevented them from demonstrating room temperature, continuous wave performance. The BCL was first introduced by van der Ziel et al. in 1982 [18]. Three bulk 850 nm active region edge emitting lasers were connected electrically in series during the epitaxial process via two tunnel junctions. The device exhibited pulsed operation at room temperature with a duty cycle of 0.1 %. A differential efficiency of 80 % was achieved. Little was done with the concept until Garcia et al. [19] realized a similar device with an eye toward high-power arrays in 1997. The devices consisted of a two-stage cascade operating at 950 nm in the top-most junction and 980 nm in the bottom-most junction. The active regions were made of three quantum wells each. These devices also operated at room temperature and pulsed. A differential efficiency of 79 % was achieved.


63

Figure 2.22 Theoretical noise figure for a series connected laser array and bipolar cascade lasers [17]. The squares show the measured noise figure for the series array [15]

Kim et al. [20] also achieved room temperature pulsed operation of a three-stage device operating at 1.55 mm in 1999. This edge emitter was unique in that all of the three gain stages were contained inside a single waveguide. A pulsed slope efficiency of 125 % was obtained. BCL designs were not limited to edge emitters. Schmid et al. [21] achieved continuous wave operation of a two-stage BCL in a vertical cavity surface emitting laser (VCSEL) at an operating temperature of 95 K in 1998. Two gain sections of three quantum wells each were cascaded at an emission wavelength of 980 nm. The first room-temperature, continuous wave operation of a BCL was achieved by Patterson et al. [22]. A two-stage device operating at 990 nm achieved a quantum efficiency of 99.3 %. Figure 2.23 shows the room-temperature,

Figure 2.23 The measured light versus current curve for a room-temperature bipolar cascade laser. The slope efficiency is 99.3 %. The inset shows the near field emission from the laser. Reproduced from [22]

64


continuous wave, L-I characteristics, of a nominally 5 mm wide and 450 mm long, bipolar cascade laser. The slope efficiency is 99.3 % (0.622 W/A) above threshold. A slope efficiency of 0.6 W/A is maintained up to a current of 58 mA, corresponding to a slope efficiency of 95.7 %. Such high efficiency is characteristic of cascade devices. Since that time a continuous wave, room-temperature demonstration of a BCL VCSEL has been reported by T. Kn€ odl et al. [23] at 980 nm and a room temperature pulsed VCSEL has been demonstrated by Kim et al. [24] at 1.55 mm. Kn€ odl et al. have recently achieved external quantum efficiencies of 130 % and have observed the enhancement in efficiency directly on the modulation properties of the device [25]. However, there is much that needs to be done to demonstrate the improved noise figure expected of these novel cascade laser devices. There is room for a new generation of directly modulated optical links which can provide unprecedented noise figures and dynamic ranges with the simplicity inherent in intensity modulated, direct detection optical links.

References [1] L.A. Coldren and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits, Microwave and Optical Engineering, John Wiley & Sons, Inc., New York, USA, 1995. [2] J. Chen, R.J. Ram and R. Helkey, “Linearity and third-order intermodulation distortion in DFB semiconductor lasers”, IEEE Journal of Quantum Electronics, vol. 35, no. 8, pp. 1231–1237, Aug. 1999. [3] R. Nagarajan, T. Fukushima, M. Ishikawa, J.E. Bowers, R.S. Geels and L.A. Coldren, “Transport limits in highspeed quantum-well lasers: experiment and theory”, IEEE Photonics Tech. Lett., vol. 4, no. 2, p. 121, 1992. [4] O. Kjebon, R. Schatz, S. Lourdudoss, S. Nilsson, B. Stalnacke and L. Backbom, “30 GHz direct modulation bandwidth in detuned loaded InGaAsP DBR lasers at 1.55 micron wavelength”, Electronics Letters, vol. 33, pp. 488–489, March 1997. [5] T.E. Darcie, R.S. Tucker and G.J. Sullivan, “Intermodulation and harmonic distortion in InGaAsP lasers”, Electron Lett., vol. 21, pp. 665–666, Aug. 1995. [6] J. Wang, M.K. Haldar and F.V.C. Mendis, “Formula for two-carrier third-order intermodulation distortion in semiconductor laser diodes”, Electron. Lett., vol. 29, pp. 1341–1343, July 1993. [7] F.S. Choa, Y.H. Lee, T.L. Koch, C.A. Vurrus, B. Tell, J.L. Jewell and R.E. Leibenguh, “High speed modulation of vertical-cavity surface emitting lasers”, IEEE Photon. Techn. Lett., vol. 3, pp. 697–699, Aug. 1991. [8] G. Shtengel, H. Temkin, P. Brusenbach, T. Uchida, M. Kim, C. Parsons, W.E. Quinn and S.W. Swirhun, “High speed vertical cavity surface emitting laser”, IEEE Photon. Tech. Lett., vol. 5, pp. 1359–1362, Dec. 1993. [9] C.J. Mahon, M.L. Majewski, M.G. Peters, F.H. Peters and L. A. Coldren, “Relative intensity noise and modulation distortion characteristics of vertical cavity surface emitting laser diodes”, in LEOS 1993 Conference Proceedings, IEEE/Lasers & Electro-Opt. Soc., IEEE, San Jose, USA, pp. 372–373, Nov. 1993. [10] V.M. Hietala, K.L. Lear, M.G. Armendariz, C.P. Tigges, H.Q. Hou and J.C. Zolper, “Electrical characterization and application of very high speed vertical cavity surface emitting lasers”, in IEEE MTT-S International Microwave Symposium Digest, Denver, USA, pp. 355–358, June 1997. [11] J.R. Wesselmann, N.M. Margalit and J.E. Bowers, “Analog measurements of long-wavelength vertical-cavity lasers”, Appl. Phys. Lett., vol. 72, pp. 2084–2086, Apr. 1998. [12] R.V. Dalal, R. J. Ram, R. Helkey, H. Roussell and K.D. Choquette, “Low distortion analogue signal transmission using vertical cavity lasers”, Electronics Letters, vol. 34, no. 16, pp. 1590–1591, Aug. 1998. [13] H.L.T. Lee, R.V. Dalal, R.J. Ram and K. D. Choquette, “Dynamic range of vertical-cavity surface-emitting lasers in multimode links”, IEEE Photonics Technology Letters, vol. 11, no. 11, pp. 1473–1475, Nov. 1999. [14] C. Carlsson, H. Martinsson, R. Schatz, J. Halonen and A. Larsson, “Analog modulation properties of oxide confined VCSELs at microwave frequencies”, Journal of Lightwave Technology, vol. 20, pp. 1740–1749, Sep. 2002. [15] C.H. Cox, III, H.V. Roussell, R.J. Ram and R.J. Helkey, “Broadband, directly modulated analog fiber link with positive intrinsic gain and reduced noise figure”, International Topical Meeting on Microwave Photonics. Piscataway, NJ, USA, pp. 157–160, 1998.


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[16] S. Ayling, D. Wight, M. Allenson, K. Hilton and G. Smith, “Intrinsically matched 50 ohm laser arrays with greater than 100% quantum efficiencies for optically coupled transistors and low loss fiber optic links”, Proceedings of the International Society for Optical Engineering, vol. 3285, pp. 199–208, 1998. [17] F. Rana and R.J. Ram, “Photon noise and correlations in semiconductor cascade lasers”, Applied Physics Letters, vol. 76, no. 9, pp. 1083–1085, Feb. 2000. [18] J.P. van der Ziel and W.T. Tsang, “Integrated multilayer GaAs lasers separated by tunnel junctions”, Applied Physics Letters, vol. 41, no. 6, pp. 499–501, Sept. 1982. [19] J.C. Garcia, E. Rosencher, P. Collot, N. Laurent, J.L. Guyaux, B. Vinter and J. Nagle, “Epitaxially stacked lasers with Esaki junctions: a bipolar cascade laser”, Applied Physics Letters, vol. 71, no. 26, pp. 3752–3754, Dec. 1997. [20] J.K. Kim, E. Hall, O. Sjolund and L. A. Coldren, “Room-temperature, electrically-pumped, multiple-activeregion VCSELs with high differential efficiency at 1.55 mu m”, Technical Digest. CLEO/Pacific Rim 99. Pacific Rim Conference on Lasers and Electro-Optics, vol. 2, pp. 553-L 554, 1999. [21] W. Schmid, D. Wiedenmann, M. Grabherr, R. Jager, R. Michalzik and K. J. Ebeling, “ CW operation of a diode cascade InGaAs quantum well VCSEL”, Electronics Letters, vol. 34, no. 6, pp. 553–555, March 1998. [22] S.G. Patterson, G.S. Petrich, R.J. Ram and L.A. Kolodziejski, “Continuous-wave room temperature operation of bipolar cascade laser”, Electronics Letters, vol. 35, no. 5, pp. 395–397, March 1999. [23] T. Knodl, R. Jager, M. Grabherr, R. King, M. Kicherer, M. Miller, F. Mederer and K.J. Ebeleing, “CW room temperature operation of a diode cascade InGaAs-AlGaAs quantum well VCSEL”, IEEE LEOS Annual Meeting Conference Proceedings, vol. 1, pp. 143–144, 1999. [24] J.K. Kim, S. Nakagawa, E. Hall and L.A. Coldren, “Near-room-temperature continuous-wave operation of multiple-active-region 1.55 mu m vertical-cavity lasers with high differential efficiency”, Applied Physics Letters, vol. 77, no. 20, pp. 3137–3139, Nov. 2000. [25] T. Knodl, M. Golling, A. Straub and K.J. Ebeling, “Multi-diode cascade VCSEL with 130 % differential quantum efficiency at CW room temperature operation”, Electronics Letters, vol. 37, pp. 31–33, Jan. 2001.

3 High-power Distributed Photodetectors for RF Photonic Applications Sagi Mathai and Ming C. Wu

3.1 Introduction Photodetector linearity is of paramount importance in external intensity modulated direct detection (IMDD) analogue fibre-optic links. This realization has created a demand for high bandwidth, high saturation current photodetectors. Additionally, high current photodetectors have the potential to simplify receiver designs by eliminating the need for impedance matched electronic amplifiers. Applications that can benefit from high-performance photodetectors include antenna remoting, fibre-radio and terahertz signal generation by photomixing. The system level benefits of high current photodetectors may be seen by plotting the link RF gain (GRF), noise figure (NF), and spurious free dynamic range (SFDR) versus photocurrent for a hypothetical external IMDD link. The curves in Figure 3.1 clearly demonstrate the benefits of high current photodetectors. As the photocurrent increases so does the link performance until laser RIN dominates the noise floor. Link performance may be further improved by utilizing balanced detection, in which case laser RIN is suppressed, the shot-noise limited regime is extended, and with increasing photocurrent, GRF, NF and SFDR improve dramatically. Space charge effects and thermal runaway are the primary factors limiting photodetector high power operation [1]. Large photocurrent density in the absorption regions can screen the applied electric field leading to a lowering of the photogenerated carrier velocity and, ultimately, the complete collapse of the applied electric field [2]. Consequently, RF photoresponse decreases and nonlinearities generated by the photodetector start to degrade the system dynamic range.


68

Microwave Photonics: Devices and Applications (a)

40

G RF (dB)

20

0

-20

-40

-60 0.01

0.1

1

100

10

1000

Photocurrent (mA)

(b) 80

NF (dB)

60

40

Conventional

20

Balanced 0 0.01

0.1

1

10

100

1000

Photocurrent (mA)

(c) 130

SFDR ( dBxHz 2/3 )

Balanced

110

Conventional

90

70 0.01

0.1

1

10

100

1000

Photocurrent (mA)

Figure 3.1 Simulated performance of an external intensity modulated direct detection analogue link, with and without balanced detection, in terms of (a) RF gain, (b) noise figure and (c) spurious free dynamic range. (Vp ¼ 6 V, hPD ¼ 0.9, link loss ¼ 15 dB, RIN ¼ 165 dBc/Hz and 50 W matched impedance)

High-power Distributed Photodetectors for RF Photonic Applications

69

High photocurrent density also causes excessive Joule heating (bias voltage photocurrent) of the absorption region leading to thermally activated dark current runaway [3], which eventually results in catastrophic photodiode failure. Dark current and the effective barrier height for dark current flow are the fundamental device parameters involved in thermal runaway [4]. Photodetectors with low dark currents and high effective barriers have been found to sustain larger amounts of Joule heating before catastrophic failure. For example, metal– semiconductor–metal (MSM) photodetectors have much lower effective barriers than p–i–n diodes, and consequently, MSMs fail at 700 K [5] whereas p–i–n junctions can withstand temperatures up to 900 K [4]. It should also be mentioned that device fabrication induced damage, such as poor surface passivation and plasma induced damage, can increase the dark current and contribute to premature device failure. These issues are especially problematic in lumped element photodetectors, operating under high-power illumination, that rely on a small absorption volume (10 mm3) to achieve high bandwidth. An intuitive approach to mitigate space charge effects and thermal runaway is to distribute the photogenerated carriers over an enlarged absorption volume. First suggested in [6] by Taylor, the travelling wave concept applied to photodetectors has received considerable attention due to its ability to distribute photogenerated carriers over a large absorption volume without succumbing to RC time speed limitations found in lumped element devices. By embedding the photodetector in a transmission line, the diode capacitance becomes part of the transmission lines distributed admittance, while the load impedance associated with the lumped element device RC time is de-embedded. Hybrid [7, 8] and monolithic [9–16] implementations have been demonstrated. Most monolithic implementations are a variation of the p–i–n waveguide photodetector (WGPD) [17, 18] with the transmission line terminated at the input by a matched impedance. As shown in Figure 3.2, two types have been demonstrated: (1) continuous and (2) distributed. The continuous type is normally referred to as the travelling wave photodetector (TWPD), while the distributed type is referred to as the velocity match distributed photodetector (VMDP). In a TWPD, the absorption region spans the entire length of the microwave transmission line. Due to capacitive loading from the thin intrinsic absorption layer, the characteristic line impedance is typically lower than 50 W, and the microwave phase velocity is much lower than the optical group velocity (typically 30 % lower). This velocity mismatch can limit the bandwidth due to phase walk-off between the optical and electrical signals. Consequently, TWPDs are kept short to mitigate the effects of velocity mismatch. In VMDPs, the absorption length is divided among discrete transit time limited photodiodes periodically placed along a transmission line. The separation between diodes is used to dilute the capacitive loading on the transmission line and simultaneously achieve 50 W impedance and velocity matching. Consequently, the photocurrents from each photodiode are coherently added along the transmission line. This chapter reviews the research our group has performed in the area of high-speed high-power distributed photodetectors. Section 3.2 develops a transmission line modelling tool to design distributed photodetectors. Section 3.3 presents our experimental work on VMDPs, including balanced VMDPs. Section 3.4 presents a means to increase the saturation photocurrent in VMDPs by using parallel optical feed. Section 3.5 addresses the issue of backward travelling wave cancellation and a summary of the chapter is given in Section 3.6.

70


Figure 3.2 Physical layout of (a) a TWPD and (b) a VMDP. In the TWPD, the transmission line spans the entire length of the photodiode, while in the case of the VMDP, photodiodes are periodically arrayed along the transmission line

3.2 Transmission Line Model Design Tool The frequency response of distributed photodetectors may be calculated using the ABCD transfer matrix approach [19]. An equivalent circuit for the transmission line is shown in Figure 3.3. It consists of an array of unit cells comprising a section of transmission line with length D and a photodidode. The photodiodes are represented using a Norton equivalent circuit comprised of a series resistance, RS, and capacitance, Cj, shunted by an effective current source, ieff. The Norton equivalent photocurrent feeding the transmission line is related to the photocurrent generated in a photodiode, iph, by the following expression: ieff ¼

1 iph : 1 þ jvRs Cj

ð3:1Þ

The ABCD matrix for the transmission line segment of length D is written in terms of its characteristic line impedance, Z, and propagation constant g, while the ABCD matrix for the I0

I1

I2

IN-1

IN

+

+

+

+

+

Z T V0

V1

V2

VN-1

-

-

-

-

M1

VN ZL

-

M2 (a) Rs Cj

ieff

(b)

Figure 3.3 Equivalent circuit representations of (a) a distributed photodetector and (b) a single photodiode


photodiode can be written in terms of an admittance Y. " # coshðg DÞ Zsinhðg DÞ 1 M1 ¼ 1 sinhðg DÞ coshðg DÞ Z 1 0 M2 ¼ Y 1 Y¼

1 Rs þ j v1Cj

71

ð3:2Þ ð3:3Þ ð3:4Þ

The voltage and currents at the terminals of the unit cell may now be evaluated iteratively using: 0 Vn Vn þ 1 ð3:5Þ ¼ M2 M1 þ F expð jbo D nÞ ieff;n þ 1 t In þ 1 In where bo, n, and Ft are the optical propagation constant, unit cell index (n 2 [0,N]), and normalized transit time frequency response [20], respectively. The relationships between VN, IN and V0, I0 are obtained from Equation (3.5) by setting ieff to zero and assuming an input termination impedance ZT. The homogeneous solutions,V 0 N ; I 0 N , are obtained by setting V0, I0 to zero. 0 VN 1 V ð3:6Þ ¼ 0 N þ ðM2 M1 ÞN M1 1 V ; 1=ZT 0 IN IN where N is the total number of diodes. The total solution is obtained by superposition [14]. To investigate the effect of periodic loading on the transmission line, consider the simple case of a lossless transmission line. When the spacing between photodiodes is small compared to the microwave wavelength on the transmission line (< ¼ l/10), it may be considered electrically smooth. In this case, the loaded microwave phase velocity (vL) and characteristic impedance (ZL) are modified by the photodiode admittance or an effective capacitance, Ceff: 1 vL ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CTL þ CDeff LTL

ð3:7Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi LTL ZL ¼ CTL þ CDeff

ð3:8Þ

Ceff ¼

1 j v Rs þ

1 Cj

:

ð3:9Þ

Note that the capacitive loading can be tailored to achieve simultaneous velocity and impedance matching. If the transmission line loss can be neglected, the bandwidth of the VMDP is essentially limited by the intrinsic speed of a single photodetector in the array.

72


3.3 Velocity Matched Distributed Photodetectors In the VMDP, photodiodes are evanescently coupled to an underlying passive optical waveguide and periodically feed a transmission line. A unique advantage of the VMDP lies in its flexibility in optimizing the optical waveguide, photodiode and microwave transmission line independently. The optical waveguide can be designed with a large mode size for low fibreto-waveguide coupling loss and left undoped to minimize free-carrier absorption. The photodiodes can be optimized for high speed (as in conventional ultrafast photodiodes), and low optical confinement in the absorber for high saturation current. Impedance and velocity matching can be incorporated in the transmission line design, as well as low microwave propagation loss. The distributed design also mitigates thermally induced catastrophic failure due to thermal runaway [5]. The VMDP concept is so flexible that numerous types of photodiode structures have been implemented: metal–semiconductor–metal (MSM) [9, 14], Schottky [21], p–i–n [22] and the uni-travelling-carrier photodiode (UTC-PD) [13]. In our group, we demonstrated MSM based VMDPs on GaAs [14] and InP [10] material systems, but switched to p–i–n structures as they are less susceptible to thermal runaway and able to achieve much higher saturation current [22]. A crucial issue in VMDPs is the photocurrent distribution along the photodiode array. To characterize the distribution, VMDPs with split electrical contacts to each photodiode were fabricated. Figure 3.4 describes the photocurrent distribution among four photodiodes along an array. When the fibre-towaveguide alignment was optimized for the first photodiode, the responsivity was maximum, but the photocurrent distribution and linear current (22 mA) were poor. By optimizing the alignment to photodiodes farther away from the input waveguide facet, lower responsivity but much higher linear photocurrents (Figure 3.5) were possible. The best response was achieved when optimizing the alignment to the third photodiode: 35 GHz bandwidth and 45 mA linear DC photocurrent were achieved. At a higher photocurrent (55 mA), the waveguide input facet experienced catastrophic failure, while the p–i–n photodiodes remained operational [22].

Figure 3.4 Measured responsivity of individual photodiodes in a split contact VMDP with the input fibre alignment optimized for maximum photocurrent in the (a) first, (b) second, (c) third and (d) fourth photodiode. Reproduced from [22] ( 2001 IEEE)

73


45.3mA R=0.36A/W

Photocurrent (mA)

50 35mA R=0.39A/W

40

22mA R=0.42A/W

30

20

Alignment optimized VMDP nd

2 PD

10

rd

3 PD

0 0

25

50

75

100

125

150

Input power (mW) Figure 3.5 Total photocurrent versus optical input power when the fibre-to-waveguide alignment was optimized for maximum responsivity in VMDP with a continuous transmission line, and to the second and third photodiodes in a split contact VMDP. Reproduced from [22] ( 2001 IEEE)

An important development in microwave photonics was the introduction of high-power balanced photodetectors for common mode optical noise (laser RIN and added amplified spontaneous emission noises) suppression. Shot-noise limited performance was demonstrated with a hybrid balanced detector built with commercially available low frequency photodetectors [23]. For high bandwidth operation, monolithic devices are required. Figure 3.6 shows the schematic and equivalent circuit of a monolithically integrated balanced photodetector based on the VMDP concept. It consists of a pair of parallel optical waveguides periodically coupled to high-speed p–i–n diodes and a coplanar waveguide (CPW) transmission line with a 50 W loaded characteristic impedance. Balanced mode operation is set by applying the reverse bias voltage between the ground electrodes of the CPW.

Figure 3.6

Schematic diagram and equivalent circuit of the balanced VMDP [22] ( 2001 IEEE)

74


Figure 3.7 Record high (a) CMRR versus photocurrent and (b) broadband laser RIN suppression in a balanced VMDP. Reproduced from [22] ( 2001 IEEE)

Figure 3.7 reports record high common mode rejection ratio (CMRR) of more than 37 dB from a few nA to 31 mA and laser RIN suppression of more than 40 dB from a few MHz to 8 GHz [22]. For comparison, in a balanced photodetector, 31 mA is equivalent to 62 mA in standard photodiodes.

3.4 Parallel Optical Feed Photodetectors The first diode in VMDPs and the input facet of continuous TWPDs usually generate the highest photocurrent density (per unit length) in the entire photodetector, and therefore failure occurs at the first diode or input facet, respectively. Techniques to improve the uniform distribution of photocurrent density include: tailoring the optical confinement factor in the absorber [24], employing electro-absorptive active materials to independently control the absorption coefficient in the propagation direction [21] and splitting the optical power equally among an array of discrete photodiodes using optical fibre delay lines [7]. Among these, parallel optical feed is the most direct avenue to achieve uniform photocurrent density. The VMDP concept is quite compatible with parallel optical feeds. A schematic of a parallel fed VMDP (PF-VMDP) is shown in Figure 3.8. It utilizes a 1 N multimode interference (MMI) optical power splitter [25], an array of high-speed photodiodes, a coplanar strip (CPS) microwave transmission line and an on-chip 50 W thin film resistor.


Figure 3.8

75

Schematic diagram of the PF-VMDP

We fabricated PF-VMDPs with MSM [26] and p–i–n photodiodes [27]. Although the saturation current was limited by the absorption volume in each individual photodiode, a higher saturation current can be achieved by increasing the MMI splitting ratio. Figure 3.9 shows DC linearity measurements on two PF-VMDPs employing identical MSM photodiodes but different MMI splitting ratios. The device with the 1 4 MMI saturates at 13.5 mA, while in the 1 8 case, linearity is maintained until device failure at 20.1 mA [28]. The maximum linear photocurrent can be further increased by increasing the splitting ratio and optimizing the MMI excess loss. A PF-VMDP implemented with p–i–n diodes showed even higher linear response. Referring to Figure 3.10, the DC photocurrent and detected RF power at 10 GHz are linear up to 52.2 mA and 9 dBm, respectively, without device failure. In this experiment, the available optical power limited the maximum photocurrent and RF power [27].

Figure 3.9 DC linearity measurements on MSM based PF-VMDP. Higher MMI splitting ratio results in higher saturation current. Reproduced from [28] ( 2000 IEEE)

76


Figure 3.10 p–i–n based PF-VMDP (a) DC saturation current measurement and (b) RF linearity at 10 GHz. Reproduced from [27] ( 2002 IEEE)

Although the saturation photocurrent can be increased by increasing the optical power splitting ratio, the quantum efficiency in PF-VMDPs is limited by the length of the individual photodiodes. Index matching layers (Figure 3.11) have been proposed as a means to increase the responsivity and reduce the length of waveguide coupled lumped element photodetectors [29].

Figure 3.11 Waveguide coupled photodiode epitaxial layer design with an index matching layer


77

Figure 3.12 (a) Frequency response and (b) RF response at 20 GHz for photodetectors with different index matching layer extension (Detector A ¼ 8 mm, and Detector B ¼ 18 mm). Reproduced from [30] ( 2002 IEEE)

By varying the matching layer extension in front of the photodiode, the absorption profile can be tailored to improve the linearity of the device without sacrificing bandwidth [30]. Figure 3.12 compares the frequency response and RF response at 20 GHz for two detectors (A and B) with different matching layer extensions (A ¼ 8 mm and B ¼ 18 mm). Detectors A and B had identical RC limited bandwidths of 30 GHz, but detector B exhibited nearly an order of magnitude improvement in RF response at 20 GHz [30].

3.5 Backward Wave Cancellation A fundamental issue for travelling wave devices is the backward propagating wave illustrated in Figure 3.13. Without the input termination being matched to the line impedance, the backward wave, reflected at the open input termination, can destructively interfere with the forward propagating wave and thus limit the bandwidth. To improve the bandwidth, an impedance matched to the line impedance may be employed, but at the expense of efficiency. This point is illustrated experimentally in Figure 3.14 for a TWPD with and without a 50 W input termination [33]. With a 50 W input termination, the RF

78


Figure 3.13 Illustration of backward and forward waves generated by photodiodes along a VMDP with (a) open input termination and (b) matched termination

response drops by 6 dB, while the bandwidth broadens by a few gigahertz. High-speed operation without sacrificing responsivity can be obtained by backward wave cancellation (BWC) using a multisection transmission line, originally proposed by Ginzton for distributed amplification in travelling wave tubes [32]. A schematic of our multisection travelling wave distributed photodetector (MS-TWDP) and its equivalent circuit is shown in Figure 3.15. Much like the VMDP, it consists of a passive optical waveguide loaded with an array of photodiodes represented by current sources. Similar structures have been proposed in [15]. The forward travelling photocurrents are coherently combined on a multisection transmission line, while the backward travelling photocurrents are eliminated. The impedance mismatch between adjacent sections causes a negative reflection coefficient, G, such that the reflected photocurrent, GI1, cancels the backward propagating photocurrent, bI2.

Figure 3.14 Effect of input termination on the frequency response of TWPD. Reproduced from [33] ( 2003 IEEE)


79

Figure 3.15 Schematic of (a) the MS-TWDP and (b) its equivalent circuit. The arrows indicate forward and backward wave current flow. Reproduced from [33] ( 2003 IEEE)

For example, between sections 1 and 2, the following condition must be satisfied. GI1 þ bI2 ¼ 0:

ð3:10Þ

By applying a similar condition at each node between transmission line segments a general condition for the line impedance can be derived. nX þ1

Zn þ 1 j¼1 ¼ n X Zn

Ij ð3:11Þ Ii

i¼1

where Zn, Zn þ 1, and Ii are the impedances of sections n and n þ 1 (n increasing from the input end) and the photocurrent generated by the i-th diode, respectively. For the case of equal photocurrent contributions from each photodiode, the equation simplifies to Zn ¼ Z1 =n, where Z1 and Zn are the line impedance of the input and n-th sections, respectively [33]. Initially, we demonstrated BWC for unequally distributed photocurrents [31], but later employed photodiode arrays with uniform photocurrent distribution [33]. Figure 3.16 compares the frequency response of a standard distributed TWDP (SS-TWDP) with a continuous CPS and MS-TWDP. The low frequency roll-off was due to the measurement equipment and not the photodetectors. In each case, the optical waveguides, total absorption volume and responsivity ( 0.25 A/W) were nearly identical. In the continuous CPS case, the efficiency reduced by 6 dB while the bandwidth increased by more than a factor of two when the input was terminated with the line impedance. In the MS-TWDP, less than 2 dB reduction in efficiency was seen when an input termination was used, which indicates that 1 dB of photocurrent was flowing towards the input. More importantly, the bandwidth of MS-TWDP

80


Figure 3.16 Experimental demonstration of bandwidth and efficiency improvement using BWC in MS-TWDP. The MS-TWDP achieves similar bandwidth to the standard distributed TWDP without sacrificing efficiency. Reproduced from [31] ( 2002 IEEE)

was comparable to the terminated continuous CPS version but with a 6 dB response improvement [31]. A scanning electron micrograph (SEM) of a MS-TWDP with uniform photocurrent distribution is given in Figure 3.17. The widths of the coplanar lines and separation between ground and signal were adjusted to obtain the desired impedances of 150 W, 75 W and 50 W in the three sections. The waveguide design employed index matching layers to optimize the absorption profile in each diode for high linearity, while the lengths of the photodiodes were adjusted for uniform photocurrent generation. Referring to Figure 3.18, the measured frequency without an input termination was 38 GHz, 2.5 times higher than the round-trip bandwidth limit of 15 GHz, thus confirming successful BWC. Note also the steep roll-off beyond the 3 dB bandwidth (much steeper than the typical RC roll-off in lumped element devices) – this is indicative of multisection transmission line designs. The 1 dB compression point at 40 GHz is 5 dBm, at which point failure occurs due to

Figure 3.17 SEM of a fabricated MS-TWDP with three p–i–n diodes and a three-section coplanar strip line. The impedances needed for BWC at each section are indicated on the respective transmission line segments [33] ( 2003 IEEE)


81

Figure 3.18 RF performance of a MS-TWDP: (a) frequency response (3 dB bandwidth equal to 38 GHz) and (b) linearity measurements at 40 GHz. Reproduced from [33] ( 2003 IEEE)

thermally induced interconnect metal breakage at the first diode. Consequently, the responsivity dropped by 30 %, but the MS-TWDP remained operational. With thicker metals and improved heat sinking, much higher linear RF power is achievable [33, 34].

3.6 Conclusion High-power, broadband, impedance matched photodetectors are crucial components in highperformance external IMDD analogue fibre-optic links. If high saturation power photodetectors are available, excess laser power can be utilized to simultaneously improve RF gain, noise figure and spurious free dynamic range. The VMDP concept provides the flexibility to design photodetectors with the potential to meet these challenges. Our toolbox for implementing high performance VMDPs includes a travelling wave transmission line model (ABCD matrix approach), novel optical waveguide designs (evanescent coupling and matching layers), multiple architectures (serial and parallel optical feed) and microwave techniques (backward wave cancellation). By selecting the best methods from our toolbox, and with more recent advances in photodiode epitaxial layer design and heat sinking, the VMDP concept has the potential to make an even greater impact on RF photonic systems.

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[23] K.J. Williams and R.D. Esman, “Optically amplified downconverting link with shot-noise-limited performance”, IEEE Photonics Technology Letters, vol. 8, pp. 148–150, 1996. [24] S. Jasmin, N. Vodjdani, J.C. Renaud and A. Enard, “Diluted- and distributed-absorption microwave waveguide photodiodes for high efficiency and high power”, IEEE Transactions on Microwave Theory and Techniques, vol. 45, pp. 1337–1341, 1997. [25] R.M. Jenkins, R.W.J. Devereux and J.M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena”, Optics Letters, vol. 17, pp. 991–993, 1992. [26] S. Murthy, T. Jung, T. Chau, M.C. Wu, D.L. Sivco and A.Y. Cho, ‘“A novel parallelly-fed traveling wave photodetector with integrated MMI power splitter”’, Baltimore, MD, USA, 2000. [27] S. Murthy, M.C. Wu, D. Sivco and A.Y. Cho, “Parallel feed traveling wave distributed pin photodetectors with integrated MMI couplers”, Electronics Letters, vol. 38, pp. 78–80, 2002. [28] S. Murthy, T. Jung, C. Tai, M.C. Wu, D.L. Sivco and A.Y. Cho, “A novel monolithic distributed traveling-wave photodetector with parallel optical feed ”, IEEE Photonics Technology Letters, vol. 12, pp. 681–683, 2000. [29] R.J. Deri and O. Wada, “Impedance matching for enhanced waveguide/photodetector integration”, Applied Physics Letters, vol. 55, pp. 2712–2712, 1989. [30] S. Murthy, T. Jung, M.C. Wu, Z. Wang and W. Hsin, “Linearity improvement in photodetectors by using indexmatching layer extensions”, 15th Annual Meeting of the IEEE Lasers and Electro-Optics Society, Glasgow, UK, vol. 2, pp. 424–425, Nov. 2002. [31] S. Murthy, T. Jung, M.C. Wu, D.L. Sivco and A.Y. Cho, “Traveling wave distributed photodetectors with backward wave cancellation for improved AC efficiency”, Electronics Letters, vol. 38, pp. 827–829, 2002. [32] E.L. Ginzton, W.R. Hewlett, J.H. Jasberg and J.D. Noe, “Distributed amplification”, Proc. I.R.E., vol. 36, pp. 956–969, 1948. [33] S. Murthy, K. Seong-Jin, T. Jung, W. Zhi-Zhi, H. Wei, T. Itoh and M.C. Wu, “Backward-wave cancellation in distributed traveling-wave photodetectors”, Journal of Lightwave Technology, vol. 21, pp. 3071–3077, 2003. [34] N. Duan, X. Wang, N. Li, H.D. Liu and J.C. Campbell, “Thermal Analysis of High-Power InGaA-InP Photodiodes”, IEEE Journal of Quantum Electronics, vol. 42, p. 1255, 2006.

4 Photonic Oscillators for THz Signal Generation Andreas St€ ohr and Dieter J€ager

4.1 Introduction The photonic oscillator concept is a rather new technique for providing low-phase noise continuous-wave signals in the THz regime. Compared to other electrical and optical generation techniques, photonic oscillators exhibit a number of unique features such as ultra-wideband tuneability, compactness and ability to operate over a broad temperature range making it an interesting device for several THz applications. According to a recent study initiated by the European Space Agency (ESA), photonic oscillators utilizing advanced photodetectors are considered as one of the most promising candidates for the generation of THz signals [1]. This chapter reviews the state-of-the-art in photonic oscillators for THz generation and compares this new technique with other existing electrical and optical approaches. Since the development of terahertz photonic oscillators is strongly related to the invention of ultra high-frequency photodetectors we will also cover recent achievements in high-frequency photodetectors in this chapter. Explicitly, we will discuss the high-frequency performance of distributed travelling-wave photodetectors which exhibit a great potential for efficient local oscillator (LO) generation at THz frequencies. This fact is experimentally proven by demonstrating compact photonic oscillators employing advanced travelling-wave photodetectors which are indeed capable of providing sufficient LO power at THz frequencies (e.g. to pump a superconductor–insulator–superconductor (SIS) mixer at around 500 GHz). A key and unique feature of a photonic oscillator compared to other THz sources is its ability to allow for tuning the LO frequency over a wide frequency range. As an example, compact photonic oscillator modules exhibiting an amazingly large tuning range of almost 1 THz will be presented.


86


1meV

1cm

10meV

1mm

100meV

energy

100 µm

1eV

wavelength 10 µm

10eV

100nm

1 µm 1.55 1.3

mm

30GHz

THz (submm)

300GHz

far-IR

3THz

frequency

IR

30THz

visible

300THz

UV

3PHz

Figure 4.1 The electromagnetic spectrum between 30 GHz and 3000 THz. The term THz is commonly applied to the submm-wave frequency range which extends from 300 GHz up to about 3 THz

4.2 THz Sources Today, the term terahertz is commonly applied to submillimetre-wave (submm-wave) energy that fills the wavelength range of 1000 mm–100 mm (300 GHz–3 THz). Below 300 GHz, we enter the millimetre-wave (mm-wave) regime covering the wavelength region of 10–1 mm (30–300 GHz). Beyond 3 THz and up to 30 THz (100–10 mm) we enter the far-infrared (far-IR), but the exact border between submillimetre and far-infrared is still rather blurred since the frequency range 3–10 THz is more or less unclaimed territory. Above 30 THz there is the infrared region covering the wavelength span 10–1 mm (frequency 30–300 THz). In Figure 4.1, the commonly assigned terms for the various frequency bands of the electromagnetic spectrum between 30 GHz and 3 PHz are indicated. So far, the THz frequency regime has been of interest for some more or less niche applications existing in that high-frequency range. Today, we notice a significantly increased interest in THz technologies which is in part stimulated by some recent space and earth exploration experiments such as the Atacama large millimetre array (ALMA) telescope project [2]. The ALMA telescope will be the largest ground telescope for astronomers in the next decade, comprising some 64 submm-wave high quality antennas. ALMA will make it possible to scan and map the emission lines of a variety of lightweight molecules within the frequency region from 30 to 950 GHz for studying the formation of stars and planets. However, besides astronomy there is also much interest in THz technology for imaging applications (Tray imaging), for security applications and even for some communication systems. An excellent overview of the various applications in the THz frequency band can be found in the review paper by Siegel [3]. Despite the fact that there is quite some interest in THz frequencies, the commercial use (e.g. the development of compact THz sources) is only just beginning to emerge. Looking at the various existing concepts for high-frequency LO power sources summarized in Figure 4.2, it is noticeable that all-electronic solutions such as Gunn diodes, IMPATT diodes, resonant tunnelling diodes (RTD) or frequency doublers and triplers are widely employed in the mm-wave and ‘lower’ submm-wave regions. On the other hand, all-optical sources, namely different types of lasers such as p-doped Ge lasers or quantum cascade lasers (QCLs) are

Photonic Oscillators for THz Signal Generation

87

Figure 4.2 Overview of available all-electrical and all-optical power sources versus operating frequency; power slopes with frequency are also indicated (original data has been prepared by J. Hesler [1])

employed in the far-IR. Among optical sources, QCLs are very promising devices for the lower far-IR region, being currently limited in terms of their lower cut-off frequency at around a few THz. For lower frequencies in the THz frequency range, there is almost no power source available as can be seen from Figure 4.2, not to mention the complexity of the few sources existing at all. Obviously, at this point the question arises as to whether optoelectronics could provide a compact source technology not only for the THz frequency range but also for lower frequencies in the mm-wave range. Recently, some promising high-frequency optoelectronic or photonic solutions have been investigated and the achievements in this field of research indicate that the photonic oscillators (PO) concept indeed has great potential for the generation of continuous-wave THz signals with reasonable power levels. As compared to purely electrical and optical solutions the PO concept exhibits some unique advantages such as ultra-wide tuneability, compactness and the possibility of room-temperature operation. These advantages have increased the interest in the PO concept but so far the implementation of optoelectronics for THz signal generation has been delayed; this is mainly because of the limited power level of POs and because of some technological uncertainties of this emerging technique. However, in the course of ongoing research and developments, the power level provided by POs is increasing while on the other hand the required power levels – for example the power level to pump a THz mixer – are decreasing. This fact will foster the future development and improvement of THz POs which do have the potential to become a baseline technology for a wide variety of high-frequency applications as we will show later in this chapter. At first, we shall discuss the effect of optical heterodyning or photomixing in a photodetector, which is the fundamental physical mechanism employed in a PO for generating a highfrequency sinusoidal signal. Then, the basic constitution of a photonic oscillator for highfrequency sinusoidal or quasi-sinusoidal signal generation is explained. Since the performance of a PO in terms of maximum operating frequency and maximum available power is to a large extent determined by the high-frequency photodetector being used, we will look at the various

88


existing types of high-frequency photodetectors and compare them in terms of their highfrequency performance. Next, the high-frequency performance of travelling-wave photodetectors (TWPDs) is investigated using an analytical model describing the vertical and longitudinal carrier transport in a TWPD. By using this model, the major physical effects determining the efficiency of TWPDs at high frequencies are studied. In Section 4.5, various fabricated photonic oscillator modules will be presented, yielding either quasi-optical free space radiation of the generated THz signals or guided transmission within a rectangular metallic waveguide. Ultra-wideband (0.02–0.7 THz) bow-tie antenna integrated and narrow band 0.46 THz slot antenna integrated photonic oscillators are presented in detail, as well as rectangular waveguide coupled TWPDs that enable ultra-wideband continuous-wave signal generation from 0.06 THz up to 1 THz.

4.3 Optical Heterodyning or Photomixing in a Photodetector The fundamental physical principle that is used in photonic THz oscillators is to down-convert optical infrared signals to the THz regime by employing a high-frequency photodetector. This principle, which is also called optical heterodyning or photomixing, is illustrated in Figure 4.3. Two phase-locked infrared waves with angular frequencies v1 and v2 are superimposed and injected into a high-frequency photodetector that down-converts the infrared input signal to the THz frequency regime by generating an electrical signal at the frequency v2-v1. To explain this in more detail, let us consider the relation between the generated electrical output signal and the two superimposed optical input waves from a more physical point of view. For simplicity, we assume that the two optical input waves are linearly polarized monochromatic plane waves in the infrared which propagate in the þ z direction. Let ^ 1 e jðv1 t k1 z þ w1 Þ e1 ; E1 ¼ E

ð4:1Þ

^ 2 e jðv2 t k2 z þ w2 Þ e2 ; E2 ¼ E

ð4:2Þ

and

Beam splitter ω2 − ω1

Photodiode

ω1

ω2~ω1, ω2,ω1>>ω2 − ω1

+z direction ω2

Figure 4.3 Principle for optical heterodyne generation employing a high-frequency photodetector. The angular frequencies of the two optical input waves v1 and v2 are in the IR region (e.g. 200 THz), whereas the difference frequency v2 - v1 of the generated output signal is much lower, typically in the THz or mmwave region

89


^ 1 and E ^ 2, be the complex electrical field vectors of the two optical waves, with field amplitudes E angular frequencies v1 and v2 and wave numbers k1 and k2. The phase of each optical input wave is considered by w1 and w2 and e1 and e2 are the unit vectors determining the orientation of the electrical field vector of the linearly polarized optical input waves. The intensities of the constituent waves are given by the magnitude of their Poynting vectors and are therefore given by rffiffiffiffiffiffiffiffiffi 1 «r «0 I1 ¼ ð4:3Þ jE1 j2 ; 2 m0 and I2 ¼

1 2

rffiffiffiffiffiffiffiffiffi «r «0 jE2 j2 : m0

ð4:4Þ

If the two incident optical waves are perfect plane waves and have precisely the same polarization (e1 ¼ e2), the resulting electrical field E0 of the optical interference signal is the sum of the two constituent input fields and hence we can write E0 ¼ E1 þ E2. Taking the squared absolute value of the optical interference signal we obtain jE0 j2

¼

jE1 þ E2 j2 ¼ jE1 j2 þ jE2 j2 þ E1 E2 * þ E1 * E2

¼

jE1 j2 þ jE2 j2 þ 2jE1 jjE2 jcosððv2 v1 Þ t ðw2 w1 ÞÞ

:

ð4:5Þ

From Equation (4.5) and by using Equations (4.3) and (4.4), it follows that the intensity of the interference signal I0 is given by pffiffiffiffiffiffiffiffi ð4:6Þ I0 ¼ I1 þ I2 þ 2 I1 I2 cosððv2 v1 Þ t ðw2 w1 ÞÞ: By launching this optical interference signal into a photodetector, a photocurrent i is generated which can be expressed as sffiffiffiffiffiffiffiffiffiffi P 1 P2 i ¼ h0 q=hf1 P1 þ h0 q=hf2 P2 þ 2hfc q=h cosððv2 v1 Þ t ðw2 w1 ÞÞ; ð4:7Þ f1 f2 where q is the electron charge and P1 and P2 denote the optical power levels of the two constituent optical input waves. The photodetector’s DC and high-frequency quantum efficiencies are represented by h0 and hf c . It is of course important to consider that the detector’s quantum efficiency is not independent of the frequency. Several intrinsic and extrinsic effects such as transit time limitations or microwave losses will eventually limit the high-frequency performance of the detector and thus the detector’s DC responsivity h0 is typically much larger than its high-frequency responsivity hf c . In our case, we can further simplify the photocurrent equation (Equation (4.7)) by considering the fact that the two optical input waves are close in frequency (f1 f2) whereas the difference frequency fc is by far smaller ( fc ¼ f2 f1 f1, f2). As an example, if we employ a photodetector operating in the infrared at 1.55 mm wavelength, we might use optical input wavelengths at l1 ¼ 1.55 mm ( f1 ¼ 193.4 THz) and l2 ¼ 1.542 mm ( f2 ¼ 194.4 THz). In this case, the difference frequency would be exactly fc ¼ 1 THz which is about 200 times smaller than the optical frequencies. A small detuning of

90


one input laser wavelength by only 0.8 nm (at 1.55 mm) thus results in a remarkable change of the beat frequency by about 100 GHz. If we further assume for simplicity that the power levels of the two optical input waves are equal (Popt P1 P2), Equation (4.7) becomes i ¼ 2s0 Popt þ 2sf c Popt cosð2pfc t þ DwÞ;

ð4:8Þ

fc ¼ f2 f1 ;

ð4:9Þ

where

denotes the difference frequency or beat frequency of the two constituent optical input waves and Dw ¼ w2 w1. Here s0 ¼ h0q/hf and sf c ¼ hf c q=hf are the photodetector’s DC and highfrequency responsivities given in A/W. Equation (4.8) is the fundamental equation describing optical heterodyning in a photodetector. The first term is the DC photocurrent generated by the constituent optical input waves and the second term is the desired high-frequency signal oscillating at the difference frequency fc (down-converter). From a physical point of view, it is important to note that by optical heterodyning no signal is generated which oscillates at the sum of the two optical frequencies. This is in contrast to nonlinear effects such as three-wave mixing in a second-order nonlinear optical medium where not only the difference frequency but also a wave at a higher frequency f1 þ f2 (up-converter) is generated. According to the theoretical discussion above, a photonic oscillator for sinusoidal LO generation thus consists of an optical heterodyne source generating the dual wavelength or dual mode optical signal and a high-frequency photodetector. Schematically, this concept is illustrated in Figure 4.4. Besides compact size, light weight and room temperature operation, a large tuning range is another important advantage of the PO concept. Slightly shifting the wavelength of one laser by only 0.8 nm results in a remarkable tuning of the beat frequency by 100 GHz as discussed above. The maximum tuning range of the PO is mainly determined by the high-frequency responsivity of the employed photodetector and the locking range of the optical heterodyne source. As we will see later in this chapter, the tuning range can be quite large and a tuning range of about 1 THz has already been achieved experimentally. Instead of using a dual-mode optical input signal to the photodetector (PD) one can also use a multimode optical input signal for generating a quasi-sinusoidal oscillator signal. This concept is shown schematically in Figure 4.5. Here the optical spectrum consists not only of two modes but of a larger number of modes, with a constant difference frequency fc between all

phase locked Phase locked optical heterodyne source

Popt

Highhigh High-frequency photodiode

λ2

λ1 ∆λ0 λ0

fc ≈ c0 ⋅

∆λ λ20

λ

Figure 4.4 Typical set-up of a photonic local oscillator consisting of a stabilized optical source generating a phase locked optical heterodyne signal and a high-frequency photodetector generating the electrical beat signal in the THz frequency regime

91


Optical multimode source

Popt

High-frequency photodetector

fc

λ0

fc

λ

Figure 4.5 Typical set-up of a photonic local oscillator consisting of a stabilized optical source for generating an optical comb signal featuring a constant difference frequency fc between the various longitudinal optical modes

neighbouring modes. In this case, the photodetector generates a quasi-sinusoidal output signal at the difference frequency fc. The multimode optical source employed in this approach could be a mode-locked laser diode (MLLD) for example. In order to generate an oscillator signal with high spectral purity and high stability the locking of the optical modes is crucial. Different injection techniques for achieving optical mode locking have been proposed and investigated. The selection of two phase locked modes from a multimode optical source, such as a Fabry–Perot laser, a mode-locked laser diode [4] or an optical comb generator [5, 6] is a comparably straightforward approach. Other approaches are based upon optical injection locking of two independent lasers using an optical phase locked loop (PLL) configuration [7]. For verification of the spectral purity and stability of the optically generated oscillator signal, phase and amplitude noise measurements have been performed. So far, this has been done mainly at ‘lower’ frequencies in the microwave and mm-wave frequency range. As an example, the phase noise of a mode-locked photonic oscillator in the microwave region has been measured to be as low as 125 dBc/Hz at 10 kHz offset from the oscillator frequency. At higher frequencies in the mm-wave regime the typical phase noise is of the order of 80 dBc/Hz to 95 dBc/Hz at 10 kHz offset. The phase and amplitude noise of a PO at THz frequencies has not been thoroughly investigated yet but from initial experiments there is evidence that the phase noise of photonic THz oscillators is comparable to the phase noise of allelectronic Gunn oscillators and warm multiplier assemblies [8]. Further key specifications of a photonic oscillator, namely the frequency and power level of the generated signal as well as the possible tuning range, depend strongly on the performance of the employed high-frequency photodetector. From Equation (4.8) we note that the output power of the generated high-frequency oscillator signal is linearly dependent on the detector’s responsivity at that frequency and the optical input power injected into the detector. Thus, for generating high-power oscillator signals in the THz frequency range, the photodetector is required to exhibit a reasonably high responsivity at THz frequencies and, secondly, it should allow for a high optical input power. In other words, the detector should exhibit a large saturation photocurrent. In the next section we will compare the various types of photodetectors in terms of their highfrequency and high-saturation photocurrent performances. This general comparison will be followed by a more detailed discussion on the high-frequency performance of so-called travelling-wave photodetectors (TWPDs). It will be shown that TWPDs offer great potential for high-power THz generation, that is they can be designed to exhibit a high responsivity at high frequencies and a high-saturation photocurrent.

92


4.4 Travelling-wave Photodetectors The high-frequency photodetector is a key component for any photonic oscillator. The most important requirement for this kind of application is a high responsivity at THz frequencies – not necessarily a large 3 dB bandwidth. In the following subsection we will review recent achievements in high-frequency photodetectors and we will look at the physical effects limiting the detector’s quantum efficiency, especially at THz frequencies. For a comprehensive review on the bandwidth–efficiency product of photodetectors the interested reader is referred to Kato [9]. The physical effects determining the detector’s high-frequency performances are usually represented by time constants describing the dynamics of the photogenerated carriers. Most important are the transit time and the carrier lifetime. Generally speaking, these two time constants represent the average time it takes a carrier to travel between the electrodes and the average time a free carrier exists before it finally recombines. Further, conventional lumped photodetectors are limited by some internal and external RC time constants. At very high frequencies ( > 100 GHz) electrical wave propagation effects must also be considered since the electrical wavelength is getting close to the device dimensions and further on microwave propagation losses become more significant. Looking at the various types of photodetectors, the conventional vertically illuminated photodetectors such as the p–n or the p–i–n photodetector introduce a trade-off between quantum efficiency or responsivity and high-frequency or bandwidth. In conventional photodetectors, light is coupled in through the upper layers of the device and is absorbed as it travels through the structure. This fundamental absorption process generates electron–hole pairs travelling under the influence of the applied electric field to the device contacts thus producing a photocurrent. The frequency response of such conventional vertical photodetectors depends on the transit time taken for the photo-induced carriers to reach the contacts. For short transit times the absorbing layer of a conventional pn-PD or pin-PD needs to be thin; this, on the other hand, results in a low efficiency and a large capacitance and thus the RC time constant is extremely large preventing the conventional vertical PD from being used at very high frequencies. An approach to reduce the RC time constant of the conventional PDs is to utilize very narrow and closely spaced contact fingers which is usually done in metal–semiconductor–metal (MSM) PDs. Obviously, due to the closely spaced contact fingers, the transit time is short and also the device capacitance is small due to the small surface area. The short transit time and the small capacitance together allow wide-bandwidth operation but the quantum efficiency of a vertically illuminated MSM-PD is comparably small for reasonable applications. A promising approach for achieving a high-efficiency is to utilize the uni-travelling carrier (UTC) concept. In the UTC-PD the absorbing layer is p-doped and therefore only electrons travel across the depletion layer, with holes disappearing quickly since they are majority charge carriers. Due to the much higher drift velocity of electrons and due to the fact that electrons can travel at overshoot velocity, the space charge effect is significantly reduced. This principle allows high-saturation currents or higher optical input power. The bandwidth of a UTC-PD is restricted by transit time effects mainly determined by the diffusion time of electrons travelling in the p-doped absorbing layer and of course it is also limited by the RC time constant. Recently, high-bandwidth UTC-PDs have been demonstrated and in terms of the bandwidth–efficiency product, UTC-PDs exhibit much better performances than conventional pin-diodes [9].


93

To circumventthetransittime limitation onecanalso employ a material with avery shortcarrier lifetime. Besides the RC time constant the transit time determines the detector’s frequency response provided that the carrier lifetime is much shorter than the transit time. For several years, research has been carried out to grow GaAs layers at low temperatures. Due to the low temperature the grown GaAs layers contain numerous impurities which capture the free carriers and thus reduce the carrier lifetime. Recently, low-temperature grown GaAs operating at around 850 nm wavelength have been utilized for high-frequency signal generation in the THz range [10]. Edge-coupled or waveguide photodetectors can overcome some of the limitations discussed above by allowing the optical signal to enter through the edge of the device. Thus the electrical carrier transport is perpendicular to the propagation of light. In principle, this approach allows for a long but narrow absorption layer having both a low transit time and a high efficiency. On the other hand, the detector’s RC time constant becomes significantly large due to the long absorbing layer, leading to the well-known lumped element RC time limitation. All approaches discussed above lead to lumped elements since the detector’s responsivities are determined by the total dimensions of the devices. These lumped element photodetectors, however, can no longer cope with the requirements as the frequencies extend into the THz regime. To overcome the RC time limitation so-called distributed or travelling-wave photodetectors (TWPDs) have been investigated since the early 1990s. In a TWPD the photoabsorption process occurs in a distributed manner along the length of the device such that it contributes to the overall electrical signal in the contact transmission line. Thus, travellingwave pin–PD (TWPDs), being two-port devices, are not limited by the RC time constant since electrically the devices are not lumped elements with a concentrated capacitance but an electrical waveguide (typically microstrip or coplanar) with a given characteristic impedance. The bandwidth of a TWPD is therefore mainly determined by its transit time. Since it is not RC time limited the travelling-wave concept can accomplish quite thin absorbing layers leading to short transit times and high bandwidths. A major drawback is that the electrical characteristic impedance of a TWPD needs to be matched to the external circuitry and, secondly, the optical group velocity needs to match with the electrical phase velocity for achieving the highest efficiencies. Although TWPDs exhibit a couple of challenges that need to be solved, they do offer a great advantage for high-power THz signal generation, namely the prospect of independently optimizing its quantum efficiency and saturation photocurrent. For this reason various TWPD structures have been investigated by different research groups in the past. These include p–i–n [11, 12], MSM [13], Schottky [14] and photo-transistor configurations [15], all showing excellent performance at high frequencies. In the following subsection we will discuss the various physical effects determining the high-frequency performance of a p–i–n TWPD in more detail using a theoretical model that describes the vertical and longitudinal transport of the photogenerated electrical carriers in a TWPD.

4.4.1 Drift-diffusion Model for p–i–n Photodetectors A sketch of a high-speed travelling-wave photodetector (TWPD) employing a pin waveguide structure is shown in Figure 4.6. The detector consists of an optical waveguide and an electrical transmission line. The optical heterodyne signal launched into the optical strip loaded waveguide is gradually absorbed resulting in a distributed current generation along the detector’s length which contributes to the overall current propagating along the electrical transmission line of the TWPD.

94


Figure 4.6 The left-hand figure schematically shows a waveguide photodetector with a coplanar metallization. On the right, a typical cross section of a detector’s layer structure is shown. It consists of an intrinsic core region with an absorbing (Wg < hf ) and two adjacent non-absorbing (Wg > hf ) waveguiding layers

As can be seen from Figure 4.6, the p–i–n waveguide structure of the detector consists of an intrinsic region sandwiched between p- and n-doped semiconductor layers. In order to enable optical waveguiding, the intrinsic core region needs to have a larger refractive index, that is a smaller bandgap energy, compared with the p- and n-doped cladding layers. Further on, the intrinsic region often consists of multiple layers instead of a single absorption layer. This is mainly to reduce the modal absorption per unit length in order to allow for a long absorption length. In our model we thus assume a waveguide core consisting of an intrinsic photon absorbing layer with a thickness d0, and two adjacent nonabsorbing layers with thicknesses dip and din as illustrated in Figure 4.6. In general, the photogenerated carrier transport in the p–i–n waveguide structure can be described by the continuity equation. By neglecting the transversal carrier transport and assuming harmonic time dependence, the one-dimensional (1D) complex continuity equations for the electron and hole densities n(x) and p(x) are given by jv nðxÞ ¼ Dn

d2 d nðxÞ ½nðxÞ vn ðxÞ Rc þ Gc ; 2 dx dx

ð4:10Þ

jv pðxÞ ¼ Dp

d2 d pðxÞ vp ðxÞ Rc þ Gc : pðxÞ 2 dx dx

ð4:11Þ

The first term in the continuity equations describes the carrier diffusion with the electron and hole diffusion constants represented by Dn and Dp. These diffusion constants are functions of carrier mobility and electric field and it has been shown in [10] that the carrier diffusion constants become very small in value for high electric fields in excess of 20 kV/cm. Assuming

95


that the intrinsic layer(s) thickness of a high-frequency p–i–n detector is well below 500 nm and also that a reverse voltage of a few volts is applied, high electric fields well above 20 kV/cm occur. Thus, we can neglect carrier diffusion in the intrinsic region of the reverse biased photodetector. The carrier recombination rate represented by Rc can also be neglected for our purposes, since the carrier lifetime is in the order of a few nanoseconds [11] which is about three orders of magnitude larger than the average transit time of the investigated structure. Thus the continuity equations (4.10) and (4.11) can be simplified to jv nðxÞ ¼

1 d ðJn Þ þ Gn ; q dx

jv pðxÞ ¼

1 d ðJp Þ þ Gp : q dx

ð4:12Þ ð4:13Þ

The first term in Equations (4.12) and (4.13) describes the carrier drift in the presence of an electric field with vn(x) and vp(x) representing the electron and hole velocity, respectively. The carrier generation rate is a function of the optical intensity at any point along the detector. We can therefore infer that the generation rates of holes and electrons are equal and can be expressed as G ¼ Gn ¼ Gp ¼ G0 expð g opt zÞ

ð4:14Þ

with G0 ¼

hl aopt Iopt : hc

ð4:15Þ

Here h denotes the external quantum efficiency, g opt is the complex propagation constant of the optical heterodyne input signal and Iopt represents the optical intensity. It should be noted that the carrier generation rate is a function of the longitudinal coordinate z due to the optical wave propagation determined by the complex heterodyne optical propagation constant g opt. Since diffusion can be neglected as discussed above, the electron and hole current densities in the absorbing layer are given by Jn ðxÞ ¼ q vn ðxÞ nðxÞ;

ð4:16Þ

Jp ðxÞ ¼ q vp ðxÞ pðxÞ:

ð4:17Þ

Here we assume that electrons and holes in the intrinsic region travel at constant saturation velocities vn and vp, an assumption which is appropriate for reverse biased photodetectors with strong internal electric fields. Introducing Equations (4.14) – (4.17) into Equations (4.12) and (4.13) we derive two first-order differential equations with constant coefficients describing the carrier densities in the absorbing layer: dJn jv ¼ Jn q G; vn dx

ð4:18Þ

96


dJp jv ¼ þ Jp þ q Gp : vp dx

ð4:19Þ

To solve the above differential equations we make use of the fact that electrons only travel in the positive x-direction and thus the electron carrier density at x ¼ 0 needs to be equal to zero. Similarly, we can state that the hole current density is equal to zero at x ¼ d0: Jn ðx ¼ 0Þ ¼ 0:

ð4:20Þ

Jp ðx ¼ d0 Þ ¼ 0

ð4:21Þ

By using the two boundary values in Equations (4.20) and (4.21) we can solve the differential Equations (4.18) and (4.19) and derive the electron and hole current densities in the absorbing layer Jn ¼

q G vn jv vx n 1 e jv

q G vp jv d0vp x e 1 Jp ¼ jv

ð4:22Þ

ð4:23Þ

In a similar way, we can now proceed to find the current densities in the adjacent nonabsorbing intrinsic layers. For simplicity, we only consider the hole current density in the following derivation; the procedure for deriving the electron current density is similar. Due to the fact that there is no photon absorption in these two layers the continuity equation for holes – Equation (4.11) – becomes quite simple. jv p ¼

1 d ðJp Þ: q dx

ð4:24Þ

This leads to the following simple differential equation for the carrier density d jv ðJp Þ ¼ Jp : dx vp

ð4:25Þ

The required boundary values to solve Equation (4.25) are given by the consistency of the current density at the boundary. From Equation (4.23) it follows that d q G vp jv vp0 e 1 Jp ðx ¼ 0Þ ¼ jv

ð4:26Þ

and by using Equation (4.26) we derive the hole current density in the nonabsorbing intrinsic layer Jp ¼

i xd q G vn h jv dv0 jv vn 0 n 1 e e : jv

ð4:27Þ

97


i0 ðzÞ ¼ 2

q G0 expð g opt zÞ w din þ dip þ d0 jv

vn vn d0 6 vn jv d0 jv exp jv v n 6 6 6 vp vp d0 6 6 þ vp d0 exp jv 6 jv jv vp 6 6 6 6 þ v exp jv d0 1 vn vn exp jv n 6 vn jv jv 6 6 6 4 vp vp d0 þ vp exp jv exp jv 1 vp jv jv

3 7 7 7 7 7 7 7 7 7 7 din 7 7 vn 7 7 7 5 dip vp

ð4:28Þ

The total current density is given by superimposing the electron and hole current densities in the absorbing region (Equations (4.22) and (4.23)) and the electron and hole current densities of the nonabsorbing regions (see Equation (4.27)). If we further proceed by integrating the total current density along y, we gain the total photogenerated current per unit length generated at any point z along the detector. This equation not only comprises the carrier transport and generation within the intrinsic absorptive layer of the photodetector but also the carrier transport through the adjacent non-absorptive intrinsic regions of the waveguide core.

4.4.2 Transmission Line Model for Travelling-wave Photodetectors In this section we will develop a transmission line model describing the contribution of the distributed current source found above to the overall electrical wave propagating along the electrical transmission line of the travelling-wave photodetector. The type of transmission line formed in this TWPD is a slow-wave hybrid coplanar/microstrip waveguide [16]. Generally, such transmission lines require ‘full-wave’ analysis for rigorous modelling. However, for our purposes the quasi-TEM analysis using a quasistatic equivalent circuit model as shown in Figure 4.7 satisfactorily describes the high-frequency properties of the detector’s transmission line. Here, the photogenerated current per unit length is represented by the distributed current source i0 (z). R0 and L0 are the resistance and the inductance of the metal centre conductor per unit length, respectively. R0 S represents the semiconductor losses associated with transverse current flow in the doped cladding layers and C 0 i and G0 i are the capacitance and the conductance of the intrinsic core layer per unit length. For high frequencies in the THz regime we also need to consider the capacitance of the doped semiconductor layers C0 S and the outer air capacitance C0 0 . For further considerations employing a transmission line model, it is advantageous to separate the active current source from the passive impedances. This is achieved by transforming the distributed current source i0 (z) into a form which is in parallel to all other passive impedances of the equivalent circuit as shown in Figure 4.8. The former current source is transferred to a distributed current source i0 0 which is in parallel with a completely passive electrical transmission line of unit length represented by its characteristic impedance Z0 and

98

Microwave Photonics: Devices and Applications ZS l Rl ZH

Ll R Sl

C Sl

G il

C il

C 0l

l

i l (z )

YV l

Z il

Figure 4.7 Equivalent circuit representing a unit-section of a travelling-wave photodetector

propagation constant g el. For the transformed distributed current source i0 0 ðzÞ we obtain i0 0 ðzÞ ¼ i0 ðzÞ

Z 0 i ðvÞ : Z 0 i ðvÞ þ Z 0 S ðvÞ

ð4:29Þ

The impedances shown in Figure 4.8 are not affected by this transformation and thus remain unchanged. Therefore we can state that the characteristic impedance and the electrical wave propagation constant are given by rffiffiffiffiffiffiffi Z0H Z0 ¼ ; ð4:30Þ Y 0V g el ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z0H Y 0V :

ð4:31Þ

Now, we can proceed and define a transmission line model for the travelling-wave photodetector which is shown in Figure 4.9. Here Ze represents the electrical impedance at the input port of the detector’s transmission line and Za is the load impedance at the output port. In order to calculate the total power delivered by the TWPD to the load impedance Za, we use a superposition approach. First, we determine the photocurrent delivered by each current source independently (the other sources are considered as open) and then we calculate the total

Z0,γel

i´0(z)

dz Figure 4.8 Equivalent circuit representing a unit section of a TWPD with a transformed current source in parallel with a passive transmission line

99


Z0, γ

..

Z0, γ

Z0, γ

Z0, γ

..

IZ a

i´0(0)

Ze

i´0(Z)

.. dz Figure 4.9

i´0(L)

Za

.. dz

dz

dz

Transmission line model for a TWPD with input impedance Ze and load impedance Za

photocurrent by integrating the contributions of all current sources. The photocurrent, delivered to the load impedance Za by the current source i0 0 ðzÞ located at z ¼ zs, can be calculated using the equivalent circuit shown in Figure 4.10 where all other current sources are considered as open. The electrical input reflection coefficient re and the output reflection coefficient ra are respectively: re ¼

ZE Z0 ; ZE þ Z0

ð4:32Þ

ra ¼

Za Z0 : Za þ Z0

ð4:33Þ

Using these two reflection coefficients, we can further simplify the equivalent circuit as shown in Figure 4.11, by transforming the input and the output impedances to the location of the photocurrent source at z ¼ zs. The resulting transformed impedances are then given by ZeT ¼ Z0

1 þ re e 2g zS ; 1 re e 2g zS

ð4:34Þ

Figure 4.10 Equivalent circuit for the TWPD considering only the current source per unit length at the position z ¼ zs

100


i´h(zs)

i´

0(zs)

Ze

T

ZaT

Figure 4.11 Equivalent circuit for the TWPD considering only the current source per unit length at the position z ¼ zs. Both the input and output impedances are transformed along the detector’s transmission line to the location of the current source

ZaT ¼ Z0

1 þ ra e 2g ðL-zS Þ ; 1 ra e 2g ðL-zS Þ

ð4:35Þ

and by using these equations, we can determine the forward propagating photocurrent generated by the current source at z ¼ zs at the position of the load impedance ZS. This photocurrent contribution is called i0 ha and is given by i0 ha ðzS Þ ¼

i0 0 ðzS Þ ð1 þ re e 2g zS Þ ð1 ra e 2g ðL zS Þ Þ e g ðL zS Þ : ð1 þ re e 2g zS Þ ð1 ra e 2g ðL zS Þ Þ þ ð1 re e 2g zS Þ ð1 þ ra e 2g ðL zS Þ Þ ð4:36Þ

Now, we can determine the total photocurrent travelling to the load impedance by integrating all contributions along the detector’s length ðL iha ðz ¼ LÞ ¼

i0 ha ðzS Þ dzS ;

ð4:37Þ

z¼0

and by considering the output reflection coefficient at the end of the detector’s transmission line we can finally determine the total photocurrent at the load impedance and thus the total electrical power delivered to the load impedance. In order to numerically calculate the generated power the circuit parameters of the TWPD equivalent circuit must be determined first. Generally, these parameters are frequency dependent but for frequencies in excess of 20 GHz the parameters L0 , R0 S , C0 i and G0 i are considered to be constant. Only R0 increases with the square root of frequency due to the skin effect. As a good approximation C 0 i can be determined by C 0 i ¼ «0«rw/di. The constant conductor resistance per unit length at frequencies below 10 GHz is given by R0 ¼ rAu/(wdmet). For frequencies in excess of 10 GHz R0 is considered to increase with the square root of the frequency. The series resistance of the doped semiconductor layers for a 6 mm wide rib waveguide with 15 mm separation between the centre and the ground electrode is typically of the order of R0 S 0.25 W mm. The parallel conductance G0 i and the transversal inductance L0 can be determined from experimental S-parameter measurements. With all the equivalent circuit parameters known, the complex characteristic impedance Z0 and the complex electrical propagation constant g el of the TWPD transmission line can be calculated.


101

Figure 4.12 Simulated frequency response of a 50 mm long and 6 mm wide TWPD. Dots indicate measured output power levels of the same device up to 110 GHz

Of course, in the above models we assumed some boundary conditions simplifying the real physical effects inside the detector, leaving enough space for future optimizations or extensions of the presented approach. Nevertheless, by using the frequency domain model developed here we can study the most relevant intrinsic effects such as transit time limitations as well as propagation effects such as microwave losses and the mismatch between the optical group velocity and the electrical phase velocity. Furthermore, external effects such as the influence of an impedance mismatch between the detector’s transmission line and the load impedance can be investigated in detail and the contribution of the different effects on the total roll-off at high frequencies can be identified. Therefore, although some simplifications were made, the model yields a very good simulation as can be seen from Figure 4.12. There is good agreement between measured and simulated data with a maximum variation of about a few dB. This proves the accuracy and reliability of the analytical model. The total rolloff of 50 dB for the full frequency span from DC to 1 THz is due to the transit time effects and intrinsic effects arising from carrier transport in the doped sections of the TWPD. In addition, propagation effects such as microwave losses and velocity mismatch contribute to the total rolloff. At frequencies in excess of 0.1 THz we found that the delivered power decreases with frequency by about f-3 for the investigated devices.

4.5 Terahertz Photonic Oscillators The first promising photonic oscillators for continuous-wave THz generation were demonstrated in the mid-1990s, using LT-GaAs photodetectors [17]. State-of-the-art LT-GaAs photodetectors utilize a vertically illuminated MSM-PD on LT-GaAs either coupled to a log-spiral antenna for wideband or coupled to a resonant dipole antenna for narrowband operation. Even LT-GaAs based MSM-TWPDs have been developed and successfully employed for quasi continuous-wave narrowband THz generation [18]. A major disadvantage associated with LT-GaAs is the thermal failure due to the high thermal resistance of the LT-GaAs which limits the maximum current density. Furthermore, the optimum optical wavelength for LT-GaAs

102


photodetetors is around 800 nm and thus advanced lasers and amplifiers developed for the communication industry operating in the optical C-band cannot be employed. The employment of photonic oscillators for continuous-wave THz signal generation using 1.55 mm lasers is a relatively new approach and there have only been a few experimental results. In the following, we will summarize the achieved results and we will explicitly describe the constitution of compact photonic THz oscillators employing 1.55 mm photodetectors. The presented photonic oscillators either yield free-space coupling by using resonant slot-antenna structures for narrowband or bow-tie antenna for wideband operation. Guided wave coupling of the generated oscillator signal using WR10 and smaller rectangular waveguides has also been achieved. In the photonic oscillators presented in the following paragraphs, a dual-mode optical heterodyne input signal was used that was generated by two free-running and tuneable 1.55 mm DFB lasers. A subsequent erbium-doped amplifier (EDFA) was used for boosting the optical power level. This concept allows one to easily sweep the frequency of the generated signal from DC to THz frequencies, which is especially important for investigating wideband performances of the POs. For detecting the generated high-frequency oscillator signals in the millimetre-wave region up to 220 GHz, external single-diode harmonic mixers have been used. At higher frequencies in the THz regime a number of detectors exist, including liquid helium cooled bolometers with a typical noise equivalent power (NEP) of about 2 pW/Hz1/2 or Golay cells with a typical NEP of 100–200 pW/Hz1/2. Although the Golay cell does not provide such a good NEP it does not require any expenditure for liquid helium cooling since it operates at room temperature. Therefore it is well suited for the experimental characterization of high-power POs. A typical experimental set-up consisting of the photonic THz oscillator and a Golay cell as THz detector is shown schematically in Figure 4.13.

4.5.1 Wideband Photonic Oscillators Employing Waveguide coupled THz Transmitter For specific applications, guided transmission in a rectangular waveguide is more desirable than free-space radiation of the generated THz signals and, consequently, efficient optical heterodyne generation of guided THz waves has already been studied and demonstrated in [19–22], [25] and [27] up to about 600 GHz using WR10 waveguide integrated high-speed photodetectors. Polarization control tuneable LD λ0+ ∆λ EDFA DFB-LD 1560 nm λ0

Golay cell

Photonic transmitter fRF

c0 ∆λ λ 20

Figure 4.13 Photonic THz oscillator consisting of two tuneable 1.55 mm DFB lasers, an EDFA and a photonic transmitter employing a TWPD. The generated THz oscillator signal is detected using a Golay cell

103


Generated (sub)mm-wave power (dBm)

0

TW-PD/WR10 -10 -20 di=100nm -30 -40

di=350nm

~f -4

-50 -60 -70 10

100 Frequency (GHz)

1000

Figure 4.14 Ultra-wideband power generation employing rectangular-waveguide (WR10) coupled TWPDs with different intrinsic region thicknesses of 100 and 350 nm

The following experiment, performed at the Universit€at Duisburg-Essen, Germany, demonstrates ultra-wideband guided transmission up to 1 THz employing a high-speed 1.55 mm TWPD coupled to different rectangular waveguides (WR10, WR8 and WR5) [23]. For experimental characterization the fabricated TWPDs have been connected using commercial coplanar to waveguide transitions. The power levels of the generated oscillator signals have been measured using a Golay cell as described in Figure 4.13 by quasi-optical coupling the THz power from the waveguide into the Golay cell. The measured THz power level is shown in Figure 4.14 for an ultra-wide frequency range up to about 1 THz. It should be pointed out that the lower cut-off frequency at around 70 GHz is given by the lower cut-off frequency of the WR10 waveguide not by the TWPD employed in the PO which can operate even at DC. As can be seen in Figure 4.14, the maximum power level of about 100 mW is achieved at frequencies around 0.1 THz within the W-band. Here, the TWPD with an intrinsic region thickness of d0 ¼ 100 nm generates about 5 dB more power than the TWPD with the 350 nm thick intrinsic region which is due to the lower transit time penalty. It can further be observed, from Figure 4.14, that the power decreases with frequency to the power of four. Similar results were found by Huggard et al. in [20]. In their work, they fully-packaged a commercial waveguide PD chip into a compact transmitter module with a WR10 waveguide output (Figure 4.15). The measured frequency response as shown in Figure 4.16 reveals a similar frequency dependence of the generated power level as shown in Figure 4.13 with a lower cut-off at 70 GHz due to the WR10 waveguide. The maximum power level is about 100 mW. To investigate the power dependence on frequency further, the smaller waveguides (WR8 and WR5) were used since those waveguides exhibit significantly fewer modes that can propagate at frequencies above 100 GHz. Figure 4.17 shows the generated power level using the same TWPD coupled to a WR8 and a WR5 waveguide. In addition, the cut-off frequencies

104


Detected power (W)

Figure 4.15 Fully packaged transmitter module developed by P. Huggard et al. at the Rutherford Appleton Laboratory, UK, in cooperation with the University of Kent and NRAO, USA. Reproduced from [20] by permission of Peter Huggard ( 2002 IEEE)

10

-3

10

-4

30 mW Optical power estimate

10-5

10-6

10

-7

10 mW Optical power

10

-8

100

Frequency (GHz)

1000

Figure 4.16 Ultra-wideband power generation employing a WR10 coupled waveguide photodetector. The experiment has been carried out by P. Huggard at the Rutherford Appleton Laboratory, UK, in cooperation with the University of Kent and NRAO, USA. Reproduced from [20] by permission of Peter Huggard ( 2002 IEEE)


105

Figure 4.17 Ultra-wideband (sub)mm-wave power generation employing a WR8 and a WR5 rectangularwaveguide coupled TWPD

of the higher-order modes that can propagate in the two waveguides are indicated by arrows in Figure 4.17. A step-like response is observed with an almost flat response around the cut-off frequencies of the higher-order modes. At lower frequencies the TWPD generates higher power levels when coupled to a WR8 waveguide but at frequencies above 220 GHz the power level is about four times larger when the TWPD is coupled to a WR5 waveguide.

4.5.2 Wideband Photonic Oscillators Employing Broadband Antennacoupled THz Transmitter Although resonant type antennas exhibit a reasonably large bandwidth (e.g. to cover a single astronomical band [12] in the ALMA telescope) it is also of great interest to develop an ultrawideband photonic transmitter that could eventually be employed not just for a single band but for a number of astronomical bands or for spectroscopic THz imaging applications. For developing an ultra-wideband photonic oscillator the high-speed TWPD in the transmitter part of the PO needs to be integrated with a wideband antenna structure which exhibits a fairly constant impedance within a large frequency range that can be matched to the detector’s impedance. As an example, TWPDs have been integrated with bow-tie antenna structures as shown in Figure 4.18 [26]. The inset shows a photograph of a fabricated chip. The length and width of the TWPD and the opening angle of the bow-tie antenna are 116 mm, 3.2 mm and u ¼ 9.4 , respectively. The chip was also mounted on a hemispherical silica lens for improving free-space coupling efficiency and in order to focus the generated THz oscillator signal. The packaged modules were investigated using the experimental set-up shown in Figure 4.13. Here the generated power was quasi-optically radiated into the Golay cell without using any imaging optics. Figure 4.19 shows the measured THz power received by the Golay cell. Coupling losses associated with the quasi-optical radiation into the Golay cell have not been excluded from the measured results. As can be seen from Figure 4.19, the maximum power received by the Golay cell is about 0.5 mW for a photocurrent of about 6 mA. The generated power level is fairly flat within a frequency range from 20 GHz to 0.1 THz. Above 0.1 THz we observed that the power

106


Figure 4.18 Schematic of a TWPD monolithically integrated with a planar ultra-wideband bow-tie antenna. The inset shows an SEM picture of a fabricated transmitter chip

level approximately decreases with frequency to a power of three which is in accordance with the simulations. Similar frequency dependence of a wideband antenna integrated photodetector was also found in [24].

4.5.3 Narrowband Photonic Oscillators Employing a Slot Antenna Coupled THz Transmitter To investigate the performances of a narrowband photonic oscillator and to demonstrate their feasibility to pump the SIS junction of an astronomical receiver, a photonic 0.46 THz

Figure 4.19 TWPD

Ultra-wideband (sub)mm-wave power generation employing a bow-tie antenna integrated


107

transmitter has been fabricated. A sketch of the developed transmitter chip is shown in Figure 4.20(a). In the transmitter, the TWPD was monolithically integrated with a planar fullwave slot antenna resonant at 460 GHz. A passive bias-T was also integrated on-chip employing radial stubs as low-pass filters to allow for external DC-bias supply to the PD. The SEM pictures in Figure 4.20(b) and Figure 4.20(c) show a top view of a transmitter chip array and a single transmitter chip, respectively. The inset in Figure 4.20(c) shows an enlarged view of the waveguide PD (top) and the radial stub low-pass filter (bottom). The covered single slot antenna, which cannot be seen in Figure 4.20, is located at the intersection between the waveguide PD and the radial-stub filter and it is horizontally oriented to the optical waveguide of the PD. The overall dimensions of a single transmitter chip are about 2.3 1.7 mm, and about 300 transmitters have been fabricated from a single 2 inch InP substrate. The transmitter chip was further mounted on a hemispherical silica lens with a diameter of 10 mm as sketched in Figure 4.20(d). The silica lens couples the antenna to free space, producing a near Gaussian submm-wave beam, which can be re-imaged on any receiver optics (lens and horn). Finally, the lens with the transmitter chip was packaged as can be seen from Figures 4.20(e) and 4.20(f). To demonstrate the capabilities of the packaged THz transmitter module to pump an astronomical receiver with an SIS junction an experiment has been undertaken using the

Figure 4.20 (a) Schematic of a photonic emitter consisting of a slot antenna integrated TWPD; (b) photograph of a fabricated array of 0.46 THz transmitter; (c) SEM picture of a single emitter; (d) schematic of an emitter mounted in the centre of a silicon ball lens; (e) and (f) photographs of the fabricated modules

108


Figure 4.21 DC current–voltage curves derived from the SIS junction of a 460 GHz astronomical receiver (photo) which was either pumped by a Gunn oscillator (black line) or by using the developed photonic 0.46 THz oscillator at different photocurrent levels (grey curves)

astronomical receiver as a mixer for down-converting the 0.46 THz signal generated by the photonic oscillator. In the experiment, all receiver components are operated at liquid helium temperature. At first, a 460 GHz solid-state oscillator chain consisting of a Gunn oscillator with a subsequent tripler was used to pump the SIS junction of the receiver. The output power of the solid-state oscillator was adjusted for optimum sensitivity (i.e. lowest noise temperature) of the SIS junction and the corresponding DC bias curve of the SIS junction was recorded (dark line in Figure 4.21). Hereafter, the solid-state oscillator signal was replaced by the optically generated LO signal from the photonic oscillator module. Different DC bias curves of the SIS junction

Figure 4.22 THz power received by the SIS junction of a receiver with respect to the detector’s photocurrent

109


Generated mm-wave power (dB)

0

fc = 100GHz

-5

Uncooled Cooled T = -14°C

-10 -15 -20 -25 -30 -35 1

10

100

Photocurrent (mA)

Figure 4.23

Generated output power as a function of DC-photocurrent

were recorded as a function of laser input power level, that is as a function of the detector’s photocurrent (grey lines in Figure 4.21). The inset in Figure 4.21 shows a photo of the employed liquid helium cooled receiver which was used. As can be seen from Figure 4.21, at a photocurrent of about 20 mA the power generated by the PO is equivalent to the power generated by the solid-state LO. Thus, the developed photonic transmitter is capable of pumping the SIS junction of the receiver under optimum conditions. The total THz power generated by the photonic oscillator module is shown in Figure 4.22 as a function of the photocurrent in the TWPD. The total power generated by the TWPD follows the square-law principle, as can be seen from Figure 4.23. No saturation effects are observed for photocurrents up to 20 mA.

References [1] B. Leone et al., “Optical Far-IR wave Generation - An ESA review study”, Proceedings of the 14th International Symposium on Space Terahertz Technology, Tucson, USA, April 2003. [2] See for example “The Atacama Large Millimeter Array”, The ESO Messenger, no. 107, March 2002. [3] P.H. Siegel, “Terahertz Technolgy”, IEEE Trans. On Microwave Theory and Techn., vol. 50, no. 3, March 2002. [4] A. Hirata, M. Harada and T. Nagatsuma, “120-GHz Wireless Link Using Photonic Techniques for Generation, Modulation, and Emission of Millimeter-Wave Signals”, IEEE J. of Lightwave Technol., vol. 21, no. 10, October 2002. [5] T. Yamamoto, H. Takara and S. Kawanishi, “Generation and Transmission of Tuneable Terahertz Optical Clock”, International Topical Meeting on Microwave Photonics, Awaji Island, Japan, T2-2, pp. 97–100, Nov. 2002. [6] P. Shen and P.A. Davies, “Millimetre Wave Generation Using an Optical Comb Generator with Optical PaseLocked Loops”, International Topical Meeting on Microwave Photonics, Awaji Island, Japan, T2-3, Nov. 2002. [7] See for example L.A. Johansson and A.J. Seeds, “Millimeter-Wave Modulated Optical Signal Generation with High Spectral Purity and Wide-Locking Bandwidth Using a Fiber-Integrated Optical Injection Phase-Lock Loop”, IEEE Photon. Technol. Lett., vol. 12, no. 6, June 2000. [8] M. Ishiguro et al., “A hybrid Option for the First LOs using Direct Photonic LO Driver”, ALMA memo 435, September 2002. [9] K. Kato, “Ultrawide-Band/High-Frequency Photodetectors”, IEEE Trans. On Microwave Theory and Techniques, vol. 47, no. 7, July 1999.

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[10] See for example E.R. Brown, “THz Generation by Photomixing in Ultrafast Photoconductors”, Int. J. of High Speed Electronics and Systems, vol. 13, no. 2, 2003. [11] A. St€ ohr, R. Heinzelmann, A. Malcoci and D. J€ager, “Optical Heterodyne Millimeter.Wave Generation Using 1.55 mm Travelling-Wave Photodetectors“, IEEE Trans. on Microwave Theory and Techn., vol. 49, no. 10, October 2001. [12] V. Hietala, G.A. Vawter, T.M. Brennan and B.E. Hammons, “Traveling-Wave Photodetectors for High-Power, Large-Bandwidth Applications”, IEEE Trans. on Microwave Theory and Techn., vol. 43, no. 9, September 1995. [13] J.-W. Shi, Y.-H. Chen, K.-G. Gan, Y.-J. Chiu, C.-K. Sun and J.E. Bowers, “High-Speed and High-Power Performances of LT-GaAs Based Metal-Semiconductor-Metal Traveling-Wave Photodetectors in 1.3-mm Wavelength Regime”, IEEE Photon. Technol. Lett., vol. 14, no. 3, March 2002. [14] M. Alles, U. Auer, F.-J. Teude and D. J€ager, “Distributed velocity matched 1.55 mm InP traveling-wave photodetector for generation of high millimeterwave signal power,” IEEE Int. Microwave Symposium, MTT-S Digest, Baltimore, USA, pp. 1233–1236, 1998. [15] D.C. Scott, D.P. Prakash, H. Erlig, M.A. Bhattacharya and H.R. Fetterman, “High Power, High Frequency Traveling Wave Heterojunction Phototransistors with Integrtaed Polyimide Waveguide”, IEEE Int. Microwave Symposium, MTT-S Digest, Baltimore, USA, pp. 1237–1240, 1998. [16] D. J€ager, “Slow-Wave Propagation Along Variable Schottky-Contact Microstrip Line,” IEEE Trans. on Microwave Theory and Techn., vol. 24, no. 9, September 1976. [17] E.R. Brown, K.A. McIntosh, K.B. Nichols and C.L. Dennis, “Photomixing up to 3.8THz in Low-Temperature Grown GaAs”, Appl. Phys. Lett., vol. 66 (3), pp. 285–287, 1995. [18] S. Matsuura and G.A. Blake, “A travelling-wave THz Photomixer based on Angle-Tuned Phase Matching”, J. Appl. Phys. Lett., vol. 74, no. 19, pp. 2872–2874, May 1999. [19] A. St€ ohr, R. Heinzelmann, C. Kaczmarek and D. J€ager, “Ultra-Broadband Ka to W-band 1.55 mm TravellingWave Photomixer,” Electron. Lett., vol. 36, no. 11, 970–972, May 2000. [20] P.G. Huggard, B.N. Ellision, P. Shen, N.J. Gomes, P.A. Davies, W.P. Shillue, A. Vaccari and J.M. Payne, “Efficient Generation of Guided Millimeter-Wave Power by Photomixing,” IEEE Photon. Technol. Lett., vol. 14, no. 2, 197–199, February 2002. [21] P.G. Huggard, B.N. Ellision, P. Shen, N.J. Gomes, P.A. Davies, W.P. Shillue, A. Vaccari and J.M. Payne, “Generation of Millimetre and Sub-millimetre Waves by Photomixing in a 1.55 mm Wavelength Photodiode”, Electon. Lett., vol. 38, no. 7, 327–328, 2002. [22] T. Noguchi, A. Ueda, H. Iwashita, S. Takano, Y. Sekimoto, M. Ishiguro, T. Ishibashi, H. Ito and T. Nagatsuma, “Millimeter-Wave Generation using a Uni-traveling-carrier Photodiode”, Proceedings of the 12th International Symposium on Space Terahertz Technology, San Diego, CA, USA, 2001. [23] A. St€ ohr, A. Malcoci, A. Sauerwald, I.C. Mayorga, R. G€usten and D. J€ager, “Ultra-Wide Band Traveling-Wave Photodetectors for Photonic Local Oscillators”, IEEE J. Lightwave Technol., vol. 21, no. 12, December 2003. [24] A. Hirata, T. Nagatsuma, R. Yano, H. Ito, T. Furuta, Y. Hirota, T. Ishibashi, H. Matsuo, A. Ueda, T. Noguchi, Y. Sekimoto, M. Ishiguro and S. Matsuura, “Output Power Measurement of Photonic Millimetre-wave and Submillimetre-wave Emitter at 100–800GHz”, Electron. Lett., vol. 38, no. 15, 798–799, July 2002. [25] A. St€ ohr and D. J€ager, “Ultra-Wideband Travelling-Wave Photodetectors for THz Signal Generation”, IEEE LEOS Annual Meeting, Puerto Rico, Nov. 2004. [26] A. Malcoci, A. St€ ohr, A. Sauerwald, S. Schulz and D. J€ager, “Waveguide and Antenna Coupled Travelling-Wave 1.55 mm Photodetectors for Optical (Sub)Millimeter-Wave Generation”, in Microwave and Terahertz Photonics, Proceedings of the SPIE, vol. 5466, ISBN 0-8194-5389-7, pp. 202–209, 2004. [27] A. St€ ohr and D. J€ager, “THz-Photomixers: An Overview”, in Millimeter-wave and Terahertz Photonics, Proceedings of the SPIE, vol. 6194, ISBN 0-8194-6250-0, April 2006.

5 Terahertz Sources R. E. Miles and M. Naftaly

5.1 Introduction The terahertz (THz) region of the electromagnetic spectrum is commonly defined as that lying at frequencies between 0.1 and10 THz. The frequently-heard expression ‘the THz gap’ refers to the fact that at these frequencies generation and detection of radiation becomes very difficult using either electronic or optical means. Nevertheless, with the growth of interest in THz research and applications and a great expansion of activities in this area, a large number and variety of sources have been developed and have become widely available. These include THz lasers, laser-activated emitters and electronic devices. Broadly speaking, in applications requiring a continuous-wave narrow-line signal at frequencies below 1 THz, electronic sources predominate. Examples include local oscillators for astronomical instruments and security scanners. On the other hand, lasers and laser-activated emitters are mainly used for broadband THz spectroscopy covering a bandwidth of several THz. This division of functions is likely to persist since electronic THz sources are, by their nature, singlefrequency devices, whereas laser-based sources are either inherently broadband or widely tuneable. Nevertheless, both types of THz emitting devices have found numerous applications, and will be described here.

5.2 Terahertz Generation from Laser Sources The recent rapid expansion of the field of terahertz research and applications owes much of its existence to the development of suitable laser sources and methods of THz generation. These developments fall into two categories: direct emission from far-infrared lasers and optical down-conversion of near-infrared lasers. Owing to the flexibility of the systems and the broad tuning range, down-conversion greatly predominates as the technique of choice, and accounts for the vast majority of work in the THz field.


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5.2.1 Far-Infrared Lasers These include molecular lasers, p-Ge lasers, and free-electron lasers (FELs). 5.2.1.1 Molecular Lasers Molecular lasers [1] use as their active media gases which have a permanent dipole moment. THz (far-infrared) emitting transitions take place between adjacent rotational levels of the same vibrational state. Excitation is via optical pumping, typically by a high-power (>10 W) CO2 laser. Depending on the gas used, several different lines can be generated, although the laser is not continuously tuneable. Narrow linewidths of a few GHz are obtainable because the gases are used at low pressures in order to reduce collisional relaxations. A variety of gases are used in molecular lasers, including CH4, CH3OH, CH3NH2 and C2H2F2, producing lines in the range of 40–1200 mm (7.5–0.25 THz). CW laser powers of the order of several mW are generated. The limitation of these sources is that they offer a discrete set of lines with no tuneability, and so are unsuitable for the majority of spectroscopic applications. 5.2.1.2 p-Ge Lasers A p-Ge laser consists of a p-doped Ge crystal cryogenically cooled to 4 K and mounted in a magnet [2]. Such lasers operate in pulsed mode, with a repetition rate of tens of Hz. The average THz power produced is 10–100 mW, with peak powers of several watts. The emission frequency can be tuned by varying the magnetic field: the typical range is 1.5–4.5 THz. The magnetic field required by the laser can be of several Tesla, and therefore necessitates a superconducting magnet. p-Ge lasers are useful for THz spectroscopy, especially where high incident THz power is required, but their applications are limited owing to the size and complexity of the auxiliary systems. 5.2.1.3 Free-electron Lasers Free-electron lasers (FELs) or synchrotron sources [3] are continuously tuneable over a range of tensofTHzandcanproduceseveralwattsofcontinuous-wavenarrow-bandradiation.Althoughan FEL is in many respects an ideal THz source, it is in fact a type of high-energy electron beam accelerator.Itisthereforealarge-scaleinstallation,whichseverelylimitsitspracticalapplicability.

5.2.2 Optical Down-Conversion THz generation by optical down-conversion falls into two types: broadband emission employing ultrafast lasers and single-frequency tuneable emission employing difference-frequencygeneration. Of these, broadband generation is by far the most widely used method, largely owing to the advantages of coherent detection available in a pump-probe configuration (these include high sensitivity and a large dynamic range). 5.2.2.1 Broadband THz By far the most widespread method of THz generation involves employing ultrafast lasers. These are mode-locked lasers whose pulse length is typically less than 200 fs, and more usually

113

Terahertz Sources

Laser intensity

(a)

Time THz amplitude

(b)

Time THz amplitude

(c)

Frequency

Figure 5.1

(a) Laser pulse, (b) THz pulse and (c) THz spectrum

well under 100 fs. The most commonly used are Ti–sapphire lasers which typically deliver pulse lengths of 50–100 fs, and can be as short as 10 fs. Ytterbium and erbium solid-state or fibre lasers have longer pulse lengths of 100–300 fs. The repetition rate of all such lasers is of the order of 50–100 MHz; the average power is typically in the range 0.2–2 W. Consequently, the peak optical pulse power is of the order of 108 W. There are two types of broadband THz emitter in common use: optical rectification by electro-optic crystals and biased photoconductive emitters (also known as Auston switches). Both of these produce a single-cycle THz pulse whose amplitude is proportional to the time derivative of the optical intensity of the laser pulse, as seen in Figure 5.1. It follows therefore that a shorter laser pulse will produce a correspondingly shorter THz pulse, with a consequent broader spectral content. 5.2.2.2 Optical Rectification Optical rectification in electro-optic (EO) crystals first emerged in the late 1980s as a means of producing broadband THz radiation from ultrafast laser sources. Typically, zinc-blende semiconductors such as ZnTe, GaP and GaSe, or organic crystals (e.g. 4-(4-Dimethylaminostyryl)1-methylpyridinium tosylate (DAST)) are used for this purpose, all having bandgaps in the 2–2.5 eV range. In order to avoid absorption of the incident radiation, the laser wavelength must be longer than the bandgap of the material, that is Ephoton ¼ hc/l < Eg, making 800 nm Ti-sapphire lasers suitable for this purpose [4]. Optical rectification arises as a result of the transient polarization which occurs when a short, high-intensity laser pulse interacts with the electro-optic medium. The THz power generated is proportional to the square of the optical power, is determined by the second-order optical nonlinear coefficient (x (2)), and varies with the relative orientation of the laser polarization and the crystallographic axes. An important issue is phase matching, which limits the interaction length in the crystal and restricts the usable crystal length. Optical rectification can be viewed as a mixing of different

114


spectral components of the laser pulse separated by the THz frequency: vopt and vopt þ vTHz. This also serves to explain why a shorter laser pulse containing a broader spectral bandwidth produces a broader THz spectrum (via Dn/Dt 1). The phase-matching condition for the wave vector k is then [5]: Dk ¼ kðvopt þ vTHz Þ kðvopt Þ kðvTHz Þ ¼ 0

ð5:1Þ

Neglecting optical dispersion, the coherence length lc for phase matching is given by: lc ¼ p=Dk ¼ pðvTHz jnopt nTHz jÞ

ð5:2Þ

where n is the refractive index. For bandwidths of up to 3 THz in commonly used EO crystals lc is of the order of 0.5 mm. However, owing to dispersion, it is reduced to < 50 mm when ultrabroadband generation ( > 3 THz) is required. Typical THz bandwidths obtained from optical rectification in EO crystals are 0.1–3 THz, with a total average THz power of a few mW. However, much broader THz emission has been achieved. In both ZnTe and GaSe bandwidths of up to 40 THz have been demonstrated, as seen in Figure 5.2 [6]. 5.2.2.3 Biased Photoconductive Emitters Broadband THz generation using biased photoconductive emitters activated by ultrafast lasers was first explored in the 1980s, and has since become the most commonly used method in both research and commercial THz systems. An emitter consists of a semiconductor wafer with bias electrodes deposited on its surface (Figure 5.3) [4]. In contrast to optical rectification, a photoconductive emitter must be excited by a laser wavelength that is shorter than the bandgap

Figure 5.2 Temporal waveform (upper figure) and spectrum (lower figure) of THz waves measured by the GaSe (solid line) crystal and the ZnTe (dotted line) crystal, respectively. Reprinted with permission from Kai Liu, Jingzhou Xu and X.-C. Zhang, Applied Physics Letters, 85, 863 (2004). 2004, American Institute of Physics

115

Terahertz Sources Small-gap emitter / antenna

Large-gap emitter

Gold electrodes Gold electrodes

GaAs substrate

GaAs substrate

Laser beam

Laser beam Stripline gap: 30-100 µm Line thickness: 10-50 µm Line length: 1-2 mm Electrode gap: 5-20 µm

Figure 5.3

Electrode length/width: 3-10 mm Electrode gap: 0.5-1 mm

Schematic drawings of typical biased photoconductive emitters

of the material, that is Ephoton ¼ hc/l > Eg. When a laser beam is incident on the semiconductor, the absorbed photons generate photocarriers, electrons in the conduction band and holes in the valence band. These are accelerated by the bias field, while simultaneously their density changes under the varying laser intensity. As a result, ultrashort high-peak currents are generated in the semiconductor, which radiate into free-space at THz frequencies. In order for the process to be efficient, the carrier lifetime of the semiconductor material must be short on the timescale of the laser pulse. Most THz emitters employ GaAs, either in its semiinsulating (SI) form or low-temperature grown (LT), owing to its short carrier lifetime and its bandgap of 1.42 eV allowing absorption of the 800 nm radiation from Ti-sapphire lasers. LTGaAs has a shorter photocarrier lifetime (< 0.5 ps) than SI-GaAs (100 ps), which improves its THz-emitting performance. The gap between the electrodes can vary from a few microns to several millimetres. In large-gap emitters ( > 0.1 mm) the shape of the electrodes has little effect on THz generation. However, in small-gap emitters the bias electrodes also act as a radiating antenna, and are designed accordingly. Owing to the additional energy supplied by the bias current, photoconductive emitters produce an average THz power of tens of mW, that is an order of magnitude higher than electrooptic crystals. It may be assumed, especially in the case of large-gap emitters, that the transient photocurrent J(t) is not affected by the electrodes, and is directly proportional to the induced conductivity s(t) and the applied bias field E [7]: JðtÞ sðtÞ E:

ð5:3Þ

This then leads to the conclusion that the average THz power Pave produced by the emitter scales with the square of the optical power Popt and the square of the applied voltage E: Pave P2opt E2 :

ð5:4Þ

116


THz amplitude (a.u.)

1

0.1

0.01

1E-3

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Frequency (THz)

Figure 5.4

A typical THz spectrum from a large-gap biased photoconductive emitter

The THz spectral content delivered by photoconductive emitters is significantly narrower than that obtainable from optical rectification. Figure 5.4 shows a typical THz spectrum generated by an emitter which was fabricated on SI-GaAs with an electrode spacing of 0.5 mm, biased at 200 V and excited by 0.8 W average power from a 60 fs Ti-sapphire laser. The usable THz spectrum extends to nearly 4 THz; however, the power decreases exponentially with frequency as explained in Figure 5.1 above. Small-gap LT-GaAs emitters employing short-pulse lasers of 10 fs are capable of generating much larger THz bandwidths, although at the cost of greatly reduced total power. A usable THz spectrum of up to 20 THz has been demonstrated as shown in Figure 5.5 [8]. Note, however, that the spectrum suffers from substrate absorption at 5.2 and 8.0 THz.

5.2.3 Difference Frequency Generation There are two types of THz source operating by difference frequency generation (DFG) and using near-infrared lasers. Both employ two laser beams which are detuned by the desired

Figure 5.5 The Fourier transform amplitude spectrum (upper trace, solid line) together with the spectrum measured in the presence of PTFE sample (lower trace, dotted line). Reprinted with permission from Y. C. Shen, P. C. Upadhya, E. H. Linfield, H. E. Beere and A. G. Davies, Applied Physics Letters, 83, 3117 (2003). 2003, American Institute of Physics

117

Terahertz Sources

THz frequency, and rely on frequency mixing to generate the desired radiation. In both cases the THz frequency can be tuned continuously by varying the wavelength of one of the lasers. The first type employs biased photoconductive emitters and the second electro-optic crystals. 5.2.3.1 CW THz DFG from Photoconductive Emitters The principle of operation is similar to that of broadband emission; however, in this case two CW lasers are used instead of a single pulsed source. THz frequencies are generated in the biased photoconductor due to the fluctuations in carrier density, which produces a signal via the heterodyne process [9]: ½E1 cosv1 t þ E2 cosv2 t2 ¼ const þ E1 E2 cosðv1 v2 Þt

ð5:5Þ

where E1 and E2 are the respective field amplitudes of the two sources, and v1 and v2 are their respective frequencies. As in the broadband case, the THz power produced scales with the square of the optical power and the applied voltage. However, it also depends crucially on the carrier lifetime of the material and on the efficiency of the antenna. A very short carrier lifetime (< 200 fs) is required for successful THz generation. The typical THz power generated is of the order of 1 mW [10] and the bandwidth is limited to approximately 1.5 THz. Owing to these limitations, such emitters have not found wide application. 5.2.3.2 Pulsed THz DFG from Electro-optic Crystals Recently there has been growing interest in difference-frequency THz generation using electro-optic crystals activated by pulsed lasers. A typical set-up employs a Q-switched Nd-YAG laser pumping an optical parametric oscillator (OPO), which together provide the two laser wavelengths detuned by the desired THz frequency. These are focused onto an EO crystal, where the THz difference frequency is generated via three-wave mixing. As with optical rectification, DFG is a parametric process which arises from transient polarization whose efficiency is dependent on the second-order optical nonlinear coefficient x(2). The emitted THz power at the frequency vTHz from a crystal of length L and using exciting beams of power P1 and P2 is [11]: PTHz v2THz ðcð2Þ Þ2 L2 P1 P2 :

ð5:6Þ

As a consequence of the dependence on vTHz, the efficiency of DFG and the obtained THz power tend to increase with THz frequency. This is the reverse of what happens in broadband generation, where THz power decreases with frequency (Figure 5.1). Since the THz power is proportional to the product of powers of the two mixing beams, pulsed lasers with high peak powers are necessary to activate the process. The laser wavelength must be well below the bandgap of the crystal, to avoid absorption. The phase matching condition for the wave vectors k is similar to that for optical rectification (Equation (5.1)): Dk ¼ kðvopt þ vTHz Þ kðvopt Þ kðvTHz Þ ¼ 0:

ð5:7Þ

118


Figure 5.6 THz output energy as a function of the THz frequency with 1 and 0.5mm thick DAST crystals: solid line, 1 mm DAST; broken line, 0.5 mm DAST. Reused with permission from T. Taniuchi, S. Okada and H. Nakanishi, Journal of Applied Physics, 95, 5984 (2004), 2004, American Institute of Physics

However, in this case noncollinear phase matching is possible, so that the vector form is retained. Owing to dispersion, the crystal must be rotated as the THz frequency is tuned, in order to preserve the relationship between the three wave vectors. This allows the phase matching condition to be maintained in crystals over a length of several millimetres, thus providing a longer interaction length and increasing the THz power produced. Using DFG, THz peak powers of the order of hundreds of milliwatts have been demonstrated. Other advantages of THz DFG include the availability of THz frequencies above 3 THz, the ability to produce a tuneable narrow-line single frequency (instead of having to generate and analyse a complete broad spectrum) and the simplicity and compactness of the systems. A number of THz DFG systems have been demonstrated. Tuning over 0.5–7 THz has been obtained in a GaP crystal, with peak THz powers of around 100 mW [12]. In an organic DAST crystal continuous tuning between 2 and20 THz has been achieved, with peak powers of > 10 W (Figure 5.6) [13].

5.3 Electronic Sources It is true to say that the progress that has occurred in terahertz technology over the last 15 years has mainly resulted from the development of the Auston switch [14] as discussed in Section 5.2. Previous to this, terahertz waves were generated electronically, but in devices based on vacuum-tube technology. Such devices as the backward wave oscillator (BWO) can deliver THz power in the tens of milliwatt range but they have a relatively short lifetime (in modern electronic terms) and are not always readily available. At the time of writing, modern semiconductor based electronic sources which can oscillate at frequencies in the range of 0.7 THz to 2 THz are still not available, but steady development, as will be discussed below, sees the maximum frequencies of operation moving slowly upward. THz power can be produced from below the THz gap by multiplication up from lower frequencies and such sources [15,16] have been used extensively in space science for remote sensing. On the other (higher frequency) side of the THz gap the frequencies delivered by

Terahertz Sources

119

quantum cascade lasers (QCLs) are slowly moving downward and have in fact reached the 1THz region, albeit with the added complexity of requiring an applied magnetic field. Although QCLs can deliver significant amounts of power (tens of mW) they do suffer from the disadvantage of having to operate at cryogenic temperatures and are not readily tuneable. Whilst it is clear that THz frequencies have significant uses, mainly in scientific areas such as spectroscopy where the cost and size of femtosecond systems are less of an issue, it can be argued that the technology will not become ubiquitous until inexpensive and robust electronic sources are available. The situation today can be compared with that of the semiconductor diode laser 50 years ago where, at that time, they could only operate at cryogenic temperatures. Who then would have predicted that every household would own a diode laser (in CD players), that we would be using them as pointers in the class room and buying them from DIY stores to replace the humble spirit level to produce horizontal lines on a wall to act as a tiling guide? Many uses for terahertz waves have been suggested, for example molecular recognition, flame tomography, gas sensing, damp detection, archaeology and various medical and security applications, but none of these has taken off because of the expense, large physical size and fragility of the femtosecond systems. Given an inexpensive electronic source, THz technology would be in a much better position to compete with existing techniques. The need is also becoming more urgent as processing speeds in integrated circuits move up into the THz region and greater bandwidths (and therefore higher frequencies) are required in communications. The section will discuss the state of the art in THz electronic sources.

5.3.1 Two-terminal Devices Gunn diodes (sometimes known as transferred electron devices), IMPATT (impact avalanche transit time) diodes and TUNNETT (tunnel injection transit time) diodes [17] are wellestablished sources at microwave and mm-wave frequencies. In each case, the device structures are designed to generate a negative slope in the current–voltage characteristic, giving rise to a region of negative differential resistance (NDR) as illustrated in Figure 5.7. When a DC voltage large enough to bias the device into the NDR is applied, it creates an inherently unstable state and the device goes into oscillation. Frequencies up into the mm-wave region can be generated but the specific mechanisms giving rise to the NDR impose an upper

Figure 5.7

Current–voltage curve showing the negative differential resistance region (shaded)

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limit to the oscillation frequency. As the name ‘transferred electron device’ suggests, the cause of the NDR in Gunn diodes is the transfer of electrons from the light to the heavy mass conduction bands. This process takes a finite time, which in turn limits the highest frequency available. Similarly, in the IMPATT diode a finite amount of time is needed to build up to the avalanche condition. If the negative resistance instability can be produced by another and faster mechanism then the way would be open for THz generation. Modern molecular beam epitaxy (MBE) growth techniques have resulted in TUNNETT diodes with very short transit time layers which are thus capable of oscillating at over 600 GHz [18], but with very low power levels. Two other types of device which can potentially exhibit NDR at high enough frequencies are possible candidates for THz generation. They are the resonant tunnelling diode (RTD) and the superlattice electron device (SLED). These devices are approaching the THz gap from the lower frequency side. The quantum cascade laser (QCL) which is approaching the 1 THz region from above is also a two-terminal device but relies on laser action rather than NDR. A common feature of all of these devices is that they take advantage of semiconductor bandgap engineering to produce the desired electrical characteristics. 5.3.1.1 Resonant Tunnelling Diodes Resonant tunnelling diodes have a double barrier structure as shown (under zero bias) in Figure 5.8(a). In the narrow space between the barriers the electron energies are quantized into discrete levels. At a particular DC bias (Figure 5.8(b)) the energy levels at the bottom of the conduction band on the left-hand side align with the lowest level in the well giving rise to a resonant condition whereby electrons can tunnel through the barriers. As the bias is increased further (Figure 5.8(c)), the resonant condition no longer holds and the current falls as the applied bias voltage increases. At even higher applied voltages the current once more increases under the combined action of electron excitation over, and tunnelling through, the barriers. This results in an I–V curve which has an NDR region and hence can lead to oscillations. Tunnelling times of about 1014 s are expected, holding out the prospect of operation into the THz region and beyond. In practice, the highest frequency demonstrated to date is 712 GHz, a result that dates back to 1991 [19]. The THz power generated was in the mW region – a level too low for most applications. The reason for this low power can be explained from the I-V curve as (c)

(b)

(a)

EF

EF

EF qV = 0

qV P

IP qV V

Figure 5.8 Double barrier resonant tunnelling diode (DBRTD) conduction band edge diagrams: (a) zero bias, (b) at resonance and (c) in the NDR region

121

Power ≈ ∆I∆V

∆I

Current (I )

Terahertz Sources

∆V

Voltage (V )

Figure 5.9 I–V characteristic of a resonant tunnelling diode showing the very steep negative differential resistance region

depicted in Figure 5.9 where it can be seen that the region of NDR is rather narrow along the voltage axis. The power generated is determined by the product DI DV where the terms represent the current and voltage swings so a small DV results in low power. The 712 GHz figure was achieved many years ago and has not been improved upon. However, research continues using materials other than GaAs/AlGaAs heterostructures and perhaps involving quantum dots. 5.3.1.2 Superlattice Electron Devices (SLEDs) As mentioned above, Gunn diodes rely on interband electron transfer for their NDR. However, if the material band structure is such that the electrons gain extra mass without transferring to another band then an NDR effect could occur which would not be transfer-time limited. The required band structure does in fact exist as illustrated in the typical semiconductor energy/ momentum (or E–k) curve of Figure 5.10(a). As the momentum increases, the curve becomes less steep and this is equivalent to an increase in effective mass for the electrons. At high enough bias, the electrons will therefore slow down producing an NDR. The trouble is that in natural semiconductors, the electrons either transfer, or begin to transfer, to another energy band before they reach this region. Superlattice devices, because of the periodicity of the artificial structure (Figure 5.10(b)), allow us to engineer a material which eliminates the band-to-band transition. A wide range of component materials can be used in SLED structures and of course the periodicity can also be optimized. At the time of writing SLEDs have demonstrated power generation but only up to around 200 GHz and then only at very low sub-microwatt power levels. However, continuous steady progress, especially in heat dissipation, is being made and 1 mW at 1 THz is predicted. Another motivation for the development of SLEDs is to produce a THz frequency Bloch oscillator. With reference to Figure 5.10(a), as an electron is accelerated from rest (k ¼ 0) by an externally applied electric field in the positive k direction up the (lower) E–k curve, it eventually reaches the edge of the Brillouin zone at k ¼ p/a, At this point its momentum is reversed and it proceeds back upon itself to k ¼ p/a where a further momentum reversal

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Microwave Photonics: Devices and Applications E

k -π/a

Reduced k space

EC

π/a

(a)

(b)

Figure 5.10 (a) Reduced energy/momentum (E–k) curves for a periodic structure; (b) superlattice structure with conduction band profile

occurs. In the ideal case this process repeats itself continuously giving rise to an oscillatory motion. Much has been published on this phenomenon but it is not clear that Bloch oscillations have actually been observed. However, from the results mentioned above, it may well be that the future of SLED THz oscillators lies in the optimization of domain formation resulting from the Bloch effect. 5.3.1.3 Quantum Cascade Lasers (QCLs) Quantum cascade lasers (QCLs) are also superlattice devices but in this case they have been engineered to emit THz radiation directly by laser action. The problem with the THz laser is that, at this frequency, the photons have energies of 4 meV. With room temperature corresponding to 25 meV normal laser action tends to be wiped out because of thermal excitation of electrons between the laser energy levels. In the superlattice structure the laser levels can be separated in space as well as energy, making laser action more likely, but for operation in the THz gap, the devices still have to be cooled to near cryogenic temperatures for useful operation. Power is not a problem with current performance figures of 0.6 mW at 1 THz rising quickly to about 10 mW at 2 THz. However, the figures at 1 THz have only been achieved with the addition of a magnetic field which of course increases the complexity, cost, power consumption and physical size. In general, the higher powers are achieved under pulsed biasing conditions and the lower the frequency the lower must be the operating temperature – temperatures as low as 40 K are needed at 1 THz. QCLs are not conveniently tuneable by, for example changing the bias voltage. This may not be a serious disadvantage, except perhaps in spectroscopy, but this has been overcome for mid-IR frequencies by Benjamin Lee et al. [20] who, on a single chip, fabricated an array of single mode distributed feedback QCLs, each emitting at a different frequency. Steady progress is being made in the performance of QCLs as the technology improves [21].

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5.3.1.4 Josephson Plasma Sources When a DC bias V is applied across a Josephson junction an AC signal of frequency f is produced given by: f ¼ 2qV=h

ð5:8Þ

where q is the charge on the electron and h is Plancks constant. For a typical DC bias of 1 mV the frequency of the AC current produced is 0.5 THz. A single junction will supply very little power but, if the currents produced by a number of interconnected junctions can be combined coherently, then a useful amount of power in the mW range may be possible. This possibility was predicted by Tilley as long ago as 1970 [22] but it is only recently (2007) that a practical device has been reported by Ozyuzer et al. [23]. Using crystals of the high-temperature superconductor Bi2Sr2CaCu2O8 (BSCCO), Ozyuzer et al. formed a stack of Josephson junctions made up of superconducting CuO2 layers separated by insulating Br–Sr–0 layers in a mesa structure about 1 mm high as shown in Figure 5.11. The vertical side walls of the mesa reflect the waves generated at the junctions backwards and forwards as in a laser bringing all of the components of the radiation into phase. The THz power output of the device scaled as n2 – where n is the number of junctions – but with too many junctions the device would not operate because the temperature would then rise above the critical value for superconductivity. At a temperature of 50 K the authors recorded a power of 0.5 mW at a frequency of 0.85 THz but predict that up to 0.5 mW could be generated in the 0.5–1.5 THz range. The frequency capability of these devices nicely fills the remaining THz gap between transit-time devices and QCLs but the power levels may still be a bit on the low side for practical applications – and of course, they do need to be cooled down to low temperatures. In principle, tuning could be achieved by varying the applied DC voltage but the length of the cavity also determines the frequency of the emitted signal.

Figure 5.11 Josephson Plasma Source using the high-temperature superconductor Bi2Sr2CaCu2O8 (BSCCO) sandwiched around nonsuperconducting insulators. (From Science, 318, No. 23, Nov 2007. Reprinted with permission of AAAS)

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Microwave Photonics: Devices and Applications GATE S

D L

Figure 5.12

Basic structure of a field effect transistor

5.3.2 Three-terminal Devices In electronics, conventional three-terminal devices are based on the flow of current over a defined distance from one region to another. For bipolar transistors the current carriers make a transition across the base region; in field effect devices the carriers must flow from source to drain (Figure 5.12). The time taken for current carriers to flow across a device – that is the ‘transit time’ determines the maximum frequency of operation. The shorter the transit length (L) and the higher the carrier velocity (v), the shorter will be the transit time and the higher will be the maximum frequency. However, current carriers (usually electrons) in semiconductors have a maximum speed (or saturation velocity vSAT – but see below) in the region of 105 ms1. (Beyond this speed they quickly give up their kinetic energy to the semiconductor lattice.) Therefore, the only way to make the devices faster is to reduce the transit distance. This in turn leads to difficulties because at small separations ( 1 THz [25]. This device has a sub 50 nm gate length, a 25% increase in electron mobility in the channel and a similar reduction in resistivity which lowers the contact resistance. The HEMTs were used in a three-stage common source low-noise MMIC amplifier which exhibited > 18 dB gain at 300 GHz and 15 dB gain at 340 GHz. Extrapolation of these results to 0 dB gain gives the fT > 1 THz. There is also another pressure on the drive to make FETs operate at ever higher frequencies. This comes from digital technology where the FET, operating as a switch, is the device of preference in integrated circuits. To keep Moores Law on course, ever faster switches are needed. In 2001 both Intel and IBM announced that they had developed ‘terahertz transistors’ aimed at the 45 nm generation of chip technology (see, for example, [26, 27]). The Intel THz transistor is fabricated on a silicon substrate, but unlike the conventional device, is separated from the substrate by a layer of oxide. This layer reduces leakage between the source and drain thus reducing parasitic power consumption. For the same reason, a new dielectric layer is used under the gate. Thicker source and drain layers are introduced to reduce the series parasitic resistance. The gate length is 45 nm. Terahertz switching speeds have also been achieved in ‘ballistic deflection transistors’ (BDTs) which have been developed at the University of Rochester [28]. These devices are fabricated using nanolithography and have dimensions less than the mean free path of electrons in the material – hence ‘ballistic’ as the motion is collision free. As illustrated in Figure 5.13, electrons directed into the BDT are deflected to the right (indicating logic 1) or to the left (logic 0) by the polarity of the potential difference between the control electrodes. Because of the nanometre dimensions, the parasitic capacitances are also very small – in the attofarad range resulting in sub-picosecond response times.

126


Figure 5.13 The ballistic defection transistor: (a) schematic and (b) micrograph of device structure. (Reproduced by permission of the University of Rochester)

5.3.2.3 Plasma Wave Device Dyakonov and Shur [29] have proposed and developed a novel application of a three-terminal device for THz wave generation. Their ‘plasma wave transistor’ looks very much like a HEMT (Figure 5.14) but operates in a very different way. In their device, plasma waves are set up in the electron gas in the channel rather like sound waves in a wind instrument – hence their name ‘electronic flute’. With a suitable choice of channel length, a THz frequency standing wave can be generated between the source and drain, which in turn causes a current at this frequency to flow in the external circuit. In 2006, Dyakonova et al. [30] described the emission of radiation in the 0.2–4.5 THz range from AlGaN/GaN HEMTs operating at room temperature. Power levels of 0.1 mW were observed.

Figure 5.14

Schematic representation of the plasma wave transistor

5.3.3 Multiplication Terahertz signal generation by multiplication up from a lower frequency is perhaps the longest established electronic technique – for example, see [31]. The motivation for this technology stems largely from the astronomy and remote sensing communities where compact and robust systems are a priority for mounting in space vehicles and cost is not a primary factor. A wide range of sources are available from companies such as Virginia Diodes (VDI) and an example of one of their THz sources is shown in Figure 5.15. The starting point for this device is a low frequency (< 25 GHz) signal which is multiplied by a factor of 72 to give an output in the 1 THz range. However, frequency multiplication is a relatively inefficient process so the

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Terahertz Sources

Figure 5.15 ATHz source consisting of a low-frequency coaxial input, an integrated doubler/amplifier, a quadrupler and two triplers. It has generated up to 25 mW in the WR-0.65 waveguide band, total length is 6 inches, no mechanical tuners are used. (Reproduced with permission from Virginia Diodes)

resulting THz power is only 25 mW, which may not be sufficient in some of the anticipated THz applications such as imaging, stand-off detection or communications. The nonlinear component that is at the heart of the VDI sources is the tried and tested Schottky diode whose history dates back to the early days of radio communications and is perhaps the first ever solid-state electronic device. Over the last few years researchers in Sweden [32] have been developing an alternative nonlinear multiplier know as the heterostructure barrier varactor (HBV). The HBVuses modern growth techniques to produce a device which has a symmetrical capacitance–voltage (C–V) characteristic (Figure 5.16) and hence, when acting as a multiplier, produces only the odd harmonics of the drive signal. This feature has the advantage of minimizing the number of different frequencies generated and removes

0.2

0.2 IEEE

0

0.1

-0.2 -60

-40

-20

0

20

40

Capacitance [fF /µm2]

Current [µA/µm2]

© 2007

60

Voltage [V]

Figure 5.16 Capacitance–voltage and current–voltage measurements for a 12 barrier 700 mm2 HBV. Reproduced by permission of Josip Vukusic, Tomas Bryllert, T. Arezoo Emadi, Mahdad Sadeghi and Jan Stake, IEEE Electron Device Letters, 28, no. 5, May 2007. ( 2007 IEEE)

128


the need to terminate the circuit at the even harmonics. Operated as a tripler, the HBV develops an output power of 240 mW at 110 GHz with a conversion efficiency of about 20%. In quintupler mode it develops 20 mW at 202 GHz at a conversion efficiency of about 3%. This performance is comparable with that of state-of-the-art Schottky diodes and further developments already in progress in material systems, heat sinking and circuit design will undoubtedly lead to significant improvements. However, at the present state of development, the frequencies achieved are still only just in the THz range! Ong and Hartnagel [33] have suggested a structure based on quasi-ballistic electron reflection (Q-BER) which according to their simulations should be superior to the HBV at the higher frequencies. At the time of writing, results for actual devices have not been published.

5.4 Conclusion Terahertz technology is a rapidly developing and expanding field. Historically, the utilization of these frequencies has been limited by the scarcity and low brightness of sources. Currently, however, a number of different technologies are increasingly bridging what used to be known as the ‘THz gap’. These include both optical techniques, based on laser down-conversion, and a variety of electronic technologies. It may therefore be expected that in the next few years terahertz technology and its applications will become as widespread and well-established as that of other spectral regions.

References [1] P. K. Cheo (Ed.), Handbook of Molecular Lasers, CRC Press, New York, USA, 1987, ISBN:0824776518. [2] A. Bergner, U. Heugen, E. Br€ udermann, G. Schwaab, M. Havenith, D.R. Charmberlin and E.E. Haller, ‘‘New p-Ge THz laser spectrometer for the study of solutions: THz absorption spectroscopy of water’’, Review of Scientific Instruments, vol. 76, 063110, 2005. [3] C.A. Brau, Free-Electron Lasers, Academic Press, Inc., Boston, USA, 1990. [4] D. Dragoman and M. Dragoman, ‘‘Terahertz fields and applications’’, Progress in Quantum Electronics, vol. 28, 1–66, 2004. [5] A. Corchia, C.M. Ciesla, D.D. Arnone, E.H. Linfield, M.Y. Simmons and M. Pepper, ‘‘Crystallographic orientation dependence of bulk optical rectification’’, Journal of Modern Optics, vol. 47, no. 11, pp. 1837–1845, 2000. [6] K. Liu, J. Xu and X.C. Zhang, ‘‘GaSe crystals for broadband THz wave detection’’, Applied Physics Letters, vol. 85, no. 6, 863–865 2004. [7] M.R. Stone, M. Naftaly, R.E. Miles, J.R. Fletcher and D.P. Steenson, ‘‘Electrical and radiation characteristics of semilarge photoconductive terahertz emitters’’, IEEE Transactions on Microwave Theory and Techniques, vol. 52, no. 10, 2420–2429, 2004. [8] Y.C. Shen, P.C. Upadhya, E.H. Linfield, H.E. Beere and A.G. Davies, ‘‘Ultrabroadband terahertz radiation from low-temperature-grown GaAs photoconductive emitters’’, Applied Physics Letters, vol. 83, no. 15, 3117–3179, 2003. [9] I.S. Gregory, W.R. Tribe, M.J. Evans, T.D. Drysdale and D.R.S. Cumming, ‘‘Multi-channel homodyne detection of continuous-wave terahertz radiation’’, Applied Physics Letters, vol. 87, 034106, 2005. [10] M.R. Stone, M. Naftaly, R.E. Miles, I.C. Mayorga and A. Malcoci, ‘‘Generation of continuous-wave terahertz radiation using a two-mode titanium sapphire laser containing an intracavity Fabry-Perot etalon’’, Journal of Applied Physics, vol. 97, 103108, 2005. [11] Y.J. Ding and W. Shi, ‘‘Widely-tunable, monochromatic, and high-power terahertz sources and their applications’’, J. Nonlinear Optical Physics and Materials, vol. 12, no. 4, 557–585, 2003. [12] T. Tanabe, K. Suto, J. Nishizawa, K. Saito and T. Kimura, ‘‘Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP’’, Journal of Physics D: Applied Physics, vol. 36, 953–957, 2003.

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[13] T. Tanuichi, S. Okada and H. Nakanishi, ‘‘Widely tunable terahertz-wave generation in an organic crystal and its spectroscopic application’’, Journal of Applied Physics, vol. 95, no. 11, 5984–5987, 2004. [14] D. H. Auston, K. P. Cheung, J. A. Valdmanis and D. A. Kleinman, ‘‘Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media’’, Phys. Rev. Lett., vol. 53, 1555–1558, 1984. [15] T.W. Crowe, ‘‘GaAs Schottky Barrier Mixer Diodes for the Frequency Range 1–10 THz’’, Int. J. lnfrared Millimeter Waves, vol. 10, no. 7, PP. 765–777, 1989. [16] J. Stake, T. Bryllert, J. Vukusic and A. Øistein Olsen, ‘‘Development of high power HBV multipliers for millimeter wave applications’’, Proc. SPIE, vol. 6739, PP. 67390U-1–8, 2007. [17] P. Plotka, J. Nishizawa, T. Kurabayashi and H. Makabe, ‘‘240–325-GHz GaAs CW Fundamental-Mode TUNNETT Diodes Fabricated With Molecular Layer Epitaxy’’, IEEE Trans Electron Devices, vol. 50, no. 4, 867–873, 2003. [18] J. Nishizawa, P. Plotka, H. Makabe and T. Kurabayashi, ‘‘GaAs TUNNETT Diodes Oscillating at 430–655 GHz in CW Fundammental Mode’’, IEEE Microwave and Wireless Components Lett, vol. 15, no. 9, 2005. [19] E.R. Brown, J.R. S€ oderstr€ om, C.D. Parker, L.J. Mahoney, K.M. Molvar and T.C. McGill, ‘‘Oscillations up to 712 GHz in InAs/AISb resonant-tunnelling diodes’’, Appl. Phys. Lett., vol. 58, no. 20, 2291–2293, 1991. [20] B.G. Lee, M.A. Belkin, R. Audet, J. MacArthur, L. Diehl, C. Pfl€ugl, F. Capasso, D.C. Oakley, D. Chapman, A. Napoleone, D. Bour, S. Corzine and G. H€ ofler, ‘‘Widely Tunable single-mode quantum cascade laser source for mid-infrared spectroscopy’’, Appl. Phys. Lett., vol. 91, 231101-1 2007. [21] B.S. Williams, ‘‘Terahertz Quantum Cascade Lasers –Review Article’’, Nature Photonics, vol. 1, 517–525, 2007. [22] D.R. Tilley, ‘‘Superradiance In Arrays Of Superconducting Weak Links’’, Phys. Lett., vol. 33A, 205–206, 1970. [23] L. Ozyuzer, A.E. Koshelev, C. Kurter, N. Gopalsami, Q. Li, M. Tachiki, K. Kadowaki, T. Yamamoto, H. Minami, H. Yamaguchi, T. Tachiki, K.E. Gray, W.K. Kwok and U. Welp, ‘‘Emission of Coherent THz Radiation from Superconductors’’, Science, vol. 318, no. 5854, pp. 1291–1293, 2007. [24] W. Snodgrass, Bing-Ruey Wu, K.Y. Cheng and M. Feng, ‘‘Type-II GaAsSb/InP DHBTs with Record fT ¼ 670 GHz and Simultaneous fT, fMAX > 400 GHz’’, Proceedings of the IEEE International Electron Devices Meeting, IEDM 07, Washington, D.C., USA, pp. 663–666, 2007. [25] R. Lai, X. B. Mei, W.R. Deal, W. Yoshida, Y. M. Kim, P.H. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska and A. Fung, ‘‘Sub 50 nm InP HEMT Device with Fmax Greater than 1 THz’’, IEEE International Electron Devices Tech. Digest, Washington, D.C., USA, pp. 609–611, 2007. [26] http://www.pctechguide.com/21Architecture_TeraHertz_technology.htm. [27] P. J. Silverman, ‘‘The Intel Lithography Roadmap’’, Intel Technology Journal, vol. 6, issue 2, pp. 55–61, May 2002. [28] Q. Diduck, M. Margala and M.J. Feldman, ‘‘ATerahertz Transistor Based on Geometrical Deflection of Ballistic Current’’, IEEE International Microwave Symposium Digest, pp. 345–347, 2006. [29] M.I. Dyakonov and M.S. Shur, ‘‘Plasma wave electronics: Novel terahertz devices with two-dimensional electron fluid’’, IEEE Trans. Electron Devices, vol. 43, no. 10, pp. 1640–1645, 1996. [30] N. Dyakonova, A. El Fatimy, J. Łusakowski, W. Knap, M. I. Dyakonov, M.-A. Poisson and E. Morvan, ‘‘Roomtemperature terahertz emission from nanometer field-effect transistors’’, Appl. Phys. Lett., vol. 88, p. 141906, 2006. [31] R. E. Miles, P. Harrison and D. Lippens(Eds), Terahertz Sources and Systems, Proceedings of the NATO Advanced Workshop on Terahertz Sources and Systems, Kluwer Academic Publishers, Holland, 2001. [32] J. Vukusic, T. Bryllert, A. Emadi, M. Sadeghi and J. Stake ‘‘A 0.2-W Heterostructure Barrier Varactor Frequency Tripler at 113 GHz’’, IEEE Electron Device Letters, vol. 28, no. 5, pp. 340–342, May 2007. [33] D. S. Ong and H. L. Hartnagel, ‘‘Enhanced THz frequency multiplier efficiency by quasi-ballistic electron reflection in double-heterojunction structures’’, EPL, vol. 81, pp. 48004–48009, 2008.

Part III Systems Applications


6 Analogue Microwave Fibre-optic Link Design Edward I. Ackerman and Charles H. Cox, III

6.1 Introduction Since the development of low-loss optical fibre in the late 1960s [1], designers of all sorts of systems for transmitting, detecting and processing electronic signals have sought to exploit its uniquely advantageous characteristics, which are discussed further at various points throughout this chapter. To do this has required the development of devices that generate light at the optical frequencies – usually expressed in terms of the corresponding optical wavelengths in free space – that propagate best in the fibre, devices that allow the electronic signal of interest to modulate this light at one end of the fibre and devices that restore the signal to electronic form at the other end of the fibre. The interconnection of these devices in a configuration that results in the conveyance of the electronic signal of interest from one point to another by means of the optical fibre is what is known as a fibre-optic link. Figure 6.1 illustrates an example of how a fibre-optic link – referred to simply as a ‘link’ in the remainder of this chapter – conveys a radio-frequency (RF) microwave signal [2]. In the example shown, a signal consisting of a single frequency fRF modulates a single-frequency optical carrier at frequency fopt for propagation in the optical fibre as sidebands at frequencies fopt fRF , which beat against the carrier in the photodetector to produce an output electronic signal at the original frequency fRF. (It should be noted that Figure 6.1 specifically depicts the spectral patterns of signals in a link that employs the intensity modulation and direct detection techniques; these techniques are fully described further on in this chapter.) For the purposes of discussion, in this chapter a straightforward or ‘intrinsic’ link is defined to include the optical source, the modulator, the fibre and the optical receiver, but not any electronic amplifiers. The link has electronic input and output ports and as such can include passive circuits which transform the impedances of these ports to match those of the modulation and detection device impedances, respectively.



134

‘Simple’ Link Detection (S/N)in

Optical source

f RF Sin

f RF

Modulation Photodetector

RF / Optical modulator

RF input

Figure 6.1

f opt

Optical fibre

(S/N)out

Sout

RF output

Definition of an ‘intrinsic’ analogue fibre-optic link. Reproduced from [2] ( 1997 IEEE)

The microwave fibre-optic link design process always involves the selection of appropriate devices for generating, modulating and detecting light, and possibly also includes special circuit designs and the selection of electronic amplifiers to modify the performance of the straightforward (i.e. without amplifier) link. However, before all these steps, microwave fibreoptic link design always begins with a definition of specifications for the link, and can be considered complete when the design meets those specifications. How the specifications are met depends on the answers to a series of questions that the designer poses in pursuing a solution. These questions are interspersed throughout the section that follows.

6.2 Requirements What constitutes a suitable link depends on the application into which it is to be inserted. The most basic question to ask oneself before beginning the design of a fibre-optic link is probably as follows. Why a fibre-optic link and not a microwave link consisting of some combination of electronic amplifiers and a coaxial cable or other metallic RF waveguide? Optical-fibre communication is an impressive technology, maturing with every passing year to address an ever-increasing range of system design issues. Like any technology, though, it is not the right tool for every job. For a system in which a coaxial cable’s performance characteristics are perfectly acceptable, it is overkill to design a fibre-optic link unless the system will benefit from leveraging one of the truly distinguishing properties of optical fibre – its light weight, small size, immunity and passivity to the electromagnetic environment, or the transparent and nondispersive properties that allow it to propagate a large range of optical wavelengths over great distances. What are the maximum tolerable size, weight, DC power consumption and cost of all the hardware at the two ends of the link? A successful design depends upon this question being asked at some point. Moreover it is prudent to ask it early on, because its answers may save time by immediately ruling out specific link architectures requiring devices that are too bulky, power-hungry or expensive. Another question that is best asked early on in the process is as follows. To what range of environmental conditions will the link be exposed, and under what conditions must it operate with the specified performance?

Analogue Microwave Fibre-optic Link Design

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This is not really a single question but rather a pair of related questions, in that often the range of environmental conditions over which the link must exhibit its promised performance is broader than the range over which it must simply survive so as to again deliver this performance once the narrower range of conditions is restored. The specified ‘range of environmental conditions’ often amounts to simply a range of temperatures, although in some systems pressures, humidity levels and vibration levels may be specified as well. This question should be asked early on in the process to avoid spending time designing a link using specific devices that are later discovered to be too sensitive to changes in environmental conditions. Sometimes system designers will answer a ‘What is required from the link?’ question with a ‘What is the best you can do?’ answer. This is quite often true of the next question the link designer must ask. Over what distance must the optical fibre carry the signal? A related question is as follows. What range of microwave frequencies comprises the signal? The combined answers to these last two questions may dictate a great deal about the link design, possibly precluding the use of certain types of optical sources, modulators, fibres and detectors. Finally, the designer must find out the answer to the following question. Which microwave figures of merit will be used to quantify the link performance, and for each of these what specific minimum or maximum values must be achieved in the link design? The most commonly specified figures of merit are summarized here.

6.2.1 Gain Performance Figure 6.2 shows how several of the figures of merit commonly used to quantify the performance of microwave components are defined. The first to be examined here is the intrinsic small-signal gain, gi, because several of the other figures of merit depend in some way upon this one. For an input RF signal power expressed in W (or mW or mW), gi is the dimensionless ratio of the output RF power to this input power. When this ratio is less than unity, it is generally called loss rather than gain. Similarly, for input and output powers expressed in dBm, Gi is the difference between these and is expressed in dB, with a negative difference representing loss rather than gain: gi ðdimensionlessÞ ¼

sout ðin WÞ sin ðin WÞ

Gi ðin dBÞ ¼ 10 logðgi Þ ¼ Sout ðin dBmÞ Sin ðin dBmÞ:

ð6:1aÞ ð6:1bÞ

The ‘small-signal’ aspect of the definitions of gi and Gi refers to the fact that these figures of merit must be specified for input signals which are not sufficiently strong enough to undergo a measurable degree of amplitude compression. As Figure 6.2 shows, for all sufficiently small input signals Gi is a constant.

6.2.2 Signal-to-noise Performance The ratio of signal output power to noise output power, usually expressed in dB, is almost always one of the most important figures of merit in any system design. For many communications


136

IPnout

Output signal powers (dBm)

Sout,max Sout,1dB

IPnin Sin,max Sin,1dB

G = Sout – Sin

ne

n me

Noise figure

F

da un

int erm

to

1

nth - or der

tal

f 2)

od s

f 1, s(

1

Spurious-free dynamic range

n

1

Nout 1-dB Compression dynamic range Full compression dynamic range

k T0 B

Minimum detectable signal

Input fundamental tone (f1,f2) signal powers (dbm) Figure 6.2 Principal figures of merit for analogue two-port devices, including analogue fibre-optic links

systems, the input signal strength is controlled and therefore known, in which case the output signal-to-noise ratio might always be designed to meet or exceed a specified value at this input power. In detection systems such as radars, however, this input signal strength is unknown, and so the output signal-to-noise ratio cannot be readily specified. For such systems a useful figure of merit is the noise figure (nf or NF), which is defined as the extent to which the signal-to-noise ratio degrades:

ðs=nÞin;a nf ðdimensionlessÞ ¼ ðs=nÞout

nin ¼kT0 B

¼

nout : kT0 B ga

NFðin dBÞ ¼ 10 logðnf Þ ¼ ðS=NÞin;a ðin dBÞ ðS=NÞout ðin dBÞ ¼ Nout ðin dBmÞ 10 logðkT0 BÞ ðin dBmÞ Ga ðin dBÞ:

ð6:2aÞ

ð6:2bÞ

In Equation (6.2a), s/n is the dimensionless ratio of signal power s to noise power n (both expressed in W), and in Equation (6.2b) S/N is the difference in dB between these two powers (both expressed in dBm). The input noise is specified as only the noise arising from thermal sources. This input noise is the product of k (Boltzmann’s constant), T0 (room temperature,


137

standardized by the IEEE as 290 K [3]) and B (the instantaneous bandwidth of the electronic receiver, sometimes called the ‘resolution bandwidth’ or ‘noise bandwidth’). Because the output noise term nout is also proportional to B, the noise figure is independent of B. The terms ga and Ga are the link’s available gain, defined as in Equation (6.1) for the special case resulting from perfect matching of the link input port impedance to the microwave signal source’s impedance. Figure 6.2 shows how NF can be determined graphically from measurable quantities, using Equation (6.2b). It also shows how to determine graphically another important figure of merit that expresses the signal-to-noise performance of a link, which is the minimum detectable signal (mds). This quantity, which is defined as the smallest signal power appearing at the link input that can be distinguished from the noise at the link output, is related to the noise figure as follows (and as shown in Figure 6.2): mdsðin WÞ ¼

nout ¼ kT0 B nf : ga

MDSðin dBmÞ ¼ Nout ðin dBmÞ Ga ðin dBÞ ¼ kT0 B ðin dBmÞ þ NFðin dBÞ:

ð6:3aÞ ð6:3bÞ

6.2.3 Dynamic Range Just as the existence of noise sets a lower limit on the link’s input signal power, there is also an upper limit on the input signal power. This upper limit exists because of the nonlinear characteristics of the link components that give rise to phenomena such as output signal compression (sometimes called gain compression) and the generation of harmonic and/or intermodulation distortion, as will be explained further below. The link’s dynamic range is defined as the ratio of the largest input power (expressed in W) that it can usefully convey to the smallest such input power, which is the mds (or as the difference in dB between these two powers if they are both expressed in dBm, which is the MDS). How one defines the largest input power that the link can usefully convey depends upon the application. In some applications this is simply the input signal power that causes full compression of the output signal, such that further increases of the input power do not cause the output power to increase (and may even cause it to decrease), and for these applications the full-compression dynamic range (cdrfull) is defined as (and as shown in Figure 6.2): cdrfull ðdimensionlessÞ ¼

sin;max ðin WÞ mds ðin WÞ

CDRfull ðin dBÞ ¼ Sin;max ðin dBmÞ MDS ðin dBmÞ:

ð6:4aÞ ð6:4bÞ

Sometimes the largest input power that the link can usefully convey is considered to be that at which the output power has been compressed by 1 dB. This input signal power, Sin,1dB, is the power for which the output power Sout,1dB satisfies the following equation: Sout;1dB ðin dBmÞ ¼ Sin;1dB ðin dBmÞ þ Ga ðin dBÞ 1 dB:

ð6:5Þ

138


From this relationship the 1-dB-compression dynamic range as shown in Figure 6.2 is defined as (where from here on we dispense with the linear expression and give only the more useful logarithmic one): CDR1dB ðin dBÞ ¼ Sin;1dB ðin dBmÞ MDS ðin dBmÞ:

ð6:6Þ

In many applications, the generation of harmonic and/or intermodulation distortion by nonlinear components in the link sets the upper limit on the useful input signal power and therefore dictates the dynamic range. If a signal consisting of a single tone at frequency f1 is present at the input to the link, harmonic distortion products caused by the link’s nonlinearity appear at the output at frequencies pf1, where p is the set of all positive integers. If the input signal instead consists of two tones f1 and f2, then the resulting output harmonics at pf1 and pf2 will be accompanied by intermodulation distortion products at pf1 qf2 and pf2 qf1, where both p and q are positive integers. Intermodulation distortion products are generally more problematic than harmonics for two reasons: 1. for two equal-strength input tones at f1 and f2, the resulting output intermodulation tones at pf1 qf2 and pf2 qf1 are stronger than the output harmonics at (p þ q) f1 and (p þ q) f2 for any given positive integers p and q for which p q, and 2. in applications covering less than an octave of bandwidth (i.e. those in which the maximum frequency of operation is less than twice the minimum frequency), all harmonics fall out of band and can therefore be filtered out, whereas, for f1 and f2 sufficiently close to one another, many of the intermodulation products whose ‘order’ n ¼ p þ q is an odd number can fall within the band of operation and therefore preclude being filtered out. In applications such as radar, in which spurious output tones at the intermodulation distortion frequencies give rise to false detections, the upper end of the spurious-free dynamic range (SFDR) is defined as the input power that causes any output intermodulation product to exceed the output noise. The dominant order of distortion, n, determines this maximum input power, and a somewhat complicated set of considerations determines n. Generally, the lower the order of distortion, the lower the input power must be to generate an intermodulation product of a given strength. Therefore, unless there is a reason not to begin with the assumption that n ¼ 2, that is the starting assumption one should make. However, if the system operates over less than one octave of bandwidth, second-order distortion products will always fall out of band and therefore permit being filtered out, so that it instead makes sense to begin with the assumption that n ¼ 3. A discussion of ‘linearization’ in a later part of this chapter goes into further detail about determining the correct value of n for a given set of link components. For an input signal consisting of two equal-power tones of small magnitude, the output intermodulation distortion products will be negligible because they will fall very far below the output noise. However, as the two-tone input signal power is increased, the output power at the intermodulation frequencies will increase as the input power to the nth power, so that on Figure 6.2’s plot of output versus input power in dBm the slope of the intermodulation products is n, compared to a slope of one for the fundamental signal tones. A useful figure of merit is the input power at which these two slopes would hypothetically intersect were they to not compress as shown in Figure 6.2. This input power is known as the nth-order intercept IPnin and the


139

corresponding output power is IPnout. The more linear the devices used in the link, the higher these powers will be. From the geometric arrangement of the lines in Figure 6.2, it can be seen that the SFDR is limited by the nth-order distortion products to: n1 ½IPnin ðin dBmÞ MDSðin dBmÞ n n1 ¼ ½IPnout ðin dBmÞ Nout ðin dBmÞ n

SFDRn ðin dBÞ ¼

ð6:7Þ

6.2.4 Other Figures of Merit Additional figures of merit are important in the design of links for certain applications. The designers of distribution systems for cable television (CATV) signals, for example, wish to have a single link carry as many channels as possible without significant distortion of any one channel. They use a measurable parameter called composite triple beat (CTB) to quantify the level of distortion resulting from a given number of channels. When channels are spaced at equal frequency intervals, a mixture of the information transmitted on three of the channels can appear as distortion on a fourth channel transmitted at a frequency that is the sum of two channel frequencies minus the third channel’s frequency. Thus CTB, like SFDR, is related to the link’s nonlinear distortion properties. It has been shown that to satisfy the CTB requirements of CATV applications, the link’s SFDR must exceed 110 dB in a 1 Hz bandwidth [4]. Microwave components are often additionally characterized in terms of their frequencydependent scattering matrix [Smn], where Smn is the complex ratio of signal intensity out of port m to the signal intensity into port n when all ports other than port n are terminated by the complex conjugates of their input impedances. For a two-port microwave component in which the input and output ports are denoted ports 1 and 2, respectively, the squares of the amplitudes of the four scattering parameters have particular significance: jS11 j2 jS12 j2 jS21 j2 jS22 j2

¼ ¼ ¼ ¼

input return loss backwards isolation insertion loss ðor insertion gain if jS21 j2 > 1Þ output return loss:

The importance of the gain (|S21|2) has been explained in Section 6.2.1. The backwards isolation (|S12|2) is identically zero in most fibre-optic links, in that most modulators cannot detect light and most detectors cannot modulate light; notable exceptions are the dual-function electro-absorption modulator/detector devices demonstrated in the laboratories of the US Navy and the University of California [5]. Because other microwave signal components are not essentially unidirectional, microwave signal reflections at the input and output ports of a link that functions in a chain of microwave components can have adverse affects on the performance of the complete chain. Therefore a link must often be designed such that its input and output return losses (|S11|2 and |S22|2, respectively) lie below a specified level. Lastly, since most of the figures of merit discussed in this chapter are frequency-dependent, a designer will often be required to minimize their variation over the specified bandwidth. With all of these specifications in mind, the designer must make a series of decisions that together


140

will ultimately result in the link design. These decisions are the subject of the section that follows.

6.3 Link Design Options The design of a microwave fibre-optic link to meet a set of performance specifications requires the making of a few important decisions.

6.3.1 What Optical Wavelength to Use A wide range of optical wavelengths can propagate in optical fibre with low attenuation. Figure 6.3 shows the attenuation per unit length versus wavelength for silica fibres, with vertical lines indicating the three wavelengths around which activity in the field of fibre-optics has centred since the invention of the optical fibre itself [6]. The availability of Si and AlGaAs sources and detectors prompted some of the earliest developers of links to use wavelengths in the region around 850 nm. By the late 1980s, however, as the designers of CATV and telecommunications systems endeavoured to produce links that spanned longer and longer distances, they began investigating the wavelength region near 1300 nm. In this wavelength region, standard single-mode optical fibre exhibits a minimum of

Infrared absorption tail from lattice transitions

50 20

–OH absorption peaks

Fibre attenuation (dB/km)

10 5 2 1 Perfectly ‘dry’ fibre

0.5

Rayleigh scattering

0.2 0.1 AlGaAs

1.0

1.2

1.30

0.8

0.85

0.02 Red 0.6

InGaAsP Ge InGaAs

Si

1.4

Sources Detectors

1.55

0.05

1.6

1.8

2.0

Wavelength (µm) Figure 6.3

Attenuation in a typical single-mode optical fibre versus wavelength. Reproduced from [6]


141

chromatic dispersion, which is often the phenomenon that limits a link’s bandwidth–length product. But by the mid-1990s the availability of erbium-doped fibre amplifiers, which can be optimized for operation at wavelengths ranging from about 1530–1565 nm, motivated most designers of long-distance links to design for this wavelength range so as to exploit this significant and advantageous technological development. It was later found that, through adjustments to the geometry and refractive index profile, the dispersion characteristic of a single-mode fibre could be tailored to have optimum propagation properties in this longerwavelength region instead of near 1300 nm, and this development was accordingly named ‘dispersion-shifted fibre’. An additional benefit of working in this longer wavelength region is the reduced attenuation that arises from Rayleigh scattering relative to shorter wavelengths, as shown in Figure 6.3. Since the development of erbium-doped fibre amplifiers and dispersion-shifted single-mode fibre, most developers of the lasers, modulators, detectors and other components used in fibreoptic links have concentrated product development in the 1550 nm wavelength region. Therefore, deciding to use 1550 nm light gives the fibre-optic link designer the widest range of component options. In some cases, however, shorter wavelengths might offer the optimum solution. Specifically, if the maximum signal frequency and/or the transmission distance are not very large, and the required RF performance is not very challenging, then a design using 850 nm light might yield the lowest-cost solution. This situation is explained further in the sections that follow.

6.3.2 What Type(s) of Optical Fibre to Use A fibre’s geometry – primarily the diameter of the higher-index core – and its index profile determine whether it will support a single, a few or many spatial modes. The larger the core diameter, the easier it is to efficiently couple light into it and the more spatial modes it supports. As is discussed in a later section of this chapter, maximizing the efficiency of coupling between the fibre and other important link components is necessary for enabling the best possible link performance. In general, to propagate light modulated at high frequencies over long distances, the ideal number of spatial modes supported by a fibre is one. Therefore, with the exception of some components – primarily ones optimized for 850 nm operation – most commercially available lasers, modulators and detectors have been designed to interface with single-mode fibre and are sold already coupled to single-mode fibre pigtails. Coupling light between single-mode fibre and larger-core multimode fibre is generally inefficient because of mode mismatch issues, and therefore it is important to use fibre of one type throughout the link. An exception to this general rule is the case when polarizationpreserving single-mode fibre is required. This situation exists when one of the devices in the link prefers a specific orientation of the light’s polarization. An external modulator made of an anisotropic inorganic material, such as lithium niobate, is one such device. Lithium niobate modulators are often pigtailed by their manufacturers with polarization-maintaining (PM) single-mode fibres (at least on the optical input port), and therefore unmodulated, continuouswave (CW) light is provided to this device most easily from a laser whose output is also coupled into this type of fibre pigtail. Polarization-preserving fibre is, however, more expensive than standard telecommunications-grade single-mode fibre, and therefore it usually does not make sense to use PM fibre anywhere in a link except between the CW laser and the polarizationsensitive modulator in an external modulation link.

142


The properties of optical fibre most likely to affect the link performance are its attenuation, nonlinearity and dispersion properties. Each of these is discussed here only briefly; for more thorough explanations of these properties, the reader is encouraged to consult the references [7–11]. 6.3.2.1 Attenuation As shown in Figure 6.3, the attenuation per unit length in standard single-mode fibre is at its absolute minimum – between 0.2 and 0.3 dB/km – at wavelengths near 1550 nm. Shorter wavelengths suffer from greater loss due to Rayleigh scattering, which arises from subwavelength-scale variations in the density of the fibre’s fused silica core [7]. Additionally, unless extreme care is taken to rid the fibre material of water ions to produce what is called a ‘dry’ fibre, OH absorption peaks cause much greater attenuation at and around specific wavelengths shorter than 1500 nm. Light at wavelengths longer than 1600 nm incurs significant attenuation by being absorbed and exciting vibrations in the silica crystal lattice [7]. Additionally, the radiative losses caused by fibre bends are more severe at longer wavelengths [12]. As is discussed further in later sections of this chapter, maximizing analogue optical link performance requires that the photodetector in the link be illuminated by nearly the maximum optical power that it can withstand without saturating. Therefore, the fibre attenuation can dictate a maximum length for a link that must meet the complete set or some subset of the performance requirements discussed in Section 2.6. Often, however, the other characteristics of the fibre – its nonlinearity and/or its dispersion properties – impose a more stringent link length limitation than the attenuation does. 6.3.2.2 Nonlinearity The two most problematic nonlinear phenomena in optical fibre are stimulated Brillouin scattering and stimulated Raman scattering. Stimulated Brillouin scattering arises because of the tendency of an intense concentration of photons to generate an acoustic wave along the fibre length, causing the refractive index of the core to be increased or decreased at the peaks and troughs of the wave. This periodic variation of the index comprises a zeroth-order grating that reflects light back in the reverse direction. The greater the optical power, the more reflective the grating that forms, and this relationship sets an upper limit on the product of the optical power and the length of transmission in the fibre. For standard telecommunications-grade fibre, stimulated Brillouin scattering sets a limit of approximately 29 mWkm [8]. The stimulated Raman scattering effect manifests itself as absorption of the photons by the silica atoms, which in turn emit new photons at an optical frequency about 17 THz lower than that of the original photons. This effect has been exploited to yield what are known as Raman fibre amplifiers, in which light injected at the higher optical frequency ‘pumps’ the silica atoms so that input photons at the lower optical frequency can stimulate the emission of more in-phase photons at this same frequency, yielding amplification of a modulated optical input. Because the threshold for stimulated Raman scattering is rather high, Raman fibre amplifiers are not as widely used as doped-fibre amplifiers (especially erbium-doped fibre amplifiers). Similarly, its high threshold makes stimulated Raman scattering a less problematic phenomenon than stimulated Brillouin scattering, imposing a less restrictive power–length limitation [8].


143

6.3.2.3 Dispersion Dispersion is the property that causes different components of a signal to propagate at different velocities in a waveguide, such that detection after sufficient length will result in reconstruction of a signal that is a distorted copy of the original. In fibre designed for multimode propagation at short wavelengths (850 nm), intermodal dispersion typically imposes a bandwidth–length product of a few hundred MHzkm. Much greater bandwidth–length products are possible in standard telecommunications-grade fibres – up to 200 GHzkm or more, depending on the type of optical source (i.e. laser), its centre wavelength and linewidth and how it is modulated. No laser exists with a truly monochromatic (single optical frequency) output characteristic, and therefore the tendency for individual wavelengths within the output spectrum to propagate at different speeds (chromatic dispersion) precludes high-fidelity restoration of a signal of a given frequency beyond a certain length. This limit has been circumvented, however, by following very long lengths of standard telecom fibre in the link either with optical gratings or with specific lengths of another type of fibre specially designed to have a dispersion slope (derivative of velocity with respect to wavelength) opposite in sign to that of the telecom fibre [9,10]. The broader the laser line, the shorter this limiting distance is for a given signal frequency. For this reason, solid-state and doped-fibre lasers – which have linewidths on the order of 1 kHz – make better optical sources for long-haul links than do semiconductor lasers, the best of which have linewidths on the order of 10 MHz. Because solid-state and doped-fibre lasers cannot be directly modulated at high frequencies like semiconductor lasers can, external modulation is more likely to be employed in a long-haul link than is direct modulation. If a semiconductor laser is preferred as the CW source – because of its much lower cost or smaller size – the largest possible bandwidth-length product is enabled by a distributed-feedback (DFB) laser. Whereas mirrors supply the required optical feedback in a simple Fabry–Perot laser, resulting in an output spectrum with multiple peaks, in a DFB a narrowband grating restricts the optical feedback to a narrower portion of the spectrum, resulting in an output spectrum more closely resembling that of a high-quality solid-state laser in its shape (although much broader in width). Another type of dispersion that can impose a link length limitation is polarization mode dispersion (PMD), which is caused by the birefringence in the fibre dictating different propagation velocities for the two orthogonal polarizations of light supported by the fibre. However, this is not often a serious problem for designers of analogue microwave fibre-optic links, and therefore the reader is referred elsewhere [11] for a discussion of methods for dynamic compensation to mitigate the effects of PMD.

6.3.3 What Detection Technique to Use Once the wavelength and the type of optical fibre have been selected, it is necessary to select components for generating and modulating the light at the input end of the link and detecting it at the output end. It is easier to proceed by selecting the detection technique first, because this choice may in turn limit the choice of a modulation technique, as is discussed further on in Section 6.3.9 of this chapter. At the output end of a fibre-optic link two different methods can be used to recover the analogue signal from the optical carrier it is modulating: direct detection and coherent detection. Figure 6.4 shows block diagrams of links using these two detection techniques.

Integrator

Input signal

∫

Phase modulator LO laser

Photodetector

Photodetector

Optical source

(b)

IF amplifier

Limiter

τ

Output signal

Output signal

only for phase modulation

∫

Output signal

Square-law device

[ ]2

Integrator

IF amplifier

IF amplifier

Envelope detector

Photodetector

Photodetector

Photodetector

Phase discriminator

LO laser

Intensity modulator Input signal

Intensity modulator Input signal

(a)

Optical source

Figure 6.4 Detection methods in fibre-optic links. Direct detection can recover an analogue signal that has been made to modulate the intensity of an optical carrier, whereas amplitude, phase or frequency modulation of an optical carrier can only be recovered by a process known as coherent detection. Reproduced from [13] ( 1994 IEEE)

only for frequency modulation

Optical source

or the frequency or phase of light

modulating the amplitude

can retrieve optical signals

Coherent detection

can only retrieve optical signals modulating the intensity of light

Direct detection

144 Microwave Photonics: Devices and Applications


145

In the direct detection process of Figure 6.4(a), a photon incident upon a photodetector has a specific probability of exciting a valence-band electron into a higher-energy conduction band, and therefore a photodetector responds to a modulation of incident photon intensity with a proportional modulation of output photocurrent, provided the detection process and the device in which it occurs are both sufficiently fast. Representing the incident optical field E as E0e j(2pnt þ u), where E0, n and u, are respectively the amplitude, frequency and phase of the light, direct detection results in a photocurrent ID, where ID ¼ rd jEj2 ¼ rd E02 :

ð6:8Þ

In Equation (6.8) the proportionality constant is known as the detector’s responsivity, rd, which is expressed in A/W (although for photodetectors designed to be used in fibre-optic links, mA/mW is a more magnitude-appropriate unit ratio). Notice that the only property of the optical field to which the photodetector responds is its intensity (which is the square of its amplitude), except to the extent that rd is itself dependent on the optical frequency. Most semiconductor photodetectors can absorb photons over a very broad range of optical wavelengths and therefore direct detection is not a viable option for recovering a signal that is modulating the optical frequency; direct detection of optical phase modulation is also implausible. From a quick examination of Figure 6.4(b), which shows the hardware necessary to perform coherent detection of amplitude, frequency or phase modulation, it is clear why most analogue fibre-optic link designers choose to work with direct detection of an intensity-modulated signal. Not only is more hardware required for coherent detection, but also greater control must be exercised to stabilize the relationship between the frequencies and phases of the two lasers so that any detected change in this relationship will be only that which is induced by the modulation signal. Additionally, the signal-to-noise ratio at the output of a coherent-detection link can be degraded by the presence of optical phase noise. This means that a coherentdetection link can have inferior performance to a direct-detection link (which is immune to optical phase noise in the absence of any phenomenon that converts this into intensity noise) unless the two optical sources in the coherent-detection link both have very narrow linewidths [13]. Because of the increased cost and challenge of implementing coherent detection architectures, to the authors’ knowledge no fielded system exists at this time in which the modulation signal is retrieved from the optical carrier using one of these coherent detection techniques. Once the detection technique has been selected, the specific detector to be used in the link must be chosen as well. High-speed photodetection can be accomplished in a variety of devices, including photoconductors, phototransistors, metal–semiconductor–metal photodiodes, p–i–n photodiodes and avalanche photodiodes. The majority of fielded RF links use p–i–n photodiodes. InGaAs and InGaAsP p–i–n photodiodes respond very efficiently and quickly (as demonstrated to frequencies of > 300 GHz [14]) to light at the 1300 nm and 1550 nm wavelengths at which single-mode optical-fibre transmission has been optimized, and are therefore the most commonly selected detectors for use in analogue fibre-optic links with operating frequencies exceeding 1 GHz. For comprehensive discussions of photodetector design, the reader is referred to descriptions of state-of-the-art devices by Magnin et al. [15] and Tulchinsky et al. [16], and to comprehensive reviews of various device types by Yu [17] and Kato [18].

146


6.3.4 What Modulation Technique to Use At the input end of the link, an optical source generates a carrier at the desired wavelength, and a modulator imposes the analogue signal on the optical carrier. If the optical source and modulator are separate devices, the light is said to be externally modulated by the analogue electronic signal. Alternatively, the optical source and modulator can be a single device, such as a semiconductor laser, whose optical output is directly modulated by an analogue signal applied in conjunction with the DC bias current that provides the electrical pump for the laser. In a direct modulation link a semiconductor laser directly converts a small-signal modulation around a bias point set by a DC current into a corresponding small-signal modulation of the optical amplitude, frequency, phase or intensity (or, most likely, all of these) of photons emitted around the average values of these quantities that occur at the bias point. Because of the complexity and challenge involved in implementing a link in which coherent detection is used to retrieve direct modulation of the optical amplitude, frequency or phase, from this point in the chapter onwards when the terms ‘directly modulated’ or ‘direct modulation’ are used, it can be assumed that the only modulated property of the light that is detected is its intensity. The modulation bandwidth of a directly modulated semiconductor laser is limited by its relaxation resonance frequency, which in turn can be shown to be proportional to the square root of its optical output power. A 3 dB modulation bandwidth of 40 GHz has been demonstrated for a multiquantum-well laser operated at a large output power (35 mW) [19]. Another key performance parameter of a directly modulated semiconductor laser is its slope efficiency, s‘, expressed in W/A (or the more magnitude-appropriate units mW/mA); this is the efficiency with which the RF modulation current is converted to modulated optical power [6]. Figure 6.5 shows the transfer functions for the diode laser and photodetector in an intensitymodulation/direct-detection (IM/DD) link in which the laser’s optical output intensity is directly modulated with slope efficiency s‘. The detector’s slope efficiency sd shown in the figure is the same as its responsivity, rd, described in Section 6.3.3. Conversely to rd, a directly modulated laser’s ideal slope efficiency is the photon energy hc/l divided by the electron charge q. The product of s‘ and sd is the change in detector output current for a given change in laser input current; gi, the output-to-input signal power ratio for an intrinsic (i.e. without amplifier) link, is thus proportional to the square of this product. Therefore, theoretically the maximum possible gi is obtained if each electron that comprises the laser’s input current generates one photon, and if each photon reaches the detector and generates one electron-hole pair; this would correspond to (s‘sd)2 ¼ 1 [6]. Most fielded direct modulation analogue links use diode lasers designed to emit 1300 nm or 1550 nm light from the edge of the semiconductor chip. In edge emitters the optical feedback necessary to enable lasing is realized using either a Fabry–Perot (FP) cavity created by end-facet mirrors or a pair of first-order Bragg gratings that achieve distributed feedback (DFB). Within the gain spectrum of the semiconductor, a DFB laser has only one longitudinal mode that is not strongly suppressed by the gratings, and therefore a single narrow line dominates its optical output spectrum; by contrast an FP laser supports many longitudinal modes within this same gain spectrum, and consequently its optical emission spectrum typically consists of several lines. The DFB’s improved spectral characteristic is usually accompanied by better noise and linearity characteristics, in addition to better fibre propagation characteristics (as explained in Section 6.3.2.3). For these reasons, most high-performance direct modulation analogue optical links use DFB semiconductor lasers.


147 +

+

ID

IL

RFIn

RFOut

P0

PD Photodiode ID (mA)

PD (mW)

Diode Laser

sl (W/A)

I L (mA)

sd (A/W)

PD (A/W)

Figure 6.5 The key components of a direct-modulation intensity-modulation/direct-detection (IM/DD) analogue fibre-optic link, and the definitions of the directly modulated laser and the photodetector slope efficiencies (after [6])

The 1990s and the earliest years of the twenty-first century have seen progress in the development of lasers that emit light from the surface of the semiconductor chip, which lend themselves much more readily to automated testing and low-cost manufacturing. To date most of the work on such devices – called vertical cavity surface-emitting lasers (VCSELs) – has been in GaAs or AlGaAs, both of which lase at short wavelengths (800–1000 nm) where fibre characteristics are less desirable than at 1300 nm or 1550 nm. Therefore, while a VCSEL can exhibit slope efficiency as high as that of an edge emitter, and costs much less to test and to align to fibre than an edge emitter, so far this type of laser has rarely (e.g. [20, 21]) been used in highperformance links for analogue applications. For more comprehensive overviews of the present state of the art in semiconductor lasers for direct modulation links, the reader is referred to reviews by Holonyak [22], Dagli [23] and Mansuripur and Wright [24]. In an external modulation link, separate devices serve as the optical source and RF/optical modulator. As is described further on in this chapter, an external modulation link’s performance improves when the optical power supplied to the modulator is increased (up to the maximum power that the modulator or detector can handle). Because the optical source does not have to be a semiconductor laser designed for high-frequency direct modulation, one can choose instead a semiconductor laser designed for high-power CW output, or can even choose a high-power solid-state or doped-fibre laser. At most RF frequencies the noise characteristics of solid-state and doped-fibre lasers are typically preferable to those of a semiconductor laser; however, they are also typically much larger and costlier. It is possible to externally modulate the amplitude, phase or intensity of the laser’s CW output. However, using coherent detection to detect external modulation of the amplitude or

148


phase of the light is much more complex and challenging than direct detection of external intensity modulation; therefore from this point in the chapter onwards all discussion pertains to IM/DD links in which the intensity of light is externally modulated. At present, the type of external modulator most commonly used in analogue fibre-optic links is the Mach–Zehnder interferometric (MZI) modulator. Selecting the material in which to fabricate an MZI modulator involves weighing the importance of several characteristics: absorptive loss of optical waveguides in the material, coupling loss between these waveguides and the input and output fibre pigtails, strength of the electro-optic effect in the material, stability of the material and the cost of manufacture. The low optical loss and strong electrooptic tensor of the inorganic material lithium niobate has made it the most commonly used material for MZI modulators. Since the latter half of the 1990s, however, MZI modulators have also been demonstrated in lower-cost polymeric materials [25, 26]. In addition, MZI modulators can be, and have been, fabricated in semiconductors like GaAs and InP [27, 28]. A semiconductor MZI modulator is most inexpensively integrated with a semiconductor laser source. However, the optical losses incurred coupling into and out of the semiconductor optical waveguides, and the limited optical power handling capability of both polymer and semiconductor modulators to date, have prevented the performance of links using modulators made in either of these materials from rivaling that of links using MZI modulators made in lithium niobate. In any MZI modulator, an optical waveguide is fashioned close to the top surface of the material, and between the input and output edge of the substrate this waveguide is made to split into two waveguides that run in parallel for a given length and then recombine into one waveguide. In the middle section the two parallel optical waveguides traverse a region in which an applied electric field changes the phase of the light in one of the waveguides relative to the other, affecting the interferometric recombination of these two guided waves. The electric field, and therefore the modulator’s optical output, is modulated by the small-signal RF modulation voltage across a set of electrodes on the surface of the substrate. The electro-optic effect, by which an applied electric field changes the phase shift incurred by an optical wave propagating through a material, can also be exploited to achieve optical intensity modulation in devices other than an MZI modulator. Interferometric conversion of the phase modulation to intensity modulation can also be accomplished in a Fabry–Perot cavity or other type of optically resonant structure [29]. Additionally, guide/antiguide structures [30] can be realized in such a way that the electro-optic effect determines how much light is coupled out of the waveguide – and therefore also how much of the light remains guided. Neither resonant interferometric nor guide/antiguide modulators, however, have matured to the point of commercial availability. Presently a commercial alternative to the MZI modulator is the electro-absorption modulator (EAM), in which an applied electric field affects the output intensity by shifting the optical absorption band edge in a semiconductor via either the Franz–Keldysh effect or the quantumconfined Stark effect. Much of the interest in EAMs stems from their potential for low-cost integration with semiconductor laser sources. A number of electro-absorption-modulated laser (EML) products have become commercially available. It is possible to derive a slope efficiency for external modulators analogous to that of a directly-modulated laser. In an external modulation fibre-optic link, gi is proportional to the square of the product of the small-signal slope efficiencies of the external modulator and the detector. As shown on the transfer function for the modulator in Figure 6.6, the modulator’s


149 +

+

ID

V RFIn

RFOut

P0

CW Laser

PD

PI

Photodiode

PD /PI

ID (mA)

Mach-Zehnder Modulator

sd (A/W)

sm (W/A)

Vπ

PD (A/W)

V

Figure 6.6 The key components of an external-modulation IM/DD analogue fibre-optic link, and the definitions of the external modulator and the photodetector slope efficiencies (after [6])

slope efficiency sm is the change in its optical output power for a given change in input current. Specifically, dpM;O ðvM Þ sm ; ð6:9Þ dv m

vm ¼0

where PM,O is the modulator’s output optical power, which is a function of vM, the total voltage on the modulator, which is in turn the sum of a DC bias voltage VM and the modulation signal voltage vm. If the modulator’s transfer function (i.e. the mathematical relationship between its output optical power and input voltage) is known, Equation (6.9) can be used to derive a useful expression for sm. An MZI modulator, for example, has the transfer function: TFF PI p vM 1 þ cos pM;O ¼ ; ð6:10Þ 2 Vp where TFF is the modulator’s fibre-to-fibre optical insertion loss, PI is the CW optical power supplied to its input fibre, and Vp is the voltage change necessary to shift the optical phase in one of the ‘arms’ of the interferometer by p radians relative to the other (and therefore to switch between completely constructive and completely deconstructive interference at the modulator output, see Figure 6.6). Remembering that vM ¼ VM þ vm, substituting (6.10) into (6.9) yields: p TFF PI RM p VM sm ¼ sin ; ð6:11Þ 2 Vp Vp where a factor RM equal to the modulator’s resistance has been included to yield the same dimensions for sm as those of the direct modulation slope efficiency s‘ (i.e. W/A).


150

Equation (6.11) shows that the MZI modulator’s slope efficiency is a function of its DC bias voltage VM, and is maximum at the so-called ‘quadrature’ bias voltage VM ¼ Vp/2. Also notice from Equation (6.11) that one can increase the modulator slope efficiency by increasing PI, such that it is theoretically possible to achieve (smsd)2 > 1 so that the intrinsic link gain Gi can exceed 0 dB. Practical considerations such as the size and cost of high-power lasers and the damage threshold of the modulator, the fibre and the photodetector preclude increasing PI indefinitely, of course, but at l ¼ 1300 nm PI values as high as 400 mW have been successfully fed through a lithium niobate MZI modulator, resulting in Gi > 30 dB [31]. Besides increasing PI, another way to increase sm is to reduce Vp. In general, one way to reduce the Vp of an MZI modulator, or its equivalent on–off switching voltage in another type of modulator, is to lengthen the region in which the optical and applied electrical fields interact. However, as this interaction length increases it becomes more likely that at the analogue frequencies of interest the modulation voltage cannot be approximated as constant during an optical transit time through this region. Therefore, to maximize modulation efficiency at microwave signal frequencies, the electrodes are typically fashioned in a travelling-wave configuration so that the analogue modulation signal propagates along a transmission line in parallel to the optical waveguides. The highest-frequency external modulation link results have been achieved when the microwave-frequency propagation velocity in the travelling-wave electrode structure has been tailored to be approximately equal to the velocity of the light in the optical waveguides [32]. For comprehensive overviews of the present state of the art in external modulators, the reader is referred to reviews by Zhou and Taylor [33], Li et al. [34] and Dagli [23].

6.3.5 How to Interface to the Link Input and Output Ports Section 6.3.4 has outlined the effect of device slope efficiencies – sl for a directly modulated laser, sm for an external modulator and sd for a photodetector – on an IM/DD link’s intrinsic gain, gi, and the equations in Section 6.2 showed the effect of this one parameter on nearly all the other important figures of merit that quantify analogue link performance. Specifically, it was shown that 2 gi / s2‘ TL-D s2d

2 or s2m TM-D s2d ;

ð6:12Þ

where the two different products of squared quantities are appropriate to direct and external modulation links, respectively, and where the terms TL-D and TM-D have been included to represent the ratios of optical power illuminating the detector to the optical power that is coupled into the output fibre pigtail of the directly modulated laser or external modulator, respectively. The products of quantities in Equation (6.12) represent squared ratios of signal current from the photodetector relative to signal current into the external modulator or directly modulated laser. Because the gain is defined as the ratio of output to input microwave signal powers (see Equation (6.1a)) rather than the squared ratio of signal currents in the devices, the missing proportionality factor in Equation (6.12) is a ratio of impedances. The exact value of this ratio depends on the types of circuits that are used to interface these devices to the link input and output ports. Figure 6.7 shows equations for direct and external modulation link gi that result from the four combinations of photodetector and external modulator or directly modulated laser interface

Resistive matching circuit

Interface from link input port to external modulator or directly modulated laser

Signal source

RS

Source resistance

Signal source

RS

Source resistance

RS

Signal modulation current

Lossless, passive impedance transformer

RS


Modulation device impedance


in

ga

Impedance matching resistor

sic

rin

Int

or sm2 TM2 − D sd2

g i = sl2 TL2− D sd2



Detector impedance

Signal photocurrent

RLOAD RM

RLOAD RL

RLOAD RS

RLOAD RS

Load resistance

R LOAD

No matching circuit




RLOAD 4 RM

RLOAD 4 RL

RLOAD 4 RS

RLOAD 4 RS

R LOAD

Impedance matching resistor


Detector impedance

Signal photocurrent

Resistive matching circuit

Load resistance

R LOAD

Figure 6.7 Equations for direct and external modulation link gi that result from four combinations of photodetector and external modulator or directly modulated laser interface circuits

Lossless, passive impedance transformation circuit

Interface from photodetector to link output

Analogue Microwave Fibre-optic Link Design 151


152

circuits that are most relevant to the types of photodetectors, modulators and directly modulated lasers presently available and most suitable for use in RF-frequency analogue fibre-optic links. In the case of the circuit that interfaces the photodetector to the link output port, the most common situations are illustrated by the two circuit diagrams across the top of Figure 6.7. The type of photodetector most commonly employed in high-frequency IM/DD links is a reversebiased p–i–n photodiode, which has a very large impedance that is dominated at low RF frequencies by its depletion region’s large capacitive reactance. Therefore, attaching the detector directly to the output port of the link causes the detected signal photocurrent to act effectively as a current source driving the link’s output load impedance (typically 50 W) without the need for interface circuitry. The commercial manufacturers of high-speed photodetectors, however, commonly include a 50-W matching resistor in parallel to the photodetector, because this tends to yield a packaged device frequency response that is flatter (relative to the ‘no matching circuit’ case) all the way from low frequencies through to high microwave frequencies at which parasitic resistances and reactances can exceed the magnitude of the depletion region’s capacitive reactance. Comparing the left-hand column in Figure 6.7 to the right-hand column, it can be seen that the penalty that comes with the flatter frequency response of the ‘resistive matching circuit’ case is a factor of four reduction in gi (or 6 dB reduction in Gi) relative to the ‘no matching circuit’ case. In the case of the interface circuit between the link input port and either the external modulator or the directly modulated laser in an IM/DD link, the most common situations are illustrated by the two circuit diagrams along the left-hand edge of Figure 6.7. The forwardbiased semiconductor diode lasers used in direct modulation links typically have a resistance RL of only a few ohms, and therefore the easiest method for achieving a broadband impedance match between the laser and the source resistance RS is to connect them via a resistor with resistance equal to RS – RL. In this case, as shown in the top row in Figure 6.7, the intrinsic direct modulation link’s gain gi is simply the squared ratio of output to input currents as shown in Equation (6.12), multiplied by the ratio of output load to input source impedances in the case of no detector matching circuit, or one-fourth of this value in the case of a resistive matching circuit in the detector package, that is 2 gi ¼ s2‘ TL-D s2d

RLOAD RS

or

2 gi ¼ s2‘ TL-D s2d

RLOAD ; 4 RS

ð6:13Þ

respectively. Equation (6.13) is further simplified in the most common case where RLOAD ¼ RS ¼ 50 W, so that RLOAD/RS ¼ 1. Higher direct modulation link gain can be achieved across any band over which the impedance match between RL and RS can be accomplished using a passive impedance transformer, provided the transformer has negligibly small resistive loss. At any frequency where a ‘perfect’ match is achieved, if the transformer is approximately without loss, then, as is shown in the bottom two equation boxes in Figure 6.7, 2 gi ¼ s2‘ TL-D s2d

RLOAD RL

2 or gi ¼ s2‘ TL-D s2d

RLOAD 4 RL

ð6:14Þ

depending on whether the detector is resistively matched. Notice that Equation (6.14) yields a value of gi that is a factor of RS/RL greater than the case of where the directly modulated laser is resistively matched [cf. Equation (6.13)].


153

In external modulation links, although most commercial manufacturers of lithium niobate MZI modulators aim to achieve a value of RM as close as possible to 50 W for their resistively terminated travelling-wave electrodes, they usually settle for a value of RM somewhere between 25 W and 45 W, because electrodes on lithium niobate having a characteristic impedance of 50 W typically do not support a microwave propagation velocity matching that of the light in the optical waveguides. Therefore, to achieve an impedance match between RM and RS, it is possible to use the same resistive matching technique as already described for the direct modulation link case. As shown in the top two equation boxes in Figure 6.7, this situation would result in an expression for gi almost identical to Equation (6.13), with sm and TM-D substituting for s‘ and TL-D, respectively. However, resistive matching to a travelling-wave modulator electrode is rarely implemented. Instead, because even a 25 W travelling-wave electrode impedance is reasonably close to 50 W, the impedance transformation to 50 W can be readily accomplished using a passive impedance matching transformer. If this transformer is approximately lossless, then 2 gi ¼ s2m TM-D s2d

RLOAD RM

or

2 gi ¼ s2m TM-D s2d

RLOAD ; 4 RM

ð6:15Þ

depending on whether or not the detector is resistively matched, as shown in the bottom row in Figure 6.7. It is important to be aware of an additional design option regarding the interface circuit between a modulator’s electrodes and an external modulation link’s input port. The equations shown in Figure 6.7 are valid for modulators with travelling-wave electrodes in inorganic materials (such as lithium niobate), polymers or semiconductors. However, it is possible to fabricate external modulators with electrodes that are not configured as transmission lines and therefore do not achieve broadband travelling-wave interaction between the modulating signal and the light in the optical waveguides. In semiconductor MZI or EA modulators, for example, the electrodes are sufficiently short that they might be validly modelled as ‘lumped-element’ circuits up to fairly high microwave frequencies. In lithium niobate or polymer MZIs, longer electrodes are typically used to achieve higher slope efficiency, and therefore a lumped-element circuit becomes an inaccurate model beginning at fairly low microwave frequencies (e.g. 1 GHz). Electrodes not configured as transmission lines might instead be thought of as a capacitance across which the modulation voltage is applied. To prevent large microwave reflections, a 50 W resistor might be connected in parallel to this capacitance. In this case, the equation for intrinsic external modulation link gain would happen to look the same as in Equation (6.15) if RS were substituted for RM. However, a likely reason that one would use a modulator with lumped-element electrodes would be to benefit from the increase in link gain that can be obtained (albeit over a narrow bandwidth and only at relatively low frequencies) by including a resonant microwave matching circuit between the electrodes and the link’s input port. For a full discussion of this resonant matching technique and its effect on the link gain equation, the reader is referred to the book by Cox [6].

6.3.6 Can the Performance Specifications be Met with an ‘Intrinsic’ Link? At the beginning of this chapter, Figure 6.1 was introduced to define what is meant by an ‘intrinsic’ link – one without any electronic amplifier before the modulation device or after the photodetector. Section 6.3.5 has given equations for the small-signal gain of an intrinsic link


154

(gi) assuming the use of direct detection and either direct or external intensity modulation, with Figure 6.7 giving the appropriate gi expressions for the most likely sets of device interface circuitry at the input and output ports. If a given small-signal gain is one of the specifications that must be satisfied by the link design, then the designer must compare this specification with what is predicted by the expressions in Figure 6.7, and determine whether electronic amplification will be needed to achieve the specified gain. Electronic amplification before the modulation device (gpre) and/or after the photodetector (gpost) simply increases the system’s small-signal gain (gs) as follows: gs ¼ gpre gi gpost :

ð6:16Þ

Amplification in the optical path between the modulation device and the photodetector increases the link gain in a different fashion, as is discussed further in Section 6.3.6.1. Because small-signal gain is seldom the only specification the designer needs to meet, it is not usually possible to simply add amplification wherever one chooses. An electronic amplifier’s gain, signal-to-noise and dynamic range performances affect the system’s overall signal-tonoise and dynamic range differently depending on where along the signal path the amplification is applied. Specifically, as has been derived elsewhere (see, for example, [35] and [36]), the noise figure, input second-order intercept power and input third-order intercept power of a system consisting of an intrinsic link preceded and followed by electronic amplifiers are: nfs ¼ nfpre þ

ip2in;s ¼

nfi 1 nfpost 1 þ gpre gpre gi

ð6:17Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 2 gpre gpre gi 1 þ þ ip2in;pre ip2in;i ip2in;post

ð6:18Þ

and

ip3in;s ¼

gpre gpre gi 1 þ þ ip3in;pre ip3in;i ip3in;post

1

:

ð6:19Þ

If the ‘intrinsic’ link has sufficiently large gi, ip2in,i and ip3in,i and sufficiently small nfi such that adding some available combination of electronic pre- and post-amplifiers yields acceptable values for gs, nfs, ip2in,s and ip3in,s, then the design process can be successfully concluded by adding such amplifiers. This is sometimes not the case, however. For example, it is relatively common for an intrinsic link’s noise figure to exceed a specified minimum system noise figure and therefore to preclude exceeding a specified output signal-to-noise ratio at a given input signal power. As Equation (6.17) shows, the only way to reduce the system noise figure is by adding pre-amplification. Unfortunately, however, Equations (6.18) and (6.19) show that the input second- and third-order intercept powers – and therefore the system’s SFDR – can be adversely affected by the addition of a pre-amplifier. In fact, the addition of any amplifier can only worsen and never be expected to improve a system’s SFDR, and therefore it is important that a link designer should be aware of techniques for improving the gain, the signal-to-noise performance and the dynamic range performance of the intrinsic link. The following three subsections describe such techniques.


155

6.3.6.1 Techniques for Improving Intrinsic Link Gain Performance As mentioned above, an optical amplifier affects the performance of a link in a manner that differs from how the addition of an electronic pre- or post-amplifier does. Specifically, the optical amplifier’s gain magnifies the transmission parameter TL-D or TM-D in Equations (6.12)– (6.15). For example, if an ‘intrinsic’ direct modulation link includes 20 dB of optical attenuation between the laser and the photodetector, this would be represented as TL-D ¼ 0.01. Hypothetically, using optical amplifiers with gains of 10 dB, 20 dB or 30 dB to partially, fully or more than fully compensate for the 20 dB of loss would yield, respectively, TL-D ¼ 0.1, 1 or 10. The use of any of these degrees of optical amplification would have an enormous effect on the link’s gain, because TL-D is squared in the equation for gi. In practice, optical amplification is an acceptable way to compensate partially, or in some cases fully, for various amounts of attenuation in the optical path between the modulation device and the detector. However, because most commercial optical amplifiers reach saturation at input levels of 1 mW or less, they can only increase the transmission factor TL-D or TM-D to greater than unity in the usually undesirable case where less than 1 mW of modulated optical power is available from the link’s directly modulated laser or external modulator, or when a higher modulated optical power has been attenuated to less than 1 mW by excessive optical path losses. Besides trying to keep the optical transmission factor high, another commonly pursued method for maximizing gi is to shop for or design a detector and either a laser (in direct modulation links) or modulator (in external modulation links) that have the maximum possible slope efficiencies. In external modulation links, an attractive option exists for increasing the modulator’s slope efficiency sm, because it is proportional to the power supplied to it by the CW laser. Equation (6.14) shows this optical power dependence clearly for MZI external modulators, but in fact it is true in general for all types of external modulators, provided that the optical waveguides in the modulator can withstand high levels of optical power. By providing 188 mW of CW optical power to a lithium niobate MZI modulator, Burns et al. [37] demonstrated an intrinsic link with Gi > 0 dB across more than a decade of RF frequencies up to 550 MHz. Precluding an even higher gain was the fact that this much optical power resulted in an average photocurrent of 8.5 mA, which was nearly the detector’s rated limit. Larger current ratings generally require larger photodetector active regions, which in turn limit the speed of detection. For this reason, most demonstrations of intrinsic links with gain have been at RF frequencies below 3 GHz. The highest gain demonstrated to date for a link without amplifiers – Gi > 30 dB – was achieved by not only further increasing the input optical power to 400 mW, but also by adding resonant circuits that matched the modulator’s lumped-element electrode impedance and the detector’s impedance to 50 W to increase the ratio RLOAD/RM in Equation (6.15) by a factor of 20 dB in a narrow (< 10%) band around 150 MHz [31]. As mentioned at the end of Section 6.3.5, this technique for increasing gi is not a viable option in links that must be designed for operation over broad bandwidths or at frequencies for which lumped-element modulator electrodes are impractical. Equation (6.15) shows that maximizing the device slope efficiencies, the optical transmission factor, and the ratio RLOAD/RM – all of which have been discussed in this subsection – constitute the complete list of methods for improving the intrinsic link’s gain performance.

156


6.3.6.2 Techniques for Improving Intrinsic Link Signal-to-noise Performance Recall from Equation (6.2a) that the intrinsic link’s noise figure NFi is defined as the degradation of signal-to-noise ratio S/N when its input noise is the thermal noise generated at T0 ¼ 290 K. This input thermal noise is amplified (or attenuated) by the link’s gain (or loss) gi. If gi is sufficiently large that the amplified input thermal noise makes the dominant contribution to the total noise at the link output, then there is virtually no degradation in S/ N from the link’s input to its output, and so its NFi approaches 0 dB. This is obviously the absolute lower limit to NFi, and it is difficult to realize in actual intrinsic fibre-optic links because of several other contributions to the output noise. Figure 6.8 shows an equivalent circuit for either a direct or an external modulation link, including the input thermal noise and all other sources of noise that contribute to a link’s total output noise. To understand the basis for techniques that can improve a link’s NFi requires an appreciation for all of these contributions to output noise. These are therefore discussed at some length in this section, beginning with two ways that the link itself generates additional thermal noise. First, because the impedance of any modulator or semiconductor laser has some ohmic component, it generates thermal noise, as does the resistive portion of any circuit interfacing this device to the link input. This thermal noise is represented in Figure 6.8 as a noise equivalent voltage source at the input to the shaded region representing the intrinsic link. Depending on the exact circuit configuration, some or all of this thermal noise will modulate the light and reach the link output just as the link’s input thermal noise does, setting a new lower limit to the link NFi that is greater than 0 dB. How much greater depends on several factors that have been documented elsewhere [38,39]. Unfortunately, very few links have been demonstrated in which either the link’s input thermal noise or the thermal noise generated by the modulation device and its interface circuit dominate the link’s total output noise; in most cases the dominant source of noise is one of the three that appear in the right-hand portion of Figure 6.8, resulting in much higher link NFi than if the input or modulation device thermal noise were dominant. The second unavoidable additional contribution to the total output thermal noise from an intrinsic link is the thermal noise generated in the photodetector circuit, which is the right-most noise source shown in Figure 6.8. This noise is usually roughly equal in amplitude to the link’s input thermal noise. Therefore if the intrinsic link has loss rather than gain, then the thermal noise generated in the photodetector circuit, rather than the attenuated input and modulation device thermal noises, will dominate the total thermal noise at the output of the link. In this case, the minimum possible signal-to-noise ratio degradation from link input to link output is equal to the signal loss in dB, or 10log(1/gi), which has been named the passive attenuation limit to fibre-optic link NFi because a passive attenuator’s noise figure equals its loss [31]. The two remaining sources of noise shown in Figure 6.8 are particularly problematic for analogue fibre-optic link designers. First, the noisy nature of the optical source is quantified by a term called its relative intensity noise (RIN). This noise is detected along with the signal, so it is shown in Figure 6.8 as a noise current source in parallel to the signal photocurrent. Secondly, the statistical nature of the photodetection process itself results in shot noise, which is also shown as a noise current source. Like the thermal noise generated in the detection circuit, these sources of noise have amplitudes that are not directly related to the link gain. Therefore, because the link’s noise figure is the ratio between its output noise and its amplified input

Input thermal noise

Impedance matching circuit

Thermal noise of modulation device and matching circuit



Optical losses

Detector impedance

Photodetected Signal photocurrent laser RIN Shot noise

Impedance matching circuit

Thermal noise of detector and matching circuit

Load resistance

Figure 6.8 Equivalent circuit of intrinsic IM/DD analogue fibre-optic link showing sources of noise that contribute to the total noise delivered to the output load, which together with the link gain determines the noise figure (after [6])

Signal source

Source resistance


158


thermal noise (see Equation (6.2a)), the RIN and shot-noise terms in the NFi equation are both inversely proportional to gi. Specifically, " # 1 hID i2 RIN RLOAD 2 q hID i RLOAD ð6:20Þ NFi ¼ 10 log 1 þ constant þ þ þ gi k T 0 gi k T0 gi for a link in which the detector circuit has no matching resistor, and " # 1 hID i2 RIN RLOAD q hID i RLOAD NFi ¼ 10 log 1 þ constant þ þ þ gi 4 k T0 g i 2 k T0 gi

ð6:21Þ

for a link with a resistively matched photodetector. The only as-yet undefined parameters in Equations (6.20) and (6.21) are the hIDi term appearing in both the RIN- and shot noisedetermined terms (the fourth and fifth addends within the brackets, respectively), and the electronic charge q that appears only in the shot-noise term. Now that all the sources of noise in a link have been identified along with their dependences on specific parameters like the link gain or average photocurrent, it is possible to explain the methods by which some link designers have improved NFi. The only unquantified term in Equations (6.20) and (6.21) is the ‘constant’, which has been explained to arise from thermal noise in the modulation device circuit, and which can usually be neglected because this noise is not a significant contributor to the link’s total output noise. The reader is referred elsewhere for derivations of this constant and descriptions of the rare set of circumstances for which its contribution to NFi is non-negligible [38, 39]. From examining Equations (6.20) and (6.21), it appears that the most obvious way to reduce NFi is to increase gi. Not all of the methods for increasing gi enumerated in the previous subsection are equally effective in reducing NFi, however, because some of these methods also affect the magnitude of other terms in Equations (6.20) and (6.21). For example, methods of increasing gi that also result in increased average photodetector current hIDi have no effect on the RIN-determined term in the NFi equation. Additionally, increasing the link gain through adjustments to the circuit that interfaces the photodetector to the link’s output port will generally have no effect upon either the RIN- or the shot noise-determined terms, because such changes will affect how well the circuit couples these noise currents to the link output to the exact same extent as they affect how well it couples the signal photocurrent to the link output. Another way to reduce the link’s NFi, which was discovered independently by three groups in 1993 [40–42], is a technique that has become known as ‘low-biasing’ an external modulator. The benefits of this technique are easiest to quantify in the case of an MZI external modulator in a linear electro-optic material like lithium niobate, because its transfer function and slope efficiency can be expressed as simple functions of its DC bias voltage VM using Equations (6.10) and (6.11), respectively. By substituting the bias-dependent expression for MZI modulator slope efficiency sm (Equation (6.11)) into the expression for the intrinsic external modulation link’s gain gi (the right-hand part of Equation (6.13)), and bearing in mind that the average photocurrent hIDi is also a function of VM, rd TFF PI p VM hID i ¼ rd hPM;O i ¼ 1 þ cos ; ð6:22Þ 2 Vp NFi can be examined as a function of VM by substituting Equations (6.13) and (6.22) into Equation (6.20) or (6.21). Figure 6.9 shows, for specific assumed photonic component values, the effect of the low-biasing technique on the NFi of an MZI modulator-based external


159

φ) Link gain is proportional to sin 2(φ

Link output noise is N thermal + NRIN + Nshot , in which N thermal is proportional to [constant + sin 2(φ)] NRIN is proportional to [1 + cos(φ)] 2 and N shot is proportional to [1 + cos(φ)] -130

RIN = –145 dB/Hz

-150

–155 dB/Hz –165 dB/Hz

100 Link 90 i (dB), NF 80 Gi (dB)

-160

–175 dB/Hz

70

Link output noise (dBm/Hz)

-140

-170

–145 d B /Hz –155 d B /Hz –165 d B /Hz –175 d B /Hz

-180 -190 -200 -210

Gi NFi

-220 -230 0

30

60

90

120

150

60

0

50

–10

40

–20

30

–30

20

–40

10

–50

0 180

As modulator is ‘low biased’ from quadrature (90°, where output signal is maximum) towards full extinction (180°), output noise is reduced more quickly than output signal. Therefore, link noise figure is reduced for an optimum ‘low bias’ condition.

–60

MZ Modulator bias, φ (degrees)

Figure 6.9 Illustration of ‘low-biasing’ technique for reducing the noise figure of an intrinsic external modulation fibre-optic link that uses an MZI modulator (assumptions: Vp ¼ 3 V, hIDi ¼ 10 mA at f ¼ 90 ). The link’s output noise (left axis) decreases more quickly than its gain Gi (right axis), causing the optimum NFi (right axis) to occur at a bias point between 90 and 180

modulation link. From the curves showing the intrinsic link gain (Gi) and the total output noise from the link, it is evident that the noise initially decreases more quickly than the signal as the modulator bias f (where f ¼ 180 VM/Vp ¼ pVM/Vp) is increased from 90 towards the lightextinguishing bias of 180 . At some optimum low-biasing point between 90 and 180 that depends on component parameters such as the laser RIN, NFi is minimized. If the bias point is moved further towards 180 , the signal gain begins to decrease more quickly than the noise, and therefore NFi begins to increase relative to its value at the optimum low-biasing point. As is explained further in Section 6.3.6.3, an external modulator produces no second-order distortion only when biased where Gi is maximum (e.g. at f ¼ 90 for an MZI modulator). Therefore, the low-biasing technique for reducing NFi has an adverse effect on the link’s second-order distortion limited dynamic range SFDR2, such that it tends not to be employed except in links with bandwidths of less than one octave, in which all second-order distortion products fall out of band [41]. An additional way to reduce NFi is to use one of several external modulation link architectures that employ a balanced differential photodetector configuration to cancel the CW laser’s RIN. In the most conventional of these architectures, shown in Figure 6.10(a), the two outputs from a quadrature-biased (f ¼ 90 ) MZI modulator in which an optical directional coupler rather than a y-branch combiner produces the necessary interferometry are connected via equal-length optical fibres to the two detectors. Because the two modulated outputs from the MZI modulator are complementary, that is 180 out of phase with one another, subtracting them in the differential detector configuration doubles the output signal (thereby increasing gi) while cancelling the common-mode component, which is the laser’s RIN [43]. The architecture shown in Figure 6.10(a) can successfully suppress RIN over wide bandwidths so long as the two fibre lengths are carefully matched to within a small fraction

180°

vRF

vRF

vRF

(c)

(b)

(a)

Polarization combiner

Att.

180°

Detector

Polarization Combiner

Detector

Detector

Detector

Figure 6.10 Techniques for cancellation of the laser’s RIN: (a) broadband method involving dual-output MZI external modulator and balanced detectors; (b) narrowband method requiring the same type of modulator but only a single photodetector; (c) narrowband method using a conventional single-output MZI modulator and a single photodetector. Reproduced from [44] ( 1998 IEEE)

Diode laser

Diode laser

Diode laser



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of the electrical wavelength. Establishing and maintaining this critical length match over even a moderate transmission distance can be difficult and costly. Over narrow bandwidths, two architectures proposed by Helkey [44] can cancel the RIN (and thereby improve NFi) without the need for balanced differential photodetectors or the length-matched fibre connections between them and the modulator. In the first of these two architectures, shown in Figure 6.10(b), the two complementary output signals from the same type of MZI modulator shown in the Figure 6.10(a) configuration are subtracted by delaying one output by half of the period at the centre frequency of modulation to cause a 180 phase shift at that frequency, and then incoherently summing these modulated optical signals in a polarization multiplexer. In the second narrowband architecture, shown in Figure 6.10(c), the modulated light is summed with a delayed portion of the unmodulated light, resulting in cancellation of the RIN but no doubling of the modulated optical signal power. To provide the correct phase difference for commonmode rejection of the RIN at the centre operating frequency in either of these two architectures, the short path lengths between where the optical power is split and recombined must satisfy length tolerances, but these are more easily maintained than those in the two long fibre lengths in the Figure 6.10(a) configuration. Using one of the methods discussed in this section may sufficiently reduce NFi either such that no pre-amplifier is required to meet the system noise figure or output signal-to-noise ratio requirement, or such that the gain that this pre-amplifier needs to have is not so large that the input second- or third-order intercept powers are reduced to the point where the link’s dynamic range specification is unachievable. 6.3.6.3 Techniques for Improving Intrinsic Link Dynamic Range In most IM/DD analogue fibre-optic links, the external modulator (or directly modulated laser) is the most nonlinear component, and therefore determines the intrinsic link’s SFDR. It is possible to operate either an MZI or a directional-coupler type of electro-optic modulator around a DC bias voltage at which the second derivative of the transfer function is zero (in fact for the MZI all even-order derivatives are ostensibly zero at this bias voltage); doing so eliminates distortion at the second harmonics and second -order intermodulation frequencies, causing third -order distortion products to dominate and usually resulting in SFDR3 of the order of 110 dB in a 1 Hz instantaneous bandwidth [45]. Better dynamic range has sometimes been achieved using directly modulated lasers, such as in the 3 GHz link with an SFDR3 of 125 dB in 1 Hz demonstrated by Pappert et al. in 2000 [46]. By judicious use of electro-absorptive (EA) phenomena in semiconductors – the Franz– Keldysh and quantum-confined Stark effects – modulators can be also designed with transfer functions that appear to be much more linear than those of other types of external modulators. Welstand et al. successfully biased a Franz–Keldysh EA modulator such that third-order nonlinearity was nulled – at least to the point where the fifth-order nonlinearity dominated; the measured SFDR3 for the resulting narrowband 4 GHz link was 124 dB in 1 Hz [5]. To improve an intrinsic link’s SFDR, many research efforts have focused on the development of ‘linearized’ modulators, in which one or more orders of nonlinear distortion are minimized. Figure 6.11 shows three linearized modulators that have undergone thorough analytical and experimental development [47–49]. Using a variation of the cascaded MZI modulator configuration of Figure 6.11(a), Betts achieved the highest third-order distortion-limited SFDR3 demonstrated to date: 133 dB in 1 Hz at 500 MHz [50].


162

(a) BIAS

BIAS

RF

(b) BIAS

BIAS RF

(c) BIAS

BIAS

RF

BIAS

Figure 6.11 Electro-optic modulator configurations that support broadband ‘linearization’ via simultaneous minimization of both second- and third-order distortion products: (a) series MZIs (after [47]); (b) parallel MZIs (after [48]); (c) modified directional coupler modulator. Reproduced from [49] ( 1990 IEEE)

Because the high-SFDR3 link demonstrated by Betts was not designed for broadband (i.e. greater than octave-bandwidth) operation, the linearized modulator was not configured to minimize both second- and third-order distortion for one set of bias conditions. It is possible, however, to design any of the three modulator configurations shown in Figure 6.11 to achieve simultaneous nulling of both second- and third-order distortion, resulting in broadband linearized performance. However, for efficient modulation at frequencies above 2 GHz or so, the modulator’s electrodes must be configured as a transmission line whose effective refractive index at RF frequencies closely matches the optical refractive index. In a directionalcoupler modulator, such as the one shown in Figure 6.11(c), there are two critical optical modes––one that remains in the input waveguide and one which couples to the parallel waveguide – with different effective indices. This intermodal dispersion precludes efficient broadband modulation at frequencies above 2 GHz. To achieve broadband linearization (i.e. both second- and third-order distortion nulling) from the dual-MZI modulators shown in Figures 6.11(a) (b), the RF signal must be split and applied in precise proportion to two different travelling-wave electrodes. All RF characteristics of the two electrodes (e.g. their RF attenuation per unit length, characteristic impedance and guided-wave velocity as determined by effective RF refractive index) must therefore precisely match one another over the entire band in which linearization is to be performed. This RF signal balancing can be exceedingly difficult over broad bandwidths, because even at moderate RF frequencies (e.g. above 2 GHz or so) the travelling-wave electrodes are electrically very large structures. Figure 6.12 shows another link architecture that has been proven to enable simultaneous even-order and third-order linearization [51]. This benefit is derived from the fact that it relies

Figure 6.12 Two-wavelength approach for achieving broadband linearization of an IM/DD analogue fibre-optic link: (a) configuration; (b) modulator transfer function and its second and third derivatives at the two wavelengths and their total. Reproduced from [51] ( 1999 IEEE)


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on the use of a single straightforward MZI modulator with only one RF travelling-wave electrode. The MZI modulates two different wavelengths of light (l1 and l2) simultaneously, and routes these modulated optical carriers to separate detectors whose outputs are combined in a hybrid coupler (or, optionally, to a balanced differential detector). This linearization architecture is analogous to the dual-parallel MZI modulator shown in Figure 6.11(b), in which the RF signal is split in specific proportion between two MZIs that are fed a single optical carrier that has also been split in a specific proportion. In the two-wavelength configuration of Figure 6.12, however, only one MZI modulator is required because it has a different half-wave voltage (Vp) at the two wavelengths; thus, an RF signal of magnitude vm applied to the single electrode results in a different modulation depth vm/Vp at the two wavelengths. Routing the two wavelengths to separate detectors enables the use of electronic circuitry to maintain precisely the ratio of RF signal currents at the hybrid coupler inputs that results in the distortion cancellation. A proof-of-principle demonstration of the two-wavelength linearization architecture yielded a link SFDR3 that was limited by fifth-order distortion to 122 dB in 1 Hz over an 800–2500 MHz band (i.e. broader than one octave). If the linearity of the modulation device has been improved using a linearization technique such as the ones discussed in this subsection, it is possible that the SFDR of the link may be limited by imperfect linearity of the photodetection process. A paper by Williams et al. [52] thoroughly discusses techniques for maximizing the photodetector linearity. As an alternative to the link dynamic range improvement methods discussed thus far in this subsection, one can also opt to design special circuits that generate distortion products of identical magnitude but opposite phase relative to the distortion produced by the nonlinear modulation and photodetection processes. Such circuit-based techniques for improving a system’s dynamic range comprise a large topic area because they are generally applicable not merely to analogue fibre-optic links but more generally to any nonlinear analogue network. However, a few approaches that have been applied specifically to fibre-optic links are worth mentioning as closing remarks for this subsection. Nazarathy et al. [53] thoroughly investigated two such circuit-based techniques – predistortion and feedforward distortion – for their ability to counteract nonlinearity in long-distance (30 km) CATV links. Patterson et al. [54] combined these two techniques into a linearization architecture they called ‘quasi-feedforward compensation’ that successfully reduced both the second- and third-order distortion in broadband links. Some work by Wu et al. [55] concentrated solely on electronic predistortion, which has the advantage of greater simplicity than feedforward compensation but depends on the modulation device characteristics remaining very stable in its operating environment. Stapleton et al. [56] later showed how feedback could be used to update the predistorter’s parameters periodically so that it adapts to changes in device nonlinearities caused by environmental factors. This technique has more recently been expanded upon and refined by a research group at UCLA [57].

6.4 Summary In this chapter, the complicated task of designing an analogue fibre-optic link to meet specified system performance requirements has been broken down into a series of critical questions that the designer should ask of himself or herself. The options the designer has when attempting to answer to these questions have been outlined and discussed.


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7 Fibre Radio Technology Dalma Novak, Ampalavanapillai Nirmalathas, Christina Lim, and Rod Waterhouse

7.1 Introduction Radio networks provide users with the attractive feature of untethered connectivity for a range of applications including cellular communications, wireless local area networks (LANs) and personal area networks (PANs), and broadband fixed wireless access. The increasing demand for broadband services has also led to the consideration of wireless networks operating at higher frequencies and extending well into the millimetre-wave band (26 GHz and above) where the total capacity of an antenna base station (BS) can approach 1-2 Gb/s [1]. The application of optical fibre links in radio communication networks for the transport and distribution of radio signals is now well and truly a reality. The mobile and fixed wireless systems where such fibre radio technology is now finding application include indoor distributed antenna systems offering mobile radio services, current and next generation microcellular mobile networks, indoor wireless local area networks and fixed broadband radio access which can provide very high bandwidth services to users. In this chapter we present an overview of fibre radio systems and review the associated enabling technologies, sub-systems and system architectures. We also describe some of the technical challenges that must be addressed for the successful integration of wireless and optical networks. The chapter is organized as follows. Section 7.2 provides a brief introduction to the evolution of wireless networks with a description of the characteristics of current and future radio services. The ability to transport radio signals over optical fibre with low loss leads to the consideration of the integration of these two technologies, which is the focus for Section 7.3. Section 7.4 then describes some key enabling technologies for the deployment of such fibre radio systems with an emphasis on the possible signal transport schemes. The advantages and drawbacks of the various techniques are outlined and the required hardware described. A comparison between the signal transport approaches from a performance perspective is also made. The successful integration of optical and radio networks also leads to a consideration of applying optical networking concepts and possible technologies to enable


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wavelength division multiplexing in fibre radio systems which are explored in Section 7.5. Section 7.6 then focuses on the implementation of the antenna base station in fibre radio networks and the key requirements for these sub-systems. Enabling technologies that will reduce the complexity of the base station architecture and lead to more cost effective solutions are discussed as well as new opportunities for optimizing the base station performance. Finally we present some concluding remarks on the future potential of fibre radio technology in Section 7.7.

7.2 The Evolution of Radio Networks In the past, the benefits of untethered connectivity and high mobility have driven the demand for wireless services. However, with the proliferation of a variety of new data communication services, the demand for broadband wireless networks is increasing rapidly. With the current generation of mobile communications, the available spectral bandwidth is limited which prohibits the provision of broadband services for a large customer base. To overcome this problem, the use of smaller radio coverage areas in microcellular and picocellular wireless networks has attracted attention as a means to increase capacity by enabling more efficient use of the limited available bandwidth. Future third- and fourth-generation mobile communication systems operating at higher microwave frequencies (< 2.5 GHz) will provide larger bandwidths; however, these are still limited to only several hundred MHz [2]. Similar carrier frequencies are also being used in new wireless LANs such as the 802.11 IEEE standards that are currently being developed based on unlicensed spectral bands near 2.4 GHz and 5 GHz. These new indoor wireless LANs offer higher data rates to users (without the mobility) with a shared capacity of up to tens of Mb/s [3]. As a result of the problem of spectral congestion limiting the provision of broadband services to users in mobile and fixed wireless networks operating at lower microwave frequencies, radio networks operating at higher frequencies, in particular the millimetre-wave (mm-wave) frequency band, are gaining more attention. Such radio networks offer the ability to provide truly broadband services to users (with total capacities extending up to multiple Gb/s [4]) by utilizing the enormous bandwidth available in a number of these frequency bands. One such mm-wave wireless access scheme is the local multipoint distribution system (LMDS) that operates in the frequency range of 27–31 GHz [5]. Due to the large atmospheric absorption that occurs at mm-wave frequencies, such radio networks operatewith significantly smaller wireless coverage areas which also enable efficient radio frequency re-use schemes. In these pico- or microcellular wireless network architectures, the totalcapacityofanantennaBScanbeaslargeas1–2 Gb/swithalargenumberofBSsrequiredpercell. Along with the progress in increasing the bandwidth offered to users in wireless networks, the nature of the data has changed dramatically, as has also occurred in wired telecommunication networks. Since data traffic now exceeds voice traffic in wired networks, the dominant data transport protocol in such networks is now the internet protocol (IP) [6]. As a result, the application of IP to wireless networks is currently being investigated for the efficient transport of data over noisy wireless channels.

7.3 Fibre Radio Systems – the Application of Optical Fibre Distribution Schemes to Wireless Networks The implementation of cost-effective radio networks poses a number of technical challenges, such as the design of small, compact and low-cost base stations which are also functionally

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Fibre Radio Technology

Figure 7.1

Schematic depicting a generic ‘fibre radio’ network architecture

simple in order to reduce maintenance costs. In addition, an appropriate backbone network to interconnect multiple base stations with the central office (CO) which performs switching and routing functions must be provided. The advantages of optical fibre as a transmission medium – such as low loss, large bandwidth characteristics, small size and low cable cost – make it the ideal solution for efficiently transporting the combined radio signals from the central office to the remote antenna sites. The generic architecture of such a ‘fibre radio’ system is shown in Figure 7.1. Here the complexity associated with the radio signal processing functions and electronics can be located back at the CO which also leads to other advantages, in addition to simplifying the BS itself. These include simplification of the management of the radio network as well as the provision of transparency since upgrades to the network can be carried out at the CO rather than at the BS. Much progress has been made in the last few years in the development of optical wavelength division multiplexed (WDM) networks for the provision of high capacity communications between major telecommunication nodes in metropolitan areas. In such metropolitan area networks (MANs), nodes are connected by optical fibre links which have the capability of supporting multiple wavelength channels each carrying high data rates, up to 10 Gb/s. In addition, self-healing WDM ring topologies have been developed to give fully interconnected connectivity with a very high level of built-in protection against unexpected failures in some parts of the network. The continued installation of fibre networks for the introduction of new services in the metropolitan area could also be exploited to support the development of future broadband wireless access networks. Therefore, for fibre radio systems to be a viable technology, it is essential that they are able to merge and integrate with current wired WDM network infrastructures [7]. Current wireless architectures are characterized by centralized switching nodes that are interconnected to geographically distributed antenna BSs via microwave links. In future broadband picocellular network architectures, due to the large capacity and large number of BSs, radio networks will be dimensioned in such a way that there will be a number of clusters of BSs serviced by a switching node. For a large metropolitan area, a number of such switching nodes will therefore be required which will be interconnected via an optical MAN ring architecture, as shown in Figure 7.2. For each cluster of BSs, the switching centre provides the role of a CO where switching and routing functions are performed. In addition, the smaller wireless coverage areas at mm-wave frequencies and the subsequent need for more BSs has

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Figure 7.2 Schematic showing the general concept of the interface between a fibre radio system employing WDM and a metropolitan WDM network

driven the development of system architectures where the functions relating to the access point in a multi-user environment are also carried out at the CO. Such a centralized control scheme enables the deployment of BSs with significantly reduced functionality and complexity. In the architecture shown in Figure 7.2, WDM channels can be dropped or added into the optical WDM MAN via the switching centre. Two possible WDM fibre radio architectures are depicted in Figure 7.2: CO1 is connected to several remote nodes (RNs) via an optical ring while the second central office (CO2) feeds its RNs via a star-tree arrangement [8]. In either arrangement individual wavelengths are demultiplexed from the WDM signal, by being dropped from the optical WDM MAN via the remote nodes which direct the optical signals to antenna BSs for signal detection and radio distribution. In the upstream direction, radio signals generated at the customer site are up-converted in frequency and radiated to the BS where an electrical-to-optical (E/O) conversion process takes place before the signal is directed to the CO for further processing. The application of wavelength division multiplexing concepts and technologies to fibre radio networks also offers advantages. For example WDM and photonic routing can simplify the network architecture since it is possible to have a shared feeder in multipoint networks (leading to a reduction of fibre-pairs in a star-tree arrangement, for example). In addition, WDM offers flexible traffic routing per cell (different wavelengths going to a particular BS can carry different data rates), independent handling of broadcast and interactive services, and other network management advantages including protection features. WDM also provides increased flexibility and scalability when upgrading capacity in the fibre radio network, whether it be by deploying additional base stations, introducing new services, increasing the quality of service or ensuring transparency to the service that is introduced. One of the key challenges in implementing fibre radio systems is developing suitable optical network architectures for efficient distribution of the radio signals while also maintaining a simple and compact BS configuration. This is particularly important for radio carrier frequencies in the mm-wave frequency range, where the deployment of mm-wave fibre


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wireless systems will require the installation of a larger number of BS units. At the antenna BS, the integration of an optical source and photodetector with electronic components such as mixers, amplifiers and diplexers, as well as printed antennas as the radiating elements, will enable the design and development of simple and lightweight BSs for easy installation on building walls and corners, street lights and telephone poles. The particular architecture of the optical network in the fibre radio system will ultimately determine the required hardware at the central office, the remote node and the base station itself. In the following sections, we describe the enabling technologies for the implementation of fibre radio networks both from the perspective of the signal transport scheme, as well as the necessary devices and components including optical sources and modulators, photodetectors and other optical devices, as well as the integration of the photonic and electronic devices. Readers are also referred to other relevant chapters in this book which give more complete overviews of device technologies for microwave photonic system applications.

7.4 Enabling Technologies for Fibre Radio Systems – Signal Transport Schemes 7.4.1 RF over Fibre The most straightforward approach to interconnecting remote antenna base stations in a fibre radio system is via an optical fibre feed network which can transport the wireless signals directly over the fibre at the radio carrier transmission frequency without the need for any subsequent frequency up- or down-conversion at the BSs. This signal transport scheme is known as ‘RF over fibre (RoF)’ and a schematic depicting the key optical and RF devices required at both the CO and the remote BS for downstream signal transmission, is shown in Figure 7.3. Such a configuration is attractive in microcellular and picocellular networks operating in the mm-wave frequency region where a large number of BSs are required to provide wide geographical coverage. In addition to LMDSs these applications include fixed wireless access (38 GHz) and indoor wireless LANs (60 GHz). The RF-over-fibre transport scheme also enables centralized control and remote monitoring of the radio signal distribution via the fibre backbone network. As shown in Figure 7.3, at the central office the wireless data obtained from the trunk network is modulated onto a number of lower intermediate frequencies (IFs) which are then combined to form a subcarrier multiplexed (SCM) signal. This SCM signal is upconverted to the wireless transmission frequency using a local oscillator (LO) source located at the CO which then

Figure 7.3 Schematic diagram depicting central office and remote antenna base station hardware for downstream signal transmission via RF over fibre

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modulates the output of a semiconductor laser (an external modulation scheme is depicted in Figure 7.3). At the remote BS, the analogue optical signal is detected, amplified, filtered and directed to an antenna for free-space transmission to a customer unit. Note that Figure 7.3 depicts only the required CO and BS hardware for downstream wireless transmission. Upstream transmission from the CU to the BS and subsequently back to the CO will require a mechanism for modulating an optical source located at the BS at the radio carrier frequency, and photodetection of this signal back at the CO. Commercial fibre radio systems based on RF-over-fibre signal transport schemes have been developed; however, the only available fibre radio products based on RF over fibre that are currently commercially available are at lower wireless frequencies for services such as cellular and PCS (personal communication system). These systems work on direct modulation of lowcost lasers, either multimode Fabry–Perot (FP) or single-mode distributed feedback (DFB) devices [9], depending on the application and the required linearity of the link. For example, Andrew Corporation market a fibre-optic based distributed antenna system called Britecell for indoor wireless coverage [10]. This system is capable of servicing 800 MHz and 2.5 GHz radio systems (cellular or wireless LANs) and since the system is RF-over-fibre based, it is also technology transparent since it can handle multiple air interface schemes. The Britecell system transmits light at a wavelength of 1.3 mm over single-mode fibre with the remote antenna located up to 3 km away. A multiband (GSM cellular 900 MHz and 1800 MHz) distributed antenna system based on RF-over-fibre technology to improve wireless coverage within buildings or in difficult areas is also available from Remec [11]. The maximum distance between the CO and remote antenna BS in this product is 15 km. For lower frequency radio networks, research is also now being focused on RF-over-fibre signal transport based on direct modulation of narrowband uncooled DFB laser diodes at 5 GHz for applications such as wireless LANs and fourth-generation mobiles [12]. The implementation of fibre radio systems based on RF-over-fibre signal transport for wireless systems operating at higher wireless transmission frequencies presents more challenges, particularly at mm-wave frequencies. One of the main issues for implementing such fibre radio architectures with RF over fibre lies in the search for both suitable highspeed optical modulation techniques that have the ability to generate mm-wave modulated optical signals and also high-speed photodetection techniques that directly convert the modulated optical signals back into mm-wave signals in the electrical domain. The simplest and most mature method for generating a high-frequency modulated optical signal is to modulate the optical carrier by an external modulator. For their application in mm-wave fibre radio systems, however, it is imperative that these devices exhibit a number of characteristics in addition to the required broad bandwidth. These features include low mm-wave drive voltages, good linearity, high bias stability, high optical power-handling ability and also low optical insertion loss. Mm-wave photodetectors (PDs) with high saturation powers and large electrical output powers are very useful in the development of antenna base stations with fewer electronic amplifiers [13]. The PD saturation power is limited by the nonlinearity of its response and it has been shown that this nonlinearity is caused by a decrease in the electric field and reduction in the carrier velocity due to a space-charge effect. A PD structure that can overcome the drawback of a low saturated carrier velocity is the uni-travelling-carrier (UTC) photodetector in which only electrons travelling at a velocity much higher than the saturation velocity, contribute to the space-charge effect. An optical receiver module incorporating a UTC PD with


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a bandwidth in excess of 100 GHz and maximum saturation output power of 11 mW has been reported [14]. As is clear from Figure 7.3, the scheme of RF-over-fibre signal transport has the direct advantage of realizing simple base station architectures. One issue, however, is that such systems also require optical components that exhibit good analogue performance over the bandwidth required by the wireless network characteristics. While this is more straightforward to achieve at lower radio frequencies using well-established approaches for linearization of directly modulated and externally modulated optical sources [15], the task becomes more difficult for mm-wave fibre radio systems employing RF-over-fibre signal transport [16]. Another drawback of this signal distribution scheme is the significant effect of fibre chromatic dispersion (at a wavelength of 1.55 mm) on the detection of the optical signal and subsequent recovery of the RF carriers, both at the BS and the CO [17]. When optical carriers are directly modulated with mm-wave signals in a conventional way, the resulting optical spectrum (to a first-order approximation) consists of the optical carrier and a modulation side-band on each side of the optical carrier spaced at a frequency from the carrier equal to the centre frequency of the modulating mm-wave signal. As the mm-wave modulated optical signal propagates through standard optical fibre, each modulation side-band will experience different amounts of phase shift with respect to the optical carrier as a result of fibre chromatic dispersion. When the optical signal is finally detected at the receiver by a square-law photodetector, each side-band will beat with the optical carrier producing two mm-wave signal components with equal amplitudes and different phase values. The vectorial addition of these two signals will then yield the resultant mm-wave signal and the RF power of the resulting signal will vary as a function of phase difference that depends on both the length of the fibre link and the dispersion parameter. These resulting RF power variations will lead to degradations in the carrier-to-noise ratio (CNR) of the link [17, 18]. As the RF frequency increases, the impact on the CNR becomes dramatic; for example, a 3 dB power penalty in detected RF power occurs for a fibre link distance of 6 km in an externally modulated link operating at 20 GHz, with the same penalty arising after a distance of only 0.7 km for radio systems operating at 60 GHz. Considerable research effort has been devoted towards developing RF-over-fibre transport schemes which are either dispersion-tolerant [19, 20] or based on dispersion compensation techniques such as chirped fibre Bragg grating filters [21], self-phase modulation in fibre [22] and mid-span phaseconjugation [23]. A key advantage of dispersion-tolerant signal transport schemes is their flexibility since ideally they can be made independent of the fibre length, wireless carrier frequency and the fibre dispersion parameter and therefore do not require a priori knowledge of the characteristics of either the optical distribution architecture or the wireless network. Figure 7.4 shows one such dispersion-tolerant modulation technique based on external modulation of an optical carrier using a dual-electrode Mach–Zehnder modulator (DE-MZM) [24]. In Figure 7.4 the DE-MZM is biased at quadrature and driven with signals at the two RF electrodes which are p/2 out of phase. Such an arrangement produces an optical modulation format known as optical single sideband with carrier (OSSB þ C), which has also been demonstrated via the use of an integrated modulator structure [25] or an optical filter that removes one of the optical modulation sidebands [26–29]. In contrast to these techniques, the DE-MZM approach for generating OSSB þ C modulation does not rely on the characteristics of the optical filter [27, 28] and the suppression of the sideband is limited only by the precision with which

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DC bias Bias Optical input

MZM

Optical output

θ = π/2 Electrical Optical RF input

Figure 7.4 Dispersion-tolerant modulation scheme for fibre radio systems based on OSSB þ C modulation obtained with a single DE-MZM

the OSSB þ C generator can be practically implemented (the two RF drive signals must also be matched in amplitude to achieve maximum sideband suppression) [24]. As described earlier, a key challenge in implementing mm-wave fibre-radio systems based on RF-over-fibre technology is the development of suitable high-speed optical modulation schemes that have the ability to generate mm-wave modulated optical signals efficiently as well as the need for high-speed photodetectors with good conversion efficiencies. A great deal of research has been carried out on investigating techniques for the generation of mm-wave modulated optical signals based on optical heterodyne or self-heterodyne approaches as well as optical nonlinearity generation methods. Although a thorough description of the various techniques is outside the scope of this chapter, a number of approaches which may have real potential for being used in mm-wave fibre-radio systems were recently summarized in [30]. Key attributes which will enable such feasibility to be achieved are schemes that have demonstrated the ability to support data modulation, are tolerant to the effects of fibre chromatic dispersion and can be made cost-effective in their practical implementation. In addition to fibre chromatic dispersion, the performance of the fibre radio system is also affected by amplified spontaneous emission (ASE) noise from any optical amplifiers that may be located within the optical link. ASE noise leads to an increase in the phase noise of the received radio signal at the antenna BS which results in degraded system performance when transmitting higher-order radio modulation formats. This effect is particularly pronounced at longer fibre lengths, typically greater than 70 km [31].

7.4.2 IF over Fibre Figure 7.5 shows a schematic diagram of the basic hardware required at the CO and remote BS for downstream signal transmission in a fibre radio system based on the distribution of the radio signal at a lower intermediate frequency (IF), the so-called ‘IF-over-fibre’ signal transport scheme. Here IF refers to microwave frequencies in the L band (such as 1–2 GHz). Wireless networks offering services such as PCS can therefore use this transport scheme directly to transport the radio signals from the CO to the BS and finally through the air interface, without any further frequency conversion. However, other radio applications at higher frequencies such as LMDSs will require frequency up- and down-conversion at the BS when using this transport scheme.


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Figure 7.5 Schematic diagram depicting central office and remote antenna base station hardware for downstream signal transmission via IF over fibre

In contrast to the transmission of higher frequency wireless signals over optical fibre, the effects of fibre chromatic dispersion on the optical distribution of IF signals are reduced significantly. For comparison, a signal at 2 GHz will experience a signal-to-noise reduction of less than 0.1 dB when recovered after transmission through 7 km of standard optical fibre while a signal at 38 GHz will suffer a CNR penalty of over 10 dB after propagation over the same fibre transmission distance. In addition, IF signal transport schemes have the advantage of only requiring optoelectronic devices with reduced bandwidths. For example, IF-over-fibre signal transport for upstream signal transmission has been reported using the direct modulation of a low-cost optical source such as a light emitting diode with a bandwidth of less than 2 GHz [32], an uncooled FP laser [33] or an electro-absorption modulator [34]. Downstream IF-over-fibre signal transport has used both direct [35] and external [36] modulation of semiconductor lasers. The IF-over-fibre signal transport approach also offers the advantage that readily available mature microwave hardware can be utilized at the BS although the requirement for frequency conversion at the BS again complicates the BS architecture as the frequency of the wireless application moves into the mm-wave frequency regime. The complexity of the BS hardware now increases since a high-frequency local oscillator (LO) and mixers for the frequency conversion processes are required (as shown in Figure 7.5). This may also be a limitation when considering the ability to upgrade or reconfigure the radio network with the provision of additional radio channels or the implementation of required changes in RF frequency. The subsequent requirement for an LO at the antenna BS in mm-wave fibre-radio access networks employing IF-over-fibre signal transport schemes, can be overcome by remotely delivering the LO signal from the central office [36–38]. This also enables the control of the LO signals themselves to be centralized thereby simplifying the architecture of the BS. This LO signal can be delivered as RF over fibre via OSSB þ C modulation in order to avoid fibre dispersion effects [37, 38] or as IF over fibre in conjunction with a sub-harmonic mixer located at the antenna BS [36]. Several methods have been reported for recovery of the LO signal in fibre-radio systems employing remote LO delivery, which can be achieved using either electrical [34, 36, 37] or optical [38] filtering techniques. The more conventional technique of frequency conversion at the BS when using IF-over-fibre transport schemes, is detection of the IF signal and then electronic frequency up-conversion using an electronic mm-wave mixer and LO. Frequency translation, however, can also be accomplished in the optical domain, by using the nonlinearity of an optoelectronic component, such as an external electro-optic modulator. One drawback of this approach, however, is the sensitivity to modulator bias voltage drift which can significantly impact the tolerance of the scheme to fibre dispersion effects [39].

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Several commercial fibre-radio products employing IF-over-fibre are often based on the distribution of radio signals over multimode fibre (MMF) since many buildings have a legacy of optical fibre infrastructure networks based on multimode fibre. For example LGC Wireless product LGCell is based on this concept [40]. Recent work has also investigated the possibility of transmitting higher-frequency radio signals as RF-over-fibre with multimode fibre by exploiting the passband response of MMF and operating the system at a frequency beyond the response minimum. For example, the transmission of a 2 Mb/s 32-QAM signal at 2 GHz over 1 km of MMF at 1300 nm was demonstrated in [41] with very little penalty. Recent research investigations have also considered the use of new vertical cavity surface emitting lasers (VCSELs) operating at 850 nm, which are currently being developed for a range of applications including Gigabit Ethernet. VCSELs are low-cost devices and their application in analogue optical links has been the subject of several papers in the last few years (for example [42]). The transmission of RF signals from VCSELs over multimode fibre is also now being reported for applications which include wireless LANs [43].

7.4.3 Baseband over Fibre The third technique that can be used to transport the data-carrying radio signals between the CO and the remote antenna base station in fibre radio systems is via a ‘baseband-over-fibre’ approach which is depicted in Figure 7.6. As shown in Figure 7.6, in the baseband-over-fibre approach the radio information for the radio carriers is transported to the BS as a time-division multiplexed data stream. The individual data channels are then demultiplexed, up-converted to intermediate frequencies and then undergo a further frequency up-conversion to the required radio frequency band via a local oscillator located at the BS. Upstream signal transport via baseband over fibre can also be accomplished by down-converting the received wireless carriers at the BS to baseband before transmission back to the CO. As with IF-over-fibre signal distribution, the effect of fibre dispersion is less severe for fibre transmission of digital baseband data signals with chromatic dispersion having a minimal effect on the delivery of subgigabits per second data streams over links less than 100 km in length. In addition, fibre radio systems based on IF- and baseband-over-fibre transport schemes can readily exploit the use of mature and reliable RF and digital hardware for signal processing at the CO and BS as well as low-cost optoelectronic interfaces with lower bandwidths. However, the need for frequency conversion at the BS complicates the BS architecture design as the air interface frequency increases. The additional LO source and

Figure 7.6 Schematic diagram depicting central office and remote antenna base station hardware for downstream signal transmission via baseband over fibre

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extensive signal processing hardware (frequency conversion and multiplexing and demultiplexing of signals from many users) in the antenna BS may also limit the upgradability of the overall fibre radio system based on baseband-over-fibre signal transport. To overcome this problem, dispersion tolerant LO transport has been investigated, using either a dualfrequency approach with only half the LO frequency required [44, 45] or OSSB þ C modulation [46]. Re-use of the LO delivered remotely from the CO for frequency downconversion at the BS and upstream data transmission, has also been achieved [44, 45]. Given the availability of digital, microwave and millimetre-wave hardware with the required performance, wireless networks ranging in operating frequency from PCS at 1.8 GHz to mmwave indoor wireless LANs at 58 GHz may be able to incorporate baseband-over-fibre signal transport schemes. One currently available commercial fibre radio product based on digitalover-fibre transport is the Digivance system developed by ADC which provides one integrated platform for transporting and distributing both 800 and 1900 MHz radio signals [47]. In this system, the CO digitizes the RF spectrum then digitally transports it over single mode fibre to remote antenna sites, up to a distance of 20 km away. This digital RF transport scheme is capable of handling multiple radio access standards and modulation schemes simultaneously and the distance between CO and BSs is limited only by the time delay requirements of these air interface standards.

7.4.4 Radio Signal Transport Scheme Trade-offs In considering the best approach for radio signal transport in fibre radio systems, a proper assessment of the various trade-offs with each technique also requires a consideration of the performance differences between the schemes. Figure 7.7 shows bit-error rate (BER) measurements for all three generic transport schemes for LMDS signal transmission over 0–50 km of SMF with 10 km increments. From the results it can be seen that the power penalties for transmission over 50 km are less than 0.5 dB for the three transport techniques with the sensitivity of the baseband-over-fibre technique being approximately 4 dB better than IF over fibre and about 7 dB better than RF over fibre. These results are not unexpected since, compared

RF over fibre

-4

10

Log (BER)

-3

-5 Baseband

-6 -7 -8 -9 -10 -11

IF over fibre

over fibre

-28

-26 -24 -22 -20 -18 Received optical power (dBm)

-16

Figure 7.7 Measured BER for a LMDS fibre radio system with baseband over fibre (622 Mb/s, fLO ¼ 29 GHz), IF over fibre (fIF ¼ 2 GHz, fLO ¼ 27 GHz) and RF over fibre (fRF ¼ 29 GHz with OSSB þ C modulation)

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to the baseband- and IF-over-fibre transport methods, RF over fibre will require the most received optical power upon detection to obtain the same bit-error rate of the recovered data due to the decreased optical link efficiency as the radio carrier frequency increases. At the same time, however, the improved sensitivity of the baseband- and IF-over-fibre transport methods for mm-wave fibre radio systems comes at the expense of requiring a stable high-frequency LO with low phase noise located at the BS. As described earlier, implementing remote delivery of the required local oscillator signal can reduce the complexity of the antenna BS hardware in higher-frequency fibre radio systems incorporating IF- or baseband-over-fibre signal transport. Recovery of the LO signal at the BS can then be achieved using either optical filtering techniques or electrical filtering after photodetection. Figures 7.8 and 7.9 show measured BERs for transmission over 0 to 50 km for IF-over-fibre and baseband-over-fibre transport schemes, respectively, incorporating remote LO delivery and recovery of the LO carried out using electrical and optical techniques. As is clear from Figure 7.8, the performance of the IF-over-fibre transport scheme with electrical LO extraction is better compared to the optical LO extraction method when delivering a fundamental LO signal remotely. This occurs because recovery of the LO at the BS using an optical filtering approach requires not only the LO optical sideband but also half of the optical carrier. Hence, the IF signal generation is less efficient than the electrical LO recovery scheme where the IF signal is generated using the entire optical carrier. When the LO signal is transported at fLO/2 as in the baseband-over-fibre transport scheme [44, 45], the sensitivity performance shows little variation between either the optical or electrical LO recovery methods as shown in Figure 7.9. In this situation, optical extraction of the LO does not require the optical carrier as it does in the IF-over-fibre case therefore the performance of the baseband-over-fibre signal transport method with optical and electrical LO recovery is similar. If the performance of the RF-over-fibre signal transport scheme is then compared to that of either baseband- or IF-over-fibre with remote LO delivery, the RF-overfibre technique now shows the best sensitivity of the three approaches. Taking into account the various trade-offs it is clear that the RF-over-fibre transport scheme can result in a simple BS design with reasonable performance and may therefore be the preferred transport scheme of the three approaches. However, the higher cost of high-speed optical/electrical interfaces with

IF over fibre with optical LO extraction

Log10(BER)

-3 -4 -5

IF over

fibre with -6 -7 electrical LO extraction -8 -9 -10 -11 -13 -12 -11 -10 -9 -8 Received optical power (dBm)

-7

Figure 7.8 Measured BER for a LMDS fibre radio system with IF over fibre and remote LO delivery ( f IF ¼ 2 GHz, fLO ¼ 27 GHz) and LO recovery via electrical and optical extraction

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Log10(BER)

-3 -4

Baseband over fibre with electrical LO extraction

-5 Baseband -6 over fibre with -7 optical LO -8 extraction -9 -10 -11 -8 -7 -6 -5 -4 Received optical power (dBm)

-3

Figure 7.9 Measured BER for a LMDS fibre radio system with baseband over fibre and remote LO delivery (622 Mb/s, fLO ¼ 29 GHz) and LO recovery via electrical and optical extraction

adequate performance characteristics is a key factor that must also be borne in mind when considering which technology to implement in mm-wave fibre radio systems.

7.5 Wavelength Division Multiplexing in Fibre Radio Systems As discussed in Section 7.2, the use of wavelength division multiplexing in fibre radio systems is being actively investigated in order to exploit the various benefits of optical networking, as well as to simplify the management of the radio network, the fibre radio network architecture and the design of the base station itself [48]. WDM can also play a key role in the design of mm-wave fibre radio systems where line-of-sight constraints imposed by signal propagation characteristics at mm-wave frequencies requires a sectorized antenna interface at the BS in order to optimize the antenna coverage area [49]. Here the distribution scheme can be further simplified using WDM in conjunction with sub-carrier multiplexing where a different WDM channel feeds each BS [8] and different SCM channels can drive the individual antenna sectors. A key issue that arises in the application of WDM to mm-wave fibre radio systems is the need to merge or integrate with current WDM infrastructures [7], in particular metropolitan area and local optical access networks. In addition, there is the challenge to improve the resulting optical spectral efficiency in the network since WDM channel spacings in excess of 100 GHz will be required if using conventional double sideband optical modulation techniques while the radio signal (spaced at the mm-wave frequency from the optical carrier) itself is only modulated with an information bandwidth of less than 2 GHz. The use of OSSB þ C modulation to overcome fibre dispersion effects in mm-wave fibre radio systems naturally leads to an increase in spectral efficiency since one of the modulation sidebands is removed.However, the spectral efficiency can be further improved via the use of novel wavelength filtering schemes [50, 51]. One such approach is shown in Figure 7.10 where wavelength interleaving is used to increase optical spectral efficiency [50]. Here the WDM channels that originate at the CO are multiplexed together via a wavelength-interleaved multiplexer (WI-MUX) and transported to remote nodes feeding a particular antenna BS. The RN selects the optical carrier at the specified wavelength and the corresponding optical sideband using a wavelength-interleaved optical add-drop multiplexer (WI-OADM).

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In the architecture shown in Figure 7.10, the upstream radio signals are carried by a WDM channel at the same wavelength and inserted back into the network via the same WI-OADM. The particular filtering characteristics required from such a WI-OADM can be achieved via the implementation of multiple fibre Bragg gratings (FBGs) in cascade in order to filter out the desired carrier wavelengths and their sidebands, or via novel FBG designs such as one grating incorporating multiple phase shifts [52]. In order to make use of existing wired WDM infrastructure as much as possible and enable cost effective realizations of fibre radio systems, it is essential that such networks are able to be merged and integrated with conventional WDM technologies [53]. Figure 7.11(a) shows a schematic diagram of such a scenario where a WDM fibre radio system incorporating

Figure 7.10 Schematic diagram of a wavelength-interleaving technique to increase optical spectral efficiency in mm-wave fibre radio systems employing OSSB þ C modulation


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wavelength interleaving in an optical ring network architecture interconnects with an optical WDM MAN backbone with 100 GHz channel spacing. Multiple blocks of 100 GHz of optical spectrum containing the interleaved WDM channels are dropped from the MAN backbone via the CO which are then distributed to RNs and a selection of wavelengths dropped at each RN. At the RN, a 100 GHz wavelength band containing a few wavelength-interleaved channels will then be distributed to the designated BS to feed the sectorized antenna interface, as shown in Figure 7.11(b). It has been shown that the way in which the interleaved WDM channels are arranged and allocated within the wavelength block can have an impact on the performance of such a merged fibre radio system [53, 54].

7.6 Base Station Technologies in Fibre Radio Systems 7.6.1 Simplifying the BS Architecture A key aspect of the successful deployment of fibre radio systems is the development of appropriate antenna base station technologies. In addition to the required optical and electrical

Figure 7.11 (a) Schematic diagram of a WDM fibre radio ring architecture merged with a 100 GHz WDM MAN incorporating wavelength interleaving and feeding a four-sector antenna interface, and (b) the WDM channel allocations within a 100 GHz block

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performance, these optical/electrical/air interfaces must feature at least three interrelated characteristics: high efficiency, low cost and small size. It is important that the BSs are as efficient as possible in terms of both power consumption and link efficiency. Since mmwave fibre radio networks will typically require a larger number of BSs due to the smaller coverage area in mm wave wireless networks, the amount of DC power required to operate the remote antenna units must be minimized. In practice this is typically achieved by reducing the component count within the BS module itself. From this perspective it would be expected that the RF-over-fibre signal transport scheme would enable the development of antenna BSs with lower power consumption due to the smaller component count required. However, a consideration of the link efficiency must also be taken into account. For example, mm-wave photodiodes are typically less efficient than smaller bandwidth devices and therefore higher gain mm-wave amplifiers may be required to boost the detected RF power to the appropriate levels needed for free-space transmission. Such high-gain mm-wave amplifiers will consume more power than lower-gain components thereby offsetting some of the perceived power dissipation advantages of antenna BSs with mm-wave optical/electrical interfaces. The concept of a completely passive base station for fibre radio systems operating at frequencies below 2 GHz has been demonstrated based on the use of a single electro-absorption modulator (EAM) [55]. The one EAM transceiver operates as both a receiver for the downlink path by detecting only some of the downstream optical signal, and then acts as a modulator (with the upstream radio signal) of the remainder of the downstream optical carrier, which is then sent back to the CO. Full duplex operation can be achieved using a frequency division duplex arrangement. The use of a single EAM for dual photodetection and optical modulator functions in an active BS has also been reported for higher-frequency fibre radio systems based on RF over fibre in combination with additional dispersion compensation [56], or IF over fibre for a 60 GHz fibre radio link [57]. Reuse of the downstream optical carrier can also be carried out in fibre radio systems employing OSSB þ C modulation for dispersion tolerant RF-over-fibre signal transport [58]. Figure 7.12 shows an optical interface of an antenna base station that could be incorporated in a WDM fibre radio system. The location of the OADM could be in a different location, for example a remote node, or at the BS itself depending on the network roll-out plan. Several techniques could be implemented for recovery of the downstream optical carrier using either low-cost optical couplers and FBGs or more specialized grating filters in conjunction with an optical circulator [58]. Figure 7.12 shows the use of OSSB þ C modulation for dispersion tolerant RF-over-fibre signal transport in both the downstream and upstream directions. An optical interface for fibre radio antenna BSs that is dispersion tolerant, incorporates wavelength reuse and also supports a wavelength interleaved architecture, has also been demonstrated [59].

7.6.2 Optimizing Base Station Performance As described earlier, one of the key benefits of the RF-over-fibre signal transport scheme is simplification of the BS hardware. This reduction in BS equipment functionality along with the need for low-profile BS terminals requires the base stations to be both compact and the various interfaces (optical, RF and antenna) integrated efficiently. The BS terminal aims to undertake efficiently the process of optical-to-radio conversion for the downlink and viceversa for the uplink. Three potential integration approaches can be implemented in order to realize a

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Downstream RF signal Photo-detector

Downstream optical fibre

Optical add drop multiplexer

BS RF interface

Optical carrier recovery

Hybrid coupler

Upstream RF signal

DCRF

RF

Upstream optical fibre

Dual-electrode MZM

Base-station interface OPTICALoptical INTERFACE

Figure 7.12 reuse

Simplified optical interface of a fibre radio base station incorporating optical wavelength

miniaturized BS: hybrid, hybrid integrated circuit (HIC) and monolithic integrated circuit (MIC) technologies, each with its advantages and disadvantages. Due to its maturity, the hybrid approach is currently the most commonly used integration technique and also offers the advantage that mature component technologies used in other systems can be used. However, the hybrid approach is very labour intensive and the interconnection of separate packaged modules each mounted in different transmission technologies, can lead to reliability and parasitic issues. The simplest integrated circuit approach is based on HIC technology where each subelement function in the BS is implemented on individually optimized islands of materials and these laminates are then interconnected by small sections of planar transmission lines and bond wires. All of these sub-elements are housed on a common mount in order to minimize the overall size of the module. The benefits of incorporating HIC technology include its flexibility and cost-effectiveness although BSs using this component integration approach often require manual ‘trimming’ to achieve optimum performance and therefore can be labour intensive. In addition, when developing base stations for mm-wave fibre radio systems accurate bond wiring procedures must be implemented. An example of the hybrid integration approach is shown in Figure 7.13, which shows a photograph of a broadband (28–43 GHz) antenna BS module developed for downstream radio signal transmission in a mm-wave fibre radio system with multi-service capability [60]. The overall size of this unit was 45 20 10 mm and also includes a diplexer and filter for recovery of a mm-wave LO signal delivered remotely from the CO. It is clear that by incorporating printed circuit technology (also used for fabrication of the mm-wave antenna) and developing appropriate alignment methods, a BS module of extremely small size can be achieved [61]. A number of hybrid integrated circuits for high-frequency fibre radio systems have been reported covering a range of mm-wave frequencies and including various functionalities. An early narrowband fibre radio transmitter operating at 60 GHz and comprising a photodiode, MMIC preamplifier and amplifier, and a planar antenna was presented in [62] while a packaged

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Figure 7.13 Photograph of an antenna BS based on a hybrid integration approach for application in mmwave fibre radio systems

60 GHz optical transceiver incorporating an EAM was reported in [63]. More recently a photonic emitter based on HIC technology comprising a UTC photodiode and an HEMT amplifier operating at 120 GHz with 16 GHz bandwidth has been demonstrated [4]. The optimum solution to the realization of a low-cost fibre radio base station terminal is most likely to be MIC technology which enables all the optical and electrical functions to be performed on a single chip technology. MIC technology offers several advantages including the potential for low-cost manufacture since the amount of manual labour is significantly reduced, as well as the reduction of parasitic effects associated with packaging and interconnects. The MIC approach also ensures device uniformity. Several monolithically integrated MIC photoreceivers (incorporating a photodetector and amplifier) with good conversion efficiencies have been demonstrated which may be suitable for mm-wave fibre radio systems operating at 28 GHz [64], 38 GHz [65], 42 GHz [66], 52 GHz [67] and 60 GHz [65, 68], although there are still some key technical issues associated with MIC technology that must be addressed. These include low yields, limited heat dissipation for the RF amplifiers, as well as the ability to integrate the electrical and optical components directly with the antennas. The poor efficiency of the MIC technique is a fundamental challenge since materials that make efficient antennas unfortunately make poor passive RF components while those that enable efficient RF amplifiers do not make good opto-electronic or electro-optic transducers. Recently several high-performance efficient antennas that could be integrated with the BS photonic and RF devices have been reported based on the electromagnetic coupling of low dielectric constant material to the monolithic microwave or optoelectronic integrated circuit wafers [69]. A monolithically integrated narrowband 60 GHz photonic emitter has also been demonstrated comprising a UTC PD, bias circuit and patch antenna fabricated on InP [68]. Despite these recent successful implementations of MIC technology for mm-wave fibre radio applications, more work must still be done to ensure that all the required BS functions can be efficiently developed using a common material. Until then, the hybrid integration approach


187

appears to be the most cost-effective solution currently available for the development of antenna BSs with optimal performance for fibre radio systems [70].

7.7 Conclusions The application of optical fibre networks for the distribution of radio signals in fibre radio systems has been an intense area of research and investigation for the last 15 years. Fibre radio technology is now a commercial reality for the implementation of mobile cellular networks and for indoor wireless local area networks in the form of distributed antenna systems. Much progress has also been made in the development of a range of technologies for fibre radio systems operating at higher frequencies, extending well into the mm-wave region for existing wireless services such as LMDS and future planned cellular, broadband fixed wireless access and indoor LAN networks. In this chapter we have presented an overview of the area of fibre radio networks with a particular focus on the basic enabling technologies for such systems, including optical networking concepts, signal transport schemes and the prospects for integration of optical and RF components in order to realize high-performance compact antenna base stations. The practical implementation of mm-wave fibre radio systems and the required enabling technologies raises a number of technical challenges and an overview of some of the key issues for these networks were also presented. Some potential solutions to these challenges were also described which may have a significant impact on the future development of novel techniques, sub-systems and system architectures for mm-wave fibre radio networks. All these developments will ultimately lead to the anticipated future commercial reality of mmwave fibre radio networks.

Acknowledgements The authors wish to thank their colleagues and students over the years who have contributed to the study of fibre radio technology: Dr Zaheer Ahmed, Dr Manik Attygalle, Dr David Castleford, Dr Kamran Ghorbani, Mr Michael Lye, Dr Hai-Feng Liu, Dr Arthur Lowery, Dr Charlotte Marra, Dr Yoh Ogawa, Dr Lawrence Reekie, Dr Wayne Rowe, Ms Oya Sevimli, Dr Graham Smith, Professor Rodney Tucker and Dr Gideon Yoffe.

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8 Microwave Photonic Signal Processing Jose Capmany, Jose Mora, Daniel Pastor, Beatriz Ortega, and Salvador Sales

8.1 Introduction The full exploitation of the advantages that radio frequency, microwave and millimetre-wave technologies bring to broadband telecommunications and other related applications requires a coordinated effort in the development of signal processing techniques suitable for them. This is especially important as novel applications demand the use of increasingly higher-frequency carriers and broadband signals. The traditional approach towards radio frequency (RF) signal processing is illustrated in the upper part of Figure 8.1. Here an RF signal originating from an RF source or coming from an antenna is fed to an RF circuit that performs the signal processing tasks either at the RF signal or at an intermediate frequency band after a down-conversion operation. In any case, the RF circuit is capable of performing the signal processing tasks for which it has been designed only within a specified (often reduced) spectral band. This approach results in poor flexibility since changing the band of the signals to be processed requires the design of a novel RF circuit and possibly the use of different hardware technology. Furthermore, even if the RF carrier is not changed, the nature of the modulating signal might be, thus requiring more bandwidth or sampling speed from the processor. This is especially true in the case where discrete time signal processing has to be carried over the RF signal. This set of drawbacks is often termed in the optical communications technology literature as the electronic bottleneck. Although important it is by no means the only source of degradation, since electromagnetic interference (EMI) and frequency dependent losses can also be sources of major impairments. An interesting approach to overcome the above limitations involves the use of photonics technology and especially fibre and integrated optics devices and circuits to perform the


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Microwave Photonics: Devices and Applications Antenna

RF input signal

RF circuit

RF output signal

Antenna

RF input signal

Optical CW source

Modulator

Figure 8.1 (lower)

Optical output signal

Optical input signal

Optical signal processor

Optical receiver

RF output signal

Traditional approach towards RF signal processing (upper) and the all-optical approach

required signal processing tasks of RF signals conveyed by an optical carrier directly in the optical domain. We will refer to this as microwave photonic signal processing (MWPSP). This approach is shown in the lower part of Figure 8.1. The RF to optical conversion is achieved by directly (or externally) modulating a laser. The RF signal is then conveyed by an optical carrier and the composite signal is fed to a photonic circuit that employs optical delay lines and other photonic elements for signal processing. At the output(s) the resulting signal(s) is converted from optical to RF by means of one or more optical receivers. The MWPSP approach has several advantages: optical delay lines have very low loss (independent of the RF signal frequency), provide very high time–bandwidth products, are immune to EMI, have low weight, can provide very short delays which result in very high-speed sampling frequencies (over 100 GHz in comparison with a few GHz with available electronic technology) and finally, but not least, optics provides the possibility of spatial and wavelength parallelism using WDM techniques. Since optical carriers are used in this approach to convey the RF signal to be processed, and since this approach relies on the combination of different delayed versions of the lightwave signal, the degree of coherence of the light transporting the RF signal plays a fundamental role. A fundamental distinction must be made on the MWPSP operation regime in terms of the relationship between the coherence time tc of the optical source and the basic delay T (time between adjacent temporal samples provided by the structure). If tc T then the processor is said to work under the coherent regime and its transfer function is linear in terms of the electric field and depends on the optical phase shifts experienced by the carrier that conveys the RF signals. These are highly dependent on environmental parameters (such as temperature) and polarization, making their implementation quite difficult under realistic conditions. In contrast, if tc T the

Microwave Photonic Signal Processing

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signal processor works under the incoherent regime and the overall structure transfer function is linear in terms of the optical intensity (i.e. power) and the effect of optical phase shifts can be discarded. Although work has been reported for both regimes, the majority of contributions focus on incoherent operation, since it is more amenable to practical implementation. In this chapter we aim to review the fundamental concepts, limitations, technologies and major milestones in RF filtering applications of MWPSP. Research contributions within this area extend over the last 25 years starting with the seminal paper of Wilner and Van de Heuvel [1] who noted that the low loss and high-modulation bandwidth of optical fibres made them ideal candidates as a broadband delay line. Several contributions during the 1970s addressed experimental work on MWPSP using multimode fibres [2, 3]. An intensive theoretical and experimental research work on incoherent MWPSP using single-mode fibre delay lines was carried out by researchers at the University of Stanford,USA, during the period between 1980 and 1990. Multiple configurations, applications and potential limitations of these structures were considered and the main results of it are summarized in [4–6]. The technology status regarding optical fibre and integrated components was in its infancy at the time and therefore the demonstrated MWPSP had serious limitations arising from losses and lack of reconfiguration. The interested reader is referred to [6] for a comprehensive and extensive treatment of the experiments that were conducted, as well as for a detailed review of the available technology at that time. The advent of the optical amplifier at the end of the 1980s and the development of optical components (variable couplers, modulators, electro-optic switches) and advanced instrumentation for fibre optics fuelled the activity towards more flexible structures employing these components [7–36]. Most of these contributions present filters that still rely on the implementation of time delays by means of fibre. The introduction of novel components, such as the fibre Bragg grating (FBG) and the arrayed waveguide grating (AWG) has opened a new perspective towards the implementation of MWPSP which can lead to fully reconfigurable and tuneable filters [37–71]. The outline of this chapter is as follows. We first review the potential applications of MWPSP, especially in the telecommunications and radar fields in order to give the reader a first sight of the range of applicability of this approach, or in other words, to provide answers to the obvious question: ‘what is MWPSP good for?’. We will then proceed with a description of the fundamental concepts and limitations related to the photonic processing of RF signals. Special attention will be paid to incoherent signal processing techniques and the different alternatives for their implementation will be presented. We turn next to review the two main consolidated technical approaches towards the practical implementation of incoherent MWPSP. The first one is based on the use of fibre coils as delay lines. In this case, the output power from an RF modulated optical source is split and the various signal samples are implemented by the delays provided by different fibre coils or by dispersive fibre elements. The second approach is based on the use of optical delay lines implemented by fibre Bragg gratings. The chapter concludes by addressing the efforts made so far to overcome the limitations in incoherent filters imposed by the positive nature of their coefficients.

8.2 Applications of MWPSP As outlined in the previous section, photonics technology brings unique characteristics (i.e. extremely low attenuation, near zero dispersion, immunity to electromagnetic interference)

194


that make it very attractive for microwave and millimetre-wave engineering applications in general. In particular, the MWPSP approach is of interest in radio-over-fibre (RoF) systems, both for channel-rejection and channel-selection applications [72]. In the first case, we deal with an optical link where not only the desired signal but also unwanted interfering signals (that are also picked up by the antenna) are carried by the fibre. For example, in radio astronomy applications [73] the signal transmission from several stations to a central site requires the removal of strong man-made interfering signals from the astronomy bands. The ability to reject these interfering RF signals directly in the optical domain is a unique characteristic of these microwave photonic filters. In the second case, the signal carried by the optical link is composed of a frequency plan that comprises several disjoint parts of the RF spectrum (universal mobile telecommunications system (UMTS), high-performance radio LAN (HiperLAN), LMDS). Here, a bandpass photonic filter can be employed to select a given RF band or spectral region [74]. Furthermore, the selected band can be changed if the filter is tuneable. In both cases the position of the frequency notch or the filter band-pass can be as low as a few MHz or as high as several tens of GHz due to the broadband characteristics of photonic delay lines. Photonic filters for RF signals can also be of interest for applications where low weight is a prime concern; as an example, analogue notch filters are needed to achieve cochannel interference suppression in digital satellite communications systems [75]. Another range of applications benefit from the MWPSM approach as it solves current bottlenecks in the electronics. Figure 8.2 depicts a typical application configuration for a moving target identification (MTI) ground radar system [76]. The MTI radar uses the Doppler effect to separate the targets of interest from clutter (such as land, sea water and rain). To do this the radar sends a pulse sequence with pulse width t and inter-pulse period PRI (¼1/PRF), where PRF is the pulse repetition frequency. Any moving object will generate a Doppler frequency shift Dn of the radar central frequency fo according to its speed (dR/dt), where R(t) designates

Land clutter

Land clutter

Target

Sea clutter Rain clutter

t) R(

Noise 0

Doppler shift ∆ν=-(2/λ)(dR/dt)

t o)

(t-

=R

+d

o

dt R/

RF /P 1 I= PR

PRF

MTI: moving target indicator radar uses Doppler effect to separate targets of interest from clutter

Figure 8.2 Example of application of a microwave photonic filter to ground moving target identification (MTI) radar

195


Down conversion

A/D

RF photonics notch/bandpass filter

Down conversion

Digital notch filter

A/D

DSP

Figure 8.3 Typical signal processing configuration in an MTI radar system (top). Modified version including a microwave photonic filter prior to downconversion (bottom)

the time-varying distance from the target to the radar. The spectral signature of each object repeats in the spectrum periodically with a period given by the pulse repetition frequency which obviously sets the limit on determining an unambiguous Doppler shift. Hence focusing on a spectral region from fo to fo þ PRF is sufficient to get all the information regarding moving targets and clutter, and what is required after signal detection is a signal processing stage to carry out the filtering of clutter and noise from the targets. This is usually performed as shown in the upper part of Figure 8.3 by using a digital notch filter placed after frequency down-conversion to base-band and analogue-to-digital conversion (ADC). In order to distinguish the small echo from the target from the large echo due to the fixed objects, high-performance (14–18 bit resolution) ADCs are required which represent a major bottleneck in the system. If the clutter can be removed before down-conversion, then the highresolution requirements on the ADCs can be relaxed. For example, with a 30 dB clutter attenuation the required ADC resolution is reduced by 5 bits. This operation is difficult and costly in the microwave domain but it is simple if the RF signal is modulated onto an optical carrier and the whole signal is processed directly in the optical domain by means of a photonic filter as shown in the lower part of Figure 8.3. The very high bandwidth and potentially low delays (5 ns/m) that can be achieved with optical delay lines make them an ideal technology option for the implementation of signal correlators for very high-speed signals [77]. These structures are similar to the photonic filters that will be discussed in this chapter but are designed to operate over the time domain characteristics of the input signals. The potential applications embrace code division multiple access (CDMA) systems as well as pattern recognition. To finalize this list of potential applications we would like to point out the use of photonic RF filters for optical prefiltering applications, especially in the field of subcarrier multiplexed label (SCML) swapping optical networks [78, 79]. Here a baseband digital label (header) is modulated onto an RF subcarrier and then multiplexed (electronically or optically) with a baseband digital signal (the packet or payload) on the same wavelength. At the network nodes

196


the packet header must be read without affecting the payload in order to redirect it to the right output. This can be done by exploiting the optical prefiltering (OP) concept. OP techniques rely on the use of optical filters and components to process microwave signals directly in the optical domain, and have been developed in the past by a limited number of research groups. Using OP allows the subcarrier label to be extracted directly in the optical domain keeping the data payload intact.

8.3 Fundamental Concepts and Limitations 8.3.1 Fundamental Concepts Any filter implemented using MWPSP tries to provide a system function for the RF signal given by [80]: N X

Hðz 1 Þ ¼

ar z r

r¼0 M X

1

ð8:1Þ bk z

k

k¼1

where z1 represents the basic delay between samples and ar, bk are the filter coefficients which are implemented by optical components. The numerator represents the finite impulse part (i.e. nonrecursive or FIR) of the system function, whereas the denominator accounts for the infinite impulse part (i.e. recursive or IIR) of the system function. N and M denote the order of the FIR (finite impulse response) and IIR (infinite impulse response) parts respectively. If bk ¼ 0 for all k, the filter is nonrecursive and is also known as a transversal filter. Otherwise the filter is recursive and it is common to use the term recirculating delay line. Figure 8.4(a) illustrates how Equation (8.1) is implemented for the specific case of an Nth order transversal incoherent1 filter using a single optical source. Figure 8.4(b) shows the signal flow (optical and electrical) for a three-tap filter. The end-to-end (electrical) impulse response2 corresponding to this situation can be directly derived from Equation (8.1) yielding: hðtÞ ¼

N X

ar dðt rTÞ

ð8:2Þ

r¼0

which, when convolved with the input RF signal si(t), yields the output signal so(t): so ðtÞ ¼

N X

ar si ðt rTÞ:

ð8:3Þ

r¼0

1 Although coherent photonic processing of microwave signals is possible in theory, in practice it is severely limited by environmental conditions as shall be explained later. Since most of the research and advances have been produced in the field of incoherent signal processing, we will focus this chapter on this approach. The meaning of coherent and incoherent signal processing is explained later in the chapter. 2 Strictly speaking, an end-to-end electrical impulse response can only be defined for incoherent filters.

197


(a)

Output electric field

Input RF signal si(t)

Eo(t)=Σ[ar si(t-rT )]1/2e j(wo(t-rT )+φ(t-rT ))

Modulator

T 2T a21/2

NT Delay line

Input electric field [si(t)]1/2e j(wo(t) + φ(t))

aN1/2

Optical signal combining element

CW laser source e j(wot+φ(t))

Optical signal tapping element

ao1/2

Receiver

weight

Output RF signal So(t)==Σ ar si(t-rT )

Incoherent regime: <e j(φ(t-kT )) e-j(φ(t-rT ))>=δk,r Delayed and weighted (b)

RF signals

RF signal

ao

CW optical source

1x3

a1 a2

T 3x1

2T 2

y (t ) = ∑ ar x(t − rT ) r =0

Possible optical interference (coherence)

RF modulated optical signal

Delayed and weighted optical signals

Figure 8.4 (a) Implementation of Equation (8.1) for the case of an N-tap transversal filter. (b) Signal flow (RF and optical) in a three-tap transversal filter

198


Optical signal

Optical signal

Electrical signal

Optical components -splitting -delay -apodization

Optical source/ sources

Electrical signal

Optical detectors

∆Ω FWHM

FSR

h(t): N taps

δ(t)

Ω: Electrical frequency

Figure 8.5 General scheme of the optical processor where the core is formed by an optical ‘cloud’ (all optical processing)

Similar expressions to Equations (8.2) and (8.3) apply for IIR or recirculating delay line filters3 with N ! ¥. Figure 8.5 shows a general scheme of the optical processor where the core is formed by an optical ‘cloud’ (all optical processing) and one or more sources at the input and one or more detectors at the end. According to Equations (8.2) and (8.3) the standard electrical–optical impulse response of the optical processor is represented by an equally time spaced (T ) pulse train. If all the samples have the same amplitude the filter is called uniform, if the samples have different amplitudes the filter is termed apodized or windowed. The electrical frequency response H(W) of such a structure can be obtained by Fourier transformation of the impulse response (8.2): HðWÞ ¼

N X

ar e jrWT :

ð8:4Þ

r¼0

The above expression identifies a transfer function with a periodic spectral characteristic (Figure 8.3). The frequency period is known as the filter free spectral range or FSR (this being inversely proportional to the time spacing T between adjacent samples in the impulse response). The resonance full-width half maximum is denoted as DWFWHM. The filter 3 In this case, however, the filter coefficients are not given by ar exclusively since there is a contribution from recirculating terms bk. The overall expression is in terms of coefficients cr which include the effects of both contributions.

199


selectivity is given by its quality (or Q) factor which is given by [80]: Q¼

FSR : DWFWHM

ð8:5Þ

The value of the Q factor is related to the number of samples (taps) used to implement it. If the number of taps is high (>10), the Q factor can be approximated for uniform filters by the number of taps Q ffi N. This relation is modified (Q < N) for apodized filters [80]. The implementation of the ‘optical cloud’ in MWPSP requires specific optical components to provide: (a) signal tapping, (b) optical delay lines, (c) optical weights and (d) optical signal combination. A variety of 2 2 and 1 N and N 1 star couplers have been proposed for the implementation of (a) and (d). Variable 2 2 couplers, erbium-doped fibre amplifiers (EDFAs) and semiconductor optical amplifiers (SOAs), electro-optic and electro-absorption modulators can be used to implement (c). Standard, high-dispersion single-mode fibre coils and fibre Bragg gratings have been proposed for the implementation of (b). Some further definitions are now introduced to complete our general description of photonic filters for microwave signal processing. (i) Coherent and Incoherent Operation Regime The schematic representation of the optical processor or, more specifically of the transversal filter of Figure 8.1, shows how multiple optical contributions carrying the RF signal are mixed at the detector end of the structure. In this detection process, the different taps (or optical contributions) can be mixed according to two different regimes, namely coherent and incoherent. Coherent regime: This regime is verified when the light arising from each tap of the filter has a deterministic optical phase relationship with the rest at the input of the photodetector. In this case the optical power to electric current conversion operation at the photodetector generates an interference term.4 This situation takes place when the ‘coherence time’ (tc) of the optical sources employed in the filter setup are much longer than the time delay T between adjacent samples or taps of the optical filter. Under the coherent regime, the optical phase of the taps plays a predominant role in the overall time and frequency response of the processor, and filters with negative and complex coefficients can be implemented. On the other hand, since the filter operation relies on optical interference, any slight change in the propagation characteristics of any part of the optical processor (such as the length of any relay line or refractive index changes due to the alteration of environmental conditions) drastically affects the filter response and its properties. This constitutes a very serious practical limitation for the implementation of these filters since a very stable platform and considerable electronic feedback must be provided for successful operation. Incoherent regime: In contrast to the previous case, in the incoherent regime the optical phase relationship between the filter taps is completely random (i.e. is lost) due to the limited source coherence time. For this to happen, tc T. The interference is lost and the optical power at the photodetector input is the sum of the optical powers of the filter 4 The optical power at the photodetector input is the squared modulus of the overall electric field at the same point, which in turn is composed of the sum of the electric fields of the different samples or taps. Hence the optical power contains the contributions of the different beatings or cross terms of the electric field.

200


samples (i.e. there is no beating term involving the optical phase). In this case the filter structure is free from environmental effects and thus very stable and its performance is quite repeatable. The main drawback of this approach is that filter coefficients can only be positive5 in principle and this leads to a serious limitation of the range of transfer functions that can be implemented. Fortunately, there are solutions available for the implementation of incoherent filters with negative coefficients and these will be presented in a later section. (ii) Filter Tuneability This property makes reference to the possibility to tune the RF bandpass position in a sufficiently fast way. Tuneability can be achieved either in a step-by-step or a continuous way and is a key feature required of high-performance flexible filters. In order to tune the RF response of the filter (Figure 8.2), the FSR has to be modified and therefore the basic time delay T between samples or taps also has to be changed. In addition, the degree of frequency change or tuning produced by a given increase or decrease of the basic time delay depends clearly on the resonance or pass-band selected to be used of the structure. If we centre our discussion on fibre devices there are quite a few techniques producing a true time delay and they can be classified as follows. .

.

.

Switched propagation paths (switched delay lines): In this technique, different paths providing different basic propagation delays (that is different values of T) can be chosen by means of an optical space switch. It allows only step-by-step tuneability, with the tuning speed being limited by the switching time (1–10 ms). Wavelength tuning of one or multiple sources combined with dispersive optical devices: This technique takes advantage of currently available modern tuneable sources. The dispersive devices can be: standard fibre, high-dispersive (dispersion compensating) fibre or linearly chirped fibre Bragg gratings (LCFBG). It can provide continuous or step tunability at high speed, limited by the tuning speed of the sources (depending on the tuneable source technology, from 100 ns to more than 100 ms). Fixed wavelength multiple sources or sliced broadband sources combined with tuneable dispersive devices: This approach is based on the use of novel devices with tuneable dispersion properties such as special chirped FBGs with actuators to change their dispersion properties. It can provide continuous and step tuneability but in this case the time and accuracy to perform a dispersion change on the fibre device is not so well controlled (100 ms to 1 s).

(iii) Filter Reconfiguration This property makes reference to the possibility of changing dynamically the values of the filter taps (ak and br coefficients) to reshape its spectral response. The windowing/weighting or apodization of the amplitude of the filter taps is also a fundamental aspect to ensure enough rejection of the unwanted bands. The uniform tap apodization (equal amplitude of the taps) provides a rejection ratio or main-to-secondary lobe ratio (MSLR) that increases linearly with 5

Since they are implemented by optical power signals which can only be positive or zero (i.e. there is no negative light).


201

the number of taps. This can be insufficient for certain applications. Different apodization functions have been demonstrated for MSLR improvement, either by adjusting the power of the optical sources or by controlling the attenuation/gain suffered by the taps when they travel through the optical processor.

8.3.2 Limitations MWPSP must overcome a series of potential limitations prior to its practical realization as has been pointed out by various researchers. We classify these limitations into two groups according to whether these limitations appear mainly in the optical domain or whether they manifest themselves in the electrical domain. 8.3.2.1 Optical Sources of Performance Limitation Limitations arising in the optical domain include nonlinear optical effects, polarization, the positive nature of the filter coefficients due to incoherent operation, the limited range of attainable spectral periods, spectral periodicity, filter reconfigurability and tuneability. (a) Source coherence: The sources spectral characteristics must be carefully chosen according to the desired working regime. While coherent operation provides the possibility of implementing any kind of desired transfer function, these structures are very sensitive to environmental conditions [4]. Thus, in the majority of cases, incoherent operation is employed since the filters are very compact and robust. Even so, coherent effects can appear even under incoherent operation [27]. These undesirable coherent effects may be overcome, for instance by the use of birefringent fibre delay lines [81] or by employing source arrays. (b) Polarization: Polarization effects are mainly important under coherent operation [4]. However, it has been outlined and experimentally demonstrated that even under incoherent operation the filter can be sensitive to signal polarization [27, 82]. The main cause for this apparent contradiction is that some signal samples experience exactly the same delay within the filter leading to coherent interference between them even if a broadband source is employed [27, 82]. Also, when using laser sources and external modulators care must be taken to adjust the source polarization to that required by the modulator. The use of polarization preserving fibre pigtails at the modulator input helps to overcome this limitation. (c) Positive coefficients: Filters working under the incoherent regime are linear in optical intensity, thus the coefficients of their impulse responses are always positive. This has two important implications as derived from the theory of positive systems [5]. The first (and most important) is that the range of transfer functions that can be implemented is quite limited. The second is that, regardless of its spectral period, the transfer function always has a resonance place at baseband. This is not a serious limitation since a DC blocking filter can be inserted at the optical receiver output. Nevertheless, incoherent filters with negative coefficients can be implemented by means of differential detection [5, 23] and cross-gain modulation in an SOA [83]. (d) Limited spectral period or FSR (free spectral range): MWPSPs have a periodic spectrum since they sample the input signal at a time rate given by T. Thus the spectral period or FSR

202

Figure 8.6


FSR–laser linewidth trade-off for single source photonic filters for microwave signals

is given by 1/T. If the MWPSP is fed by only one optical source then the source coherence time (which is inversely related to the source linewidth) limits the maximum (minimum) value of the attainable FSR under incoherent (coherent) operation. This is depicted in Figure 8.6. To overcome this limitation it has been proposed to feed the MWPSPs with source arrays [65]. In general the spectral periodicity of microwave photonic filters limits the bandwidth of the RF signals to be processed to a fraction of the FSR in order to avoid spectral overlapping. Single resonance (i.e. nonperiodic filters) is therefore desired for certain applications. (e) Reconfigurability: As defined previously, this property refers to the possibility of dynamically changing the values of ar and bk in Equation (8.1). Passive structures are incapable of this feature. Several solutions have been proposed to overcome this limitation including the use of optical amplifiers [7–9], modulators [10, 46], fibre gratings and laser arrays [65]. Some of these are addressed later in the chapter. (f) Tuneability: As defined previously, this property refers to the possibility of dynamically changing the position of filter resonances or notches. To provide tuneability it is necessary to alter the value of the sampling period T. Solutions that include the use of switched fibre delay lines [14], high-dispersion fibres [30] and fibre Bragg gratings [37] have been proposed. In the last two options a tuneable source is required. Some of these are reviewed in the following sections. (g) Fibre nonlinearities: The filter linearity can be compromised if the optical carriers used in the filter implementation deliver enough power to stimulate fibre nonlinearities. The main

203


sources of optical nonlinearities are self-phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM) and stimulated Brillouin and Raman scattering (SBS and SRS). The requirements for each one of these are the same as those for typical communication systems and can be found elsewhere in the literature [81].

8.3.2.2 Electrical Sources of Performance Limitation Microwave photonic (MWP) filters are a particular case of an analogue fibre optic link and suffer from the same electrical limitation sources, including noise and intermodulation. The performance study of the complete MWP filter from the point of view of a black box with an RF input port and an RF output port, is therefore essential for the sake of comparison with other existing technologies, and also in order to verify if it meets the specification in terms of gain, noise factor and intermodulation characteristics. An important starting point for the analysis is the knowledge of the aforementioned features in a radio-over-fibre (RoF) system [82–86]. In fact, the more general structure of an MWP filter shown in Figure 8.5 can be treated as an RoF system with intensity modulation (IM) or external modulation (EM), followed by an optical transmission section that in this case includes the necessary FIR or IIR tap replication scheme, and finally the detection front-end. Nevertheless MWP filters can include some optical components not specific to RoF systems, such as multiple optical source arrays instead of a single source, broadband optical sources (LED, SLED or ASE (amplified spontaneous emission) spectrum from EDFAs) or even sliced versions of broadband sources. We now proceed to present the gain and noise factor concepts applicable to the general case of RoF and MWP systems and proceed to include the necessary specializations applicable to MWP filters. Gain The total RF gain of the MWP filter can be derived from the general setup of Figure 8.7. The filter can be divided into the three main blocks from input to output, namely, the electro-optical

GRF (dBe)

RF input

Popt E/O

Optical processing

O/E RF output

Gopt (dBo) = 10 log(Topt)

Figure 8.7 General MWP filter structure including electrooptical conversion, all optical process and optical detection. Definition of the optical span and RF gain reference planes

204


conversion module (E/O), an all optical processing part and finally an optical to electronic conversion (O/E) module. For the E/O module there are two main options, intensity modulation of a semiconductor source, or external modulation employing a continuous wave source. Both alternatives are equivalent from the point of view of the general operation concept of MWP filters, since amplitude modulation of the RF signal over the optical carrier is performed in both. The IM alternative is suitable for low-cost and medium-to-low frequency range applications due to their limited modulation bandwidth ( Ith, and it is proportional to the known differential quantum efficiency.


205

It is interesting to point out that sIM is independent of the mean optical power delivered by the laser (I > Ith) and that it only depends on the slope of the PI curve. This is in contrast to seom; this varies linearly with the CW power applied to the EOM, and therefore TRF varies quadratically. This in principle allows EOM-based systems to compensate for their own EOM losses or even compensate optical insertion losses of the remaining optical processor if Popt can be increased. If we take typical values, such as Popt ¼ 10 mW, an EOM with V ¼ 6 V and Z0 ¼ 50 W, and Gopt ¼ 10 dBo then we obtain GE/O&O/E(dBe) ¼ 16 dBe and the total gain is GRF(dBe) ¼ 36 dBe. This negative gain (i.e. loss) can be compensated up to 0 dB in different ways: (a) by 36 dBe of electrical amplification (before, after or at both ends of the MWP filter), (b) by optical gain (in this case the required gain will be 18 dBo) or (c) a combination of electrical and optical amplification (for example, 12 dBo þ 12 dBe). All these possibilities have important implications in terms of noise figure and distortion behaviour of the MWP filter as will be shown later. The total RF gain has been calculated without any reference to the particular frequency response of the MWP structure because it has to be considered as the absolute value to be added to the normalized filter response independent of the number of taps or particular optical process. In that sense, it has to be pointed out that Popt inside Equations (8.6) and (8.7) should include the total optical power applied to the MWP structure by the set of sources when the MWP filter is of the multiple source type as discussed later. Noise Figure The noise figure of a microwave photonic filter can be defined as the ratio between the total noise power spectral density at the device output Nout and the noise power due to only the thermal noise spectral density applied to the input at the reference temperature and affected by the device gain. More specifically in our case: NRIN þ Nshot þ Nsig ASE þ NPIIN þ Nth Nout NFðdBÞ ¼ 10 log ¼ 10 log ð8:8Þ 4kT0 TRF =R ð4kT0 TRF =RÞ where k is Boltzmanns constant, T0 is 298 K and R is the load resistance at the RF source applied to the MWP filter. The total noise spectral density at the output of the MWP filter is composed of different sources of noise generated along the MWP filter as we can see schematically represented in Figure 8.8. Relative intensity noise (RIN) produced in the optical source (Figure 8.8(a)) propagates along the optical processor up to the detector and is one of the dominant sources of noise when IM is employed. Its spectral power density is NRIN ¼ Ip2 RIN A2 =Hz ð8:9Þ Ip ¼ RPopt Topt where Ip is the average detected photocurrent. Notice that this noise contribution increases with the square of Popt. Also, for the case of multiple laser arrays feeding the MWP filter, the different sources can be considered to be uncorrelated in general and with similar RIN values and therefore the total intensity noise is the addition of the individual ones, Equation (8.9) being applicable where Popt contains the aggregated array power. Moreover, the intensity noise spectral density depends on the RF frequency under consideration RIN(W)[Hz1] and therefore depends on the resulting noise figure.

206


Topt G0A

T1

Popt

T2 RF output

(a)

EOM

Optical processor

O/E

(d)

(c) (b)

G0A F0

RF input

Figure 8.8 EOM-based general MWP filter basic structure. Optical amplification can be included after or before optical processing. Noise sources are represented: (a) optical intensity noise, (b) shot noise, (c) ASE noise and (d) thermal noise

Externally modulated systems relax the constraints over the laser source, and the intensity noise effects can be reduced by employing CW sources with low RIN parameters. In this case the dominant noise source is shot noise produced at the detector output, with spectral density: Nshot ¼ 2qIp ½A2 =Hz:

ð8:10Þ

Optical amplifiers are used in many cases to compensate for the high optical losses of the passive components in a MWP filter. EDFAs or SOAs can be used, depending if their respective gain dynamics behaviour is a limitation or not, or whether this dynamic behaviour is used for some purpose (for example, cross gain modulation to generate negative coefficients). When optical amplifiers are used, new sources of noise produced by the ASE should be considered. Detailed derivation of ASE noise sources and OA noise factor can be found in [87]. We will provide here some expressions for the easy calculation of the more general case with dominant signal-ASE beating contribution, and the procedure is extended to an arbitrary chain of optical amplifiers and optical losses [87]. According to the previous notation the noise power spectral density due to signal to ASE beating is [87]: Nsig ASE ¼ 4qhnsp Ip ðGOA 1ÞT2

½A2 =Hz

ð8:11Þ

where h is the quantum efficiency of the detector, nsp is the population inversion parameter for the amplifier that is connected with the gain (GOA) and noise factor (F0) through: F0 ¼

ðGOA 1Þ 1 2nsp þ : GOA GOA

ð8:12Þ

Notice also that Equation (8.12) includes the term T2 that embraces the optical transmission between the OA and the detector. In this way the expression can be applied to cover any location of the OA along the optical processing chain, leaving Topt ¼ T1G0AT2, where T1 is the optical transmission before the OA (just between the source output and the OA input). To include the noise effect of more than one amplifier along the optical chain, we can use the equivalent OA


207

gain (GOA,Eq) and OA noise factor (F0,Eq) of a chain of {GOA1,FO1} þ Intermediate Losses (TINT) þ {GOA2,FO2}, being: GOA;Eq ¼ GOA1 TINT GOA2 FO2 FO;Eq ¼ FO1 þ : GOA1 TINT

ð8:13Þ

Expression (8.13) assumes that G0A,Eq, G0A1 and G0A1 are all much greater than unity and therefore Equation (8.12) reduces to F0 ¼ 2nsp. Note that any combination of amplifiers and losses can be calculated by recursive iteration employing (8.13). (i) Phase Induced Intensity Noise (PIIN) PIIN is usually the dominant noise source in single source incoherent microwave photonic signal processors. PIIN arises since, as mentioned previously, the incoherent regime implies the use of wide linewidth sources in order to obtain a robust transfer characteristic irrespective of environmental perturbations. The price to be paid is that the laser linewidth, which arises from random phase variations of the optical output with time, is larger than the processor FSR. Inside the optical processor, the input power is tapped into different paths (samples) and recombined at the output. The summation of the multiple optical samples at the photodetector transforms the laser phase fluctuations into intensity fluctuation noise (PIIN) at the output. PIIN noise has been studied in passive structures [88] and active recirculating delay lines [89, 90]. Recently an excellent and detailed consideration of its impact and the techniques to overcome the effect of PIIN has been published in the literature [91]. Among these it is worth mentioning the use of multiple source architectures. Finally, added to the optical type noise sources, we have also to consider the thermal noise propagated along the MWP filter added to that produced at the detector load resistance and the electrical amplifier: 4kT0 Nth ¼ ðF þ TRF Þ A2 =Hz : ð8:14Þ R In the simplest case of thermal noise being dominant, if the MWP filter has considerable losses (TRF 1), then NF(dB) ¼ F(dB) þ LRF (dB), with LRF(dB) ¼ GRF(dB). In the opposite case, if TRF 1 then NF(dB) ! 0 dB, but this will be very difficult to achieve in practice because TRF 1 involves high optical power and therefore an increase of RIN and shot noise or optical gain with added ASE. Harmonic and Intermodulation Distortion Harmonic and intermodulation distortion features are the other major constraint that should be addressed for MWP filters. The main source of signal distortion is normally the E/O conversion stage. If we consider directly modulated lasers, both static distortion produced by the L–I curve and dynamic distortion produced by the laser rate equation dynamics are produced. External modulation is dominated by static distortion and depends on the E/O device employed (EOM or EAM). Extensive compilation of all these possibilities can be found in [85, 86]. Whichever E/O approach is finally used, the distortion will translate into harmonic distortion (HD) terms and intermodulation distortion (IMD) terms. Of all the intermodulation terms the third-order terms (IMD3) are the most deleterious because they fall into the system frequency band, being difficult to reject by simple filtering. In the case of an EOM modulator (without linearization),

208


the raised-cosine static L–V curve implies distortion. Traditionally the biasing point chosen is the QB, thus ensuring maximum optical amplitude modulation and minimum even-order distortion terms (IMD2, HD2). In this case IMD3 can be reduced by decreasing the RF power and therefore the optical modulation index (m). Nevertheless, reduction of the modulation index will lead to a reduction of the carrier-to-noise ratio (CNR) at the MWP filter output due to the noise floor. There are two aspects limiting the system in opposite directions, first the noise floor level and second the RF power limit at the input due to intermodulation. This balance is summarized by the spurious-free dynamic range (SFDR). Figure 8.9(a) shows schematically the SFDR definition and how a specific application could operate with RF channels with maximum power difference DP between the strongest and weakest signals. The SFDR should be higher than DP þ CNRmin, CNRmin being the minimum CNR for the specific application. Two strong level channels

∆P SFDR= CNR=C/IM3

Weak channel

CNRmin Base noise level at the receiver in the system bandwidth

(a)

Third-order intermodulation term from two frequencies (IMD3d)

IP3

Output RF power (dBm)

1x

SFDR C

IMD3 2x

Ntot

2x

(b) Input RF power (dBm)

Figure 8.9 (a) Spurious free dynamic range (SFDR) schematic definition and its relation with the system requirements. (b) IMD3 and C versus input RF power. Linearly extrapolated third-order intercept and its relation to SFDR

209


A general procedure to compute IMD3 output power versus output carrier power (C) for an arbitrary input RF power employs the linearly extrapolated third-order intercept point IP3 (Figure 8.9(b)). SFDR can be easily obtained from the schematic of Figure 8.9 as: h i 2 IP3 SFDR ¼ 10 log ð8:15Þ dB Hz2=3 3 Nout R where NoutR is the power noise spectral density (W/Hz). For the case of using EOMs without linearization [85], IP3 ¼ 4Ip2 R and: ! h i 4Ip2 2 2=3 SFDR ¼ 10 log dB Hz : ð8:16Þ 3 RIN Ip2 þ 2qIp þ NsigASE þ Nth

8.3.3 Different Alternatives for Incoherent MWPSP Figures 8.10 to 8.13 illustrate four possible different approaches for the implementation of incoherent MWPSP according to the type of source/sources employed, the minimum time delay difference between taps and the maximum attainable FSR [92]. Figure 8.10 shows the first possibility, where only one modulated optical source is employed. The filter taps are therefore implemented from delayed versions of the output signal from this source. Using high-quality (low linewidth) sources results, as has been explained before, in the limitation of the maximum attainable filter FSR if interference effects need to be avoided (Figure 8.6). The alternative method to increase the filter FSR is to use single-mode sources with moderate line width such as low quality DFB lasers. A second option is shown in Figure 8.11. Here multiple (N) optical sources modulated by the same RF signal are used to implement the filter. Each source implements a limited set of taps. In the first case, no phase correlation between them exists so it is equivalent to the prior case with zero coherence time; in other words, there is no limitation in the minimum time delay or maximum FSR. In the second case (one source implements a limited set of samples), coherence effects will be avoided if the interval between two consecutive samples generated by the same source (i.e. NT) is much bigger than the source coherence time. A third possibilityis shown in Figure 8.12. Here a modulated broadband optical source (LED, EDFA or SOA ASE source) with very low coherence time (almost zero) is employed to generate

1 Optical source (DFB or tuneable)

Optical components

Optical detectors

δ(t )

Τ

Figure 8.10

Filter based on only one optical source

210


N singlemode optical sources

Optical detector

Optical components

δ(t )

Τ

Figure 8.11 Filter based on N optical sources, one tap per source

all the filter taps. Therefore, each tap carries all the spectral components of the broadband source. Since the source linewidth can be considered almost infinite, the coherence length of each tap is zero and there is no limitation in the minimum time delay or maximum FSR. An important limitation appears if the filter delays are provided by dispersive elements. Since each sample is carried by a broadband source, the exact value of the delay is affected, not only by first-order dispersion, but also by second-order dispersion. This can lead (as will be shown later in the chapter) to an undesired low-pass envelope effect affecting the overall filter transfer function. A final option is shown in Figure 8.13 which is similar to the previous case, the only difference being that the broadband optical source is sliced. Here each tap is implemented by a different part of the sliced spectrum. If each slice is carried by a broad enough portion of the optical spectrum then, as in the previous case, there are no limitations on the filter FSR.

8.3.4 Implementation Approaches for Incoherent MWPSP To date, two main approaches have been followed by most of the research groups throughout the world to implement incoherent MWPSP. These are: (a) Implementation of MWPSP using fibre coils as delay lines together with single/multiple sources and signal tapping combination and weighting by means of discrete fibre or integrated optics components. We will refer to these as FDLFs (fibre delay line filters).

Figure 8.12

Transversal filter based on one broadband optical source


211

Figure 8.13 Transversal filter based on a sliced broadband optical source

(b) Implementation of MWPSP using fibre gratings as delay lines and/or weighting elements in conjunction with single or multiple tuneable source arrays. We will refer to these as FGDLFs (fibre grating delay line filters). The main activities in FDLFs were carried out during the period 1980–1994, although some relevant work has been reported during the last five years as well. The work on of FDLFs has been relevant since 1994 and extends to the present time. In the following we briefly outline the work on FDLFs, focusing more effort in describing the main results obtained in FGDLFs.

8.4 Fibre Delay Line Filters Intense research work on passive FDLFs was carried out during the period between 1980 and 1990, including the development of special purpose components (such as variable 2 2 couplers and star couplers) and the experimental demonstration of simple passive structures performing basic signal processing operations such as transversal and notch filtering, correlation, and data storage [4–6]. Both noise and signal analysis methods were developed for these structures. The advent of optical amplifiers (OAs) opened the possibility of overcoming the limitations imposed by the static nature of passive structures both in terms of reconfiguration and loss compensation. The inclusion of OAs provided the structures with enhanced flexibility as sample weighting could be altered. Several contributions proved these advantages both theoretically as well as experimentally [7–23]. Synthesis methods where developed [25, 26] and filters with negative coefficients resulting from the application of some of the above methods were experimentally demonstrated [23]. By the mid-1990s it was thus clear that the main restriction faced by FDLFs was that related to resonance tuneability and filter reconfiguration. In 1994 a solution for resonance tuneability was proposed by implementing a tuneable delay consisting of a tuneable source and high dispersion fibre delay lines [29]. The concept was extended by Frankel and Esman [30] who demonstrated the implementation of a transversal filter with continuously tuneable unit time delays consisting of eight taps with progressively longer segments of high-dispersion fibre, but completed with dispersion-shifted fibre to nominally identical overall lengths. The time delay tuning at each tap was achieved by tuning the wavelength of the optical carrier. A Q ¼ 30 bandpass RF filter tuneable over one octave was demonstrated. The main features are shown in Figure 8.14.

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Coppinger and co-workers proposed a different alternative based on the use of an array waveguide grating (AWG) device as a wavelength selective true time delay device [31–33]. The principle is shown in Figure 8.15 for a simple two-stage discretely tuneable notch filter. The key element is the AWG in symmetric feedback configuration shown in the inset which exploits the reciprocity and geometrical symmetry of this device to perform wavelengthdependent true time delay.

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Figure 8.15 Two-stage notch filter implemented using a variable true time delay element based on an AWG device in fold-back configuration [32]

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A signal entering the AWG centre input will emerge from different outputs depending on its wavelength. Each output is then fed back to its symmetric input port with an optical fibre of different length (i.e. a different delay is achieved for different input wavelengths). The light will then be focused by the grating to the common output port. This variable delay line element can then be introduced in any filter configuration as, for instance, the two-stage notch configuration shown in the same figure. Both discrete and continuous tuneability has been demonstrated for a simple notch filter. In the first case (shown in Figure 8.10) first notch positions were tuned from 154.03 MHz to 153.97 MHz and 153.83 MHz respectively by using three different wavelengths (1550 nm, 1550.8 nm and 1550.4 nm) which were sent by the AWG to three different fibres of incremental lengths given by 0, 18.4 cm and 69.3 cm. The continuous tuning operation can be achieved by using a mixed coarse- and fine-tuning configuration which is explained in detail in [33] and shown in Figure 8.16. In essence the coarse-delay tuning is achieved by means of the AWG-based delay line element, while the fine tuning is achieved by means of a complex RF phase shifter which requires the splitting of the optical signal and the use of two different optical attenuators prior to detection. With proper adjustments the notch position can be tuned over the whole filter FSR.

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Figure 8.16 Two-stage continuously tuneable notch filter implemented using a variable true time delay element based on an AWG device in fold-back configuration. Reproduced from [33] ( 1997 IEEE)

214


A similar scheme has also been proposed by Yu and Minasian [34] for implementing tuneable filters fed by a single wavelength source where the AWG is replaced by fixed delay lines. In this latter case, notch tuneability across a range of FRS/2 has been reported. The main drawback of this approach is that the RF microwave shifter is frequency dependent and also perfect matching and coordination between the coarse- and the fine-tuning mechanism is required. An advantage of the AWG delay line scheme is that the losses do not scale with the output ports of the AWG; thus, with current available technology, delay elements with more than 128 outputs are feasible. Another advantage is that the full set of AWG and feedback waveguides can be integrated on a single substrate, leading to the possibility of very small delay increments (finer tuning steps). Research on tuneable and reconfigurable delay line filters has also been carried by means of using broadband sliced optical sources in conjunction with wavelength selective delay lines. The first proposal came from Foord and co-workers [35] who proposed the use of a single length of fibre relying on chromatic dispersion to impart different time delays to different wavelengths selected from a single broadband source using optical filters. In this first demonstration, the broadband source was implemented by means of a two-stage EDFA which was then followed by a tuneable Michelson interferometer to provide tuneable source slicing and an external modulator to achieve the RF modulation of the optical spectrum. The combined signal was then sent to a dispersive fibre which provided the differential delay between the wavelength slices. A Gaussian windowed filter with seven samples was demonstrated up to 2 GHz. In this case the main limitation was the low finesse of the slicing filter. Clearly using higher-quality slicing filters would provide the possibility for a filter with higher-performance characteristics. This was experimentally proposed by Capmany and co-workers [36] who demonstrated a 34 tap FIR transversal filter with more than 35 dB of sidelobe suppression ratio by means of using a transmissive low spectral period optical Fabry–Perot filter to achieve subnanometre resolved optical sampling. A drawback of this approach is that it is difficult to achieve filter tuneability since this requires the change of the slicing filter FSR. The former drawback can be alleviated if slicing is performed with tuneable optical filters such as fibre Bragg gratings. For instance, Pastor [37] has demonstrated a tuneable notch filter where the broadband optical source is sliced by means of two FBGs, one of which is tuned by means of a strain application stage. Mora and co-workers [38] have extended this approach to four FBGs and hence four samples by using both a series and a parallel approach where FBGs are glued onto the substrate of a mechanical platform. The stress applied to the platform produces a uniform change in the spectral separation of the FBG resonances and thus a uniform incremental delay change between the filter consecutive samples. Figure 8.17 shows an example for the serial configuration. Another interesting option is to employ AWG devices with high port counts in order to implement source slicing with a high number of samples [39]. Pastor and co-workers [40] have recently reported a 12 sample transversal filter using a two-stage 1 40 AWG configuration shown in Figure 8.18. This structure has the advantage of also allowing filter reconfiguration if switches or variable attenuators are placed in between the demultiplexing and the multiplexing stages. We finally address the efforts that have been carried out in order to implement the possibility of filter reconfiguration (i.e. windowing). Filter reconfiguration is possible using hybrid optoelectronic approaches. Here, the optical part provides the delay between samples while the electronic partis in chargeofprovidingvariableand even negative coefficients to the filter samples.

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Figure 8.17 Four-tap tuneable notch filter using a broadband optical source sliced by means of four FBGs, tuned by means of a strain application stage [38]

For instance, Yost and co-workers [41] have demonstrated a 48-stage transversal filter using monolithic microwave integrated circuits (MMICs) and optical fibre delay lines. This approach has the inconvenience that it is not all-optical and therefore is bandwidth-limited by the MMIC performance. Furthermore, since MMICs are active, considerable noise is added. In the case of

23 km SSMF coil

1X40 AWG

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Figure 8.18 source [40]

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Transversal filter using high port count AWG devices to slice an input broadband

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40 SLM array Diffraction grating

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lens

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GPIB

Figure 8.19 40-sample reconfigurable transversal filter using a two-stage 1 40 AWG configuration and a 40 SLM free space array [28]

all-optical approaches, the filter apodization requires the possibility of changing the power of the optical slices from the broadband source. This usually requires the use of controllable attenuators, as reported by Mora et al. [42]. If the sliced source is not an LED or an EDFA source, but a multimode laser, then the sample amplitudes can be controlled through the injected bias current to the device as shown in [43]. However, a most versatile alternative has been recently proposed which is based on the combined use of AWG devices to implement broadband source slicing with a high number of taps [93, 94] and an array of spatial light modulators (SLMs) to implement signal tapping. Figure 8.19 depicts the scheme for this configuration. In this particular case the structure implements a 40-tap reconfigurable microwave photonic filter. This structure has great potential because the spectrum slices can be independently adjusted or switched on or off by optical components as electronically operated attenuators providing fast tuneability or reconfigurability. For instance, Figure 8.20 shows different transfer functions obtained when programming standard windowing functions well known in the literature. These window functions were dynamically loaded into the SLM array by a computer thus demonstrating the possibility of adaptive filtering.

8.5 Fibre Grating Delay Line Filters In 1994 Ball and co-workers [44] proposed a programmable delay line capable of generating 50 ns true time delay in discrete 10 ns intervals based on the combination of an externally modulated tuneable fibre laser and a six-element wavelength multiplexed uniform fibre Bragg grating array with the grating spacing set to yield the desired delay (Figure 8.21). This fuelled research towards the application of recently available fibre gratings in the implementation of optical processors of radio frequency signals. As discussed above, uniform fibre Bragg gratings can also be employed as weighting elements, since their reflectivity changes with the signal

217

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wavelengths and their Bragg wavelength is adjustable. In this section we discuss their role when they are used as delay elements which depend on the grating position on the fibre. This limitation is removed by the use of linearly chirped gratings. A simple discretely tuneable notch filter was demonstrated [45] using two Bragg gratings written in series in one of the arms of a coupler. In such a structure, they are used as tapping elements and the delay between taps is fixed by the distance between the gratings. Continuous tuning was demonstrated by Hunter and Minasian in a similar structure but using chirped

Figure 8.21

Programmable fibre optic delay line (Ball et al. [44]) ( 1994 IEEE)

218


Figure 8.22 Microwave optical filter using in-fibre Bragg grating arrays. Reproduced from [47] ( 1996 IEEE)

gratings on separate ports of a coupler [46]. The variation of the wavelength of the source over the chirp range of the gratings shifts linearly the point of reflection of the grating; therefore, a continuously variable time delay of the processor is achieved by controlling the distance between the reflection points of the two gratings. The notch frequency spacing of the filter is changed up to 4.8 GHz, with notch depths from 20 to 30 dB. In a further step [47], a multitap (29 taps) transversal bandpass filter was demonstrated by spectrally slicing a broadband source with wavelength multiplexed Bragg grating arrays equispaced in time (Figure 8.22) showing the possibility of shaping the tap element profile to obtain windowing for the design of the filter response. By apodizing the reflectivity of the gratings in the array according to a Kaiser window, the main- to side-lobe level was measured at 18 dB. To improve the performance characteristics shown by previous devices, a tuneable bandpass transversal filter was proposed in [48]. In this filter, light from a tuneable laser is reflected by a four-grating array, each of which has four fibre Bragg gratings. Changing the wavelength of the tuneable laser allows selection of operating gratings. For each grating array, the location of each grating element is precisely arranged to give a particular desired bandpass filtering frequency which can be selected within a set of four different FSRs. Although the tuneability is certainly restricted, the response of the filter can be improved by weighting the reflections of the gratings (stop-band attenuation of 12 dB). Another scheme using eight grating elements [49] enables the choice of more appropriate tap weighting functions and provides stopband attenuation of over 30 dB by using a Hamming windowing function. Since this filter works incoherently, the FSR is therefore limited by requiring differential delays greater than the optical coherence length of the laser source. Using a laser array can prevent optical coherent interference; but it would limit the practical applications when larger optical bandwidths are required. An alternative method to realize incoherent operation is to use polarization synthesis by using a Hi–Bi fibre grating array, which has been demonstrated in notch [50] and bandpass filtering [51] although only discrete tuneability has been achieved. In order to double the number of taps without doubling the number of gratings used in this structure, the addition of a Mach–Zehnder section was proposed in [52] (see Figure 8.23). One beam of the reflected optical signal from the eight-grating arrays passes directly and the other is reflected at an induced grating with the same Bragg wavelength. This grating is so placed that


219

Figure 8.23 Tap multiplexed fibre-grating-based optical transversal filter. Reproduced from [52] ( 2000 IEEE)

the optical path difference between the two arms is exactly eight times that of the unit delay time which is related to the spacing between the adjacent two taps. Therefore, the filter Q factor has been doubled and the filter rejection level has been enhanced with respect to results published in previous work [49]. An optical fibre recirculating delay line offers a compact configuration and can provide a steeper notch response than a Mach–Zehnder notch filter. In such a filter, the frequency response is controlled by the coupling coefficient of the coupler and the length of the recirculating loop [53] but the incorporation of a fibre grating array [54] enables one to obtain a tuneable free spectral range, as shown in Figure 8.24, and a maximum notch depth (36.6 dB) was achieved by adjusting the insertion loss in the fibre loop. Furthermore, continuous tuneability can be obtained in these infinite impulse response (IIR) filters by using a chirped fibre grating instead of a fibre grating array. The introduction of gain into recirculating delay lines can generate a bandpass response with high quality factor.

Figure 8.24 Optical fibre recirculating delay line incorporating a fibre grating array. Reproduced from [54] ( 2001 IEEE)

220


In fact, high Q filters had been achieved previously, both in fixed and tuneable operation by placing a section of an active fibre either in a loop structure [55] or within a pair of fibre Bragg gratings [56]. The first scheme is based on a single fibre Bragg grating inside a loop with a gain medium. Multiple reflections are obtained from the same grating, and the losses are compensated by means of an active fibre, showing a narrowband bandpass response with a Q of 200. In the second scheme one of the fibre gratings is partially reflecting (50%) while the second one is 100% reflecting. Hence, the signal is reflected successively from the gratings by passing it back and forth between the gratings and the active fibre, which is used to compensate for the light coupled out and for other losses. This configuration produces a very high number of samples and ensures the tapped delay time spacing and weights are uniform, and thus, enables the realization of filters with high selectivity (Q ¼ 325), where filter frequency can be tuned if wavelength selective chirped fibre Bragg gratings are used as the tapping elements. The main drawback is that although the weight of the samples can be reconfigured by changing the amplifier gain, it cannot be done independently sample by sample. Furthermore, the length of the active medium severely restricts the filter FSR. A solution for this last inconvenience has been proposed in [57] by placing the former filter in tandem with a Mach–Zehnder lattice filter the period of which is N times larger than that of the former (Figure 8.25). The passive sections are used to eliminate the intermediate peaks and to select the multiple that corresponds to the desired filter frequency. In this system, the coherence length of laser must be less than the minimum delay path difference in all possible paths in the structure to avoid coherent interference effects. Q factors over 800 have been demonstrated operating at a fundamental frequency of 1.1 GHz. Furthermore, there has been a proposal of a new topology based on the hybrid filter previously reported, but adding a passive small free spectral range filter [58]. This filter operates with a small FSR large delay line difference passive filter, the length of which is a high integer multiple of the active fibre length. Therefore, one of the passbands coincides with the filter frequency of the hybrid filter, the response peak of the filter is narrowed and Q of the filter is significantly increased (Q ¼ 983). The active fibre Bragg grating pair structure has also been employed in a topology to provide simultaneously both a narrow excision band for rejecting RF interference and at the same time to transmit the wanted signal over a flat and wide passband in a large frequency range. In this

Figure 8.25

Main results of [57] (courtesy of Dr R.A. Minasian)


221

structure [59], the fibre-optic signal is split and routed into two different parallel paths: a fibre direct path to provide a broadband all-pass structure for the RF signal and a parallel path which contains a high-Q optical bandpass filter operating in transmission rather than in reflection mode [56]. Each output is detected using a photodiode in a balanced configuration so as to subtract the photocurrents and, hence, a notch filter is realized (notch depth over 40 dB) with the squareness or shape factor of the stopband response significantly improved. Another approach based on a dual-cavity bandpass optical structure in which two pairs of active fibre Bragg grating cavities are used with optical gain offset to control the poles and stopband attenuation characteristics of the filter has been proposed recently [60] to solve the problem of simultaneously presenting both high Q and a high skirt selectivity filter response. The approaches described above do not usually address dynamic tuneability and reconfiguration simultaneously. The dispersive nature of linearly chirped fibre Bragg gratings (LCFBGs) can be employed to obtain tuneable RF transversal filters. Linear and continuous tuning was demonstrated for the first time in an optical notch filter consisting of a fibre optic Mach– Zehnder section combined with a linearly chirped fibre grating [61]. The notch frequencies of this filter are given by the difference of the time delays between two light beams, consisting of a fixed time delay difference provided by a fibre delay line in one of the interferometer arms, and a tuneable time delay difference supplied by a linearly chirped grating in the other, as shown in Figure 8.26. The time delay introduced by the grating is wavelength dependent and thus tuneable by varying the operating wavelength in a tuneable laser with a coherence length significantly less than the optical path difference of the notch filter. High-resolution bandpass and widely tuneable filters, together with a high-Q characteristic, have been demonstrated in a similar configuration to that described in [56], but using chirped Bragg gratings and a section of active fibre [62]. Tuning is achieved by selecting the reflected wavelength by the gratings and limitations imposed by the interaction of the dispersion of the chirped gratings with the modulation sidebands can be overcome by using SSB modulation techniques. Linearly chirped fibre Bragg gratings can also be employed to obtain programmable RF transversal filters by means of feeding the RF modulated output of an array of sources to the

Figure 8.26 Fibre optic radio frequency tuneable notch filter based on a chirped fibre grating. Reproduced from [61] ( 1998 IEEE)

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Layout of an RF transversal filter composed of an LCFBG fed by a laser array [65]

device [63–65]. The layout of the filter for a specific case of a laser array of five elements is shown in Figure 8.27, although in general it is composed of N sources. The advantage of using a laser array as a feeding element to the delay line is twofold. The first advantage is that the wavelengths of the lasers can be independently adjusted. Thus spectrally equally spaced signals representing RF signal samples can be fed to the fibre grating, suffering different delays, but keeping constant the incremental delay T between two adjacent wavelengths emitted by the array if the delay line is implemented by means of a linearly chirped fibre grating. Referring to Figure 8.27, this means for instance that the delay between the signals at l1 and l2, l3, l4, l5, . . . lN is respectively T, 2T, 3T, 4T and (N 1)T. Hence the configuration can act as a transversal filter, where the basic delay is given by T. Furthermore, T can be changed by proper variation of the laser central wavelengths in the array. Thus this structure provides the potential for implementing tuneable RF filters. The second advantage stems from the fact that the output powers of the lasers can be adjusted independently and at high speed [66, 67]. This means that the time response of the filter can be apodized or in other words, temporal windowing can be easily implemented and therefore the filter transfer function can be reconfigured at high speed. We have experimentally succeeded in the demonstration of both tuneability and reconfigurability. For instance, Figures 8.28 (a) and (b) show the results when the samples of the five-stage uniform filter where weights are given by a truncated Gaussian window. The upper trace in Figure 8.28 (a) shows the spectrum corresponding to the uniform filter (i.e. unapodized) where the normalized output powers from the lasers in the array is [1 1 1 1 1] and the middle trace corresponds to a five-stage Gaussian windowed filter where the normalized output powers from the lasers in the array is given by [0.46 0.81 1 0.81 0.46]. For the sake of comparison, the

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(a) Filter reconfigurability demonstration; (b) filter tuneability demonstration [66]

broken trace shows the theoretical results as expected from Equation (8.1). Figure 8.28 (b) demonstrates the resonance tuneability. An additional advantage of employing laser arrays is the possibility of exploiting WDM techniques for parallel signal processing [68] and to provide both a large number of taps and arbitrary coefficients [69]. In the first case, the possibility of implementing a bank of parallel transversal filters is feasible by extending the concept of a single fibre-optic RF transversal filter based on multiple linearly chirped fibre Bragg gratings and dispersive elements into the implementation of a bank of transversal filters, by means of wavelength division multiplexing techniques. The use of this technique allows for the simultaneous processing of a single RF signal by various filters. Figures 8.29(a) and 8.29(b) represent the concept and the transfer functions resulting from the implementation of a bank of two filters (bandpass and notch). In the second case, WDM combined with the regularity characteristics of the sampling process allows for the implementation of a high number of taps by exploiting the concept of spectral mapping and partitioning. A structure that implements a typical square-type filter response with negative coefficients employing Bragg grating arrays is shown in Figure 8.30 [69]. The array of taps is divided into N sets of M elements, and tap weighting and time slot delay for each set are obtained using a spectral filter comprising an array of Bragg gratings at different wavelengths and strengths, together with lengths of fibre delay line. The structure includes tap weighting and sampling section for the positive taps and a tap weighting and sampling section for the negative taps. By using differential detection both signals can be combined to generate arbitrary discrete impulse response functions. Chirped fibre Bragg gratings have also been proposed to obtain tuneable dispersion slope gratings showing suitable optical bandwidth for RF applications. By acting on them, it is possible to vary the time delay of each optical wavelength carrier. Temperature and strain gradients on the CFBG or the use of a piezoelectric transducer are some of the most extended approaches. Recently, we demonstrated the dynamic chirp of an original uniform fibre Bragg grating which is controlled by using a nonuniform magnetic field and a magnetostrictive alloy as a transducer [70], as shown in Figure 8.31. Thus, setting the optical wavelengths at fixed values, a tuneable transversal filter is achieved by changing the dispersion slope of the grating [71] from 300 to 900 ps/nm. These magnetic systems show advantages such as good dynamic response and easy implementation in an FSR tuning range of several GHz. Other

224


Figure 8.29 Implementation of parallel RF signal processing by means of exploiting WDM [68]. (a) Filter bank implementation concept (above), and (b) implementation of two different filters in parallel (below)

τ

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Figure 8.30 The concept of spectral mapping and partitioning to implement a filter with a high number of taps [69] (courtesy of Dr R.A. Minasian)

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Transversal filters based on tuneable dispersion fibre Bragg grating [70]

similar approaches employ tapered fibre Bragg gratings (TFBG) disturbed by the magnetic field inside a simple coil and a magnetostrictive transducer and have also demonstrated their suitability for implementing variable transversal filters.

8.6 Implementation of MWPSP with Negative and Complex-valued Coefficients As was mentioned in Section 8.3, incoherent structures can only implement filters with positive coefficients. This is a serious limitation, since the range of impulse responses or transfer functions that can be implemented with positive coefficients is very limited [95, 96]. For instance, it is not possible to implement filters with flat bandpass and sharp transitions and also there is always a filter resonance present at baseband (frequency zero). In order to have higher flexibility it is interesting to be able to implement incoherent filters either with negative or complex-valued coefficients. This problem is not new, but researchers working in the field of spatial incoherent signal processing have faced it and come to several imaginative solutions. In the context of guidedwave signal processing, work has been carried out in the 1980s and 1990s and it is being continued. In this section we briefly review some of the most important attempts to overcome this limitation. The first technique, known as differential detection, was proposed by Moslehi and coworkers as early as 1984 [4], and was itself a particular case of an elegant solution proposed by Goodman and Woody in 1977 [97] to implement incoherent spatial filters with complex coefficients. The basics of this technique are explained in Figure 8.32. The impulse response of an arbitrary filter can be decomposed into a positive h1(t) and negative h2(t) part. The first one includes all the positive samples, whereas the latter includes all the negative taps. Each part can be implemented by a different section with only positive coefficients. The output of each section is fed to a pair of photodiodes placed in a differential configuration. Thus, signal subtraction is achieved in the final optoelectronic conversion. Although this approach was proposed in the 1980s, the first demonstration of its applicability

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Figure 8.32 Basic principle of the technique of differential detection to implement incoherent filters with negative coefficients [4]

on a RF photonic filter was performed by Sales et al. in 1995 [23] and has been employed successfully by other authors [69]. The differential detection technique allows the implementation of any kind of negative coefficient filter. However, it requires a structure duplication needing extra components and also careful path balance must be achieved in the microwave section of the receiver before signal combination. It is also difficult to apply to reconfigurable filters since new responses might have different values of h1(t) and h2(t) requiring different sections. A second alternative is the so-called hybrid optoelectronic approach [41, 98]. Here, delay lines are implemented optically, but the filter taps are implemented electronically, that is after photodetection. Since current signals can be positive or negative, this allows the implementation of filters with positive and negative coefficients. Figure 8.33 shows the first implementation of this approach, proposed by Swelka and MacDonald for a 16-stage transversal filter [98].

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Figure 8.33 Implementation of an incoherent RF optical filter with negative coefficients using a hybrid optoelectronic approach [98]

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RF combiner

RF

Optical combiner

4τL

Tap #4 Tap #3 Tap #2 delay Tap #1 delay delay phase shift delay phase shift phase shift gain phase shift gain gain gain

τL

2τ L

3τ L

4τ L

RF combiner Output

1x4 MMIC

Figure 8.34 Implementation of an incoherent RF optical filter with negative coefficients using MMICs [41]

Light from a directly modulated laser is split by a coupler to implement the different signal samples. Each coupler output is then fed to a different optical delay line and converted by a different photodetector. The value and sign of the bias voltage to the photodetectors implements the magnitude and sign of the tap coefficients. Figure 8.34 shows another approach proposed by Yost and co-workers which benefits from the characteristics of MMICs [41]. Tap weighting and sign is carried out at 1 4 MMIC stages. Tap delay is achieved in a two stage process, first in the optical domain, secondly in the 1 4 MMIC. A 48-tap MMIC filter at 11.5 GHz was experimentally demonstrated yielding better noise performance than pure MMIC based filters. However, the filter bandwidth was limited to that of the MMIC circuits. A final drawback is that tap weighting adds thermal noise. Hybrid optoelectronic approaches provide the desired flexibility of the coefficients at a high cost, since the filter performance is band-limited to that of the electronic elements providing the taps. Also, since tap weighting is provided by active elements, a substantial increase in noise contribution is expected. Ideally it would be better to achieve the possibility of implementing negative coefficients directly in the optical domain. Recent research approaches have been directed towards this objective. For instance, Coppinger and co-workers [99] have proposed to exploit the phase shift that is obtained in cross-gain and cross-phase wavelength conversion using SOAs in the modulating signal of the converted carrier. Figure 8.35 illustrates this concept for co-directional XGM wavelength conversion, although the principle works exactly the same for counter-directional propagation. This property can be exploited to implement filters with negative coefficients when different wavelengths implement different filter taps. In this case the wavelengths carrying negative samples must be converted using an SOA device (they can be converted to the same wavelength!). λ1 λ2

SOA

Filter

λ1

Figure 8.35 -phase experienced by the modulating signal upon XGM SOA-based wavelength conversion. Reproduced from [99] ( 1995 IEEE)

228


Figure 8.36 Layout and results for a two-sample notch filter with negative coefficients using phase inversion in SOA-based wavelength conversion. Reproduced from [99] ( 1995 IEEE)

Figure 8.36 shows the layout and results for the implementation of a two-sample notch filter with negative coefficients. This technique has the main advantage that phase inversion, and hence negative coefficients, are obtained directly in the optical domain. However, the filter bandwidth is limited by the bandwidth conversion of the SOA (which can be above 40 GHz). They are also difficult to reconfigure (i.e. it is difficult to change a tap sign from positive to negative and vice versa). Another disadvantage is that it is not easy to implement multi-tap filters (in fact only notch filters have been demonstrated so far). A final question of concern is the potential polarization sensitivity of these structures since SOA devices are polarization sensitive. Two all-optical techniques for the implementation of negative coefficients have been reported recently. The first one is based on the slicing of a broadband ASE source by means of uniform fibre Bragg grating (UFBG) filters [100]. The principle is shown in Figure 8.37. Here positive coefficients are implemented by tuneable sources amplified by an EDFA, while

Figure 8.37 Technique for the implementation of negative coefficients by spectral carving of the ASE spectrum of a broadband source with FBGs. Reproduced from [100]

229


R (dB)

5 0 -5

-20

1528

1530

1532

1534

λ (nm)

H (dB)

-40

-60

0.0

2.5

5.0

7.5

10.0

f (GHz)

Figure 8.38

Five-tap transversal filter with two negative samples

negative coefficients are obtained by ‘carving’ notches in the EDFA ASE spectrum by means of FBGs in transmission. With this technique phase inversion (negative coefficients) is directly achieved in the optical domain with no bandwidth limitation. Furthermore, filters can be reconfigured by tuning the sources and the FBGs. A main drawback of this approach is that the average optical radiation level is not zero; that is, positive and negative coefficients are obtained relative to the average ASE radiation. This implies that there is always a DC component present in the filter transfer function, but this can be easily suppressed at photodetection with a blocking filter. A final advantage is that due to its all-fibre format, this technique is polarization insensitive. In Figure 8.38 we show the results obtained for a five-tap transversal filter with three positive taps and two negative taps. The DC main lobe can be appreciated in the filter transfer function. Otherwise the obtained transfer function corresponds to a filter with negative coefficients. The second technique recently reported [101] relies on the counter-phase modulation in Mach–Zehnder external modulator devices by means of employing the linear part of the transfer function with positive and negative slopes. The concept is illustrated in Figure 8.39 with a simple RF modulating source. The left part of the figure depicts the typical output versus input optical power sinusoidal transfer function of an electro-optic Mach–Zehnder modulator (EOM) as a function of the applied bias voltage VBIAS. Two linear modulation regions with opposite slopes can be þ observed centred at VBIAS and VBIAS respectively. As shown in the right part of the figure, the same RF modulation signal applied to the modulator at each of the former bias points will produce an optical modulated output signal with the same average power but where the modulating signals are shifted or in counter-phase. In other words they can be considered as being of different signs. This principle can be employed to implement RF photonic filters with

230

Microwave Photonics: Devices and Applications π shifted RF modulation Negative slope

of the optical carriers

sal

output POpt

Positive slope

POpt (dBm)

sal

POpt (dBm)

VBIAS

− VBIAS

+ VBIAS

VBIAS

Same RF modulation

VBIAS

Figure 8.39 Counter-phase RF modulation in a Mac–Zehnder device by changing the device bias voltage [101]

negative coefficients if the output wavelengths from a multi-wavelength source (either a laser þ array or a sliced broadband source) are applied to an MZM modulator biased at either VBIAS or VBIAS depending on whether they are employed to implement positive or negative filter samples. The output from both modulators are combined and sent to a dispersive element (i.e. a linearly chirped fibre Bragg grating or a fibre coil) that implements the constant differential time delay between the filter samples. The feasibility of this approach has been experimentally demonstrated with a six-sample uniform RF photonic filter with three positive and three negative coefficients using the laser array implementation described in [65]. Figure 8.40 shows the experimental layout. An array of six tuneable lasers, emitting at l1 ¼ 1546.65 nm, l2 ¼ 1548.43 nm, l3 ¼ 1550.11 nm, Tuneable sources

Polarization controllers(PC)

Laser at λ1 Laser at λ3

Star coupler

DC bias control

EOM 1

Laser at λΝ−1 2x1 coupler

Laser at λ2 Laser at λ4

Laser at λΝ

3dB RF coupler

Dispersive device (fibre coil or LCFBG)

Star coupler

EOM 2 DC bias control

Vector network analyser

Figure 8.40 Experimental set-up of a six-tap transversal filter with three negative coefficients using the EOM phase inversion technique [101]

231


l4 ¼ 1551.86 nm, l5 ¼ 1553.47 nm and l6 ¼ 1555.24 nm, was selectively fed to two MZM þ ¼ 0 V and VBIAS ¼ 3:9 V respectively. Wavelengths l1, l3 and modulators biased at VBIAS þ l5 were fed to the MZM biased at VBIAS (positive samples), whereas wavelengths l2, l4 and l6 were fed to the MZM biased at VBIAS (negative samples). Both EOMs were modulated by the same RF signal, a 5 dBm sinusoidal signal provided by a lightwave component analyser (LCA). The frequency of the RF modulating signal was varied from 130 MHz to 5 GHz in order to measure the transfer function characteristic of the filter. Figure 8.41 shows the measured modulus of the transfer function for a filter with six uniform coefficients. Both the experimental (solid line) and the theoretical (broken line) results are shown for reference and comparison. As expected, the filter resonance at baseband (typical of positive coefficient filters) has been eliminated thus confirming the feasibility of the proposed scheme for the implementation of negative coefficients. With this technique phase inversion in the modulation process is limited by the modulator bandwidth which can be high enough so as to reach 40 GHz. Although in principle as shown in Figure 8.41 two modulators are required in the transmitter, in practice this requirement can be reduced to only one modulator if this device is provided with two input ports. A main advantage of this configuration is that there is no need to duplicate the optical structure of the filter to implement positive and negative coefficients since the taps already carry their sign prior to being delayed. Another interesting feature is that the sign is decoupled from any sample weighting process. Further work has provided novel approaches for the implementation of filters with negative coefficients. For instance, a new all-optical technique based on a dual-output EOM connected to undergo double-pass modulation has been used to obtain a frequency response equivalent to

5

Normalized amplitude(dB)

0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Frequency (GHz)

theory experiment

Figure 8.41 Measured modulus (solid line) and predicted results (broken line) of the transfer function for a filter with uniform coefficients using the set-up of Figure 8.40 [101]

232


a two-tap negative notch filter [102] under two different topologies. The first one connects the two outputs via an isolator, and the second one uses a reverse connection of the EOM together with a grating reflector, which can be integrated on a planar circuit and extended to tuneable filters when a chirped grating is employed. In another approach, a novel configuration to implement microwave photonic filters featuring positive and negative coefficients has been reported which is based on the use of a single-phase modulator to modulate an array of optical sources followed by a filtering stage to choose the optical carrier and higher or lower radiofrequency sideband depending on the sign of the desired coefficient. Experimental results have proved the feasibility of this concept. All in all, maximum flexibility is obtained if filters with complex-valued coefficients can be implemented since an extra degree of freedom is available. This feature is essential, for example, to obtain tuneable filters free from the requirement of changing the value of the free spectral range in order to achieve resonance tuneability. The implementation of filters with complex coefficients depends on the possibility of obtaining by optical means a tuneable phase shift that remains constant over the microwave spectral region of interest. In [103] a first proposal and experimental demonstration has been reported of a two-tap incoherent microwave photonic filter with complex-valued coefficients implemented in the optical domain. The system is based on a tuneable optically induced RF phase shift that is obtained by means of combining optical single-sideband modulation and stimulated Brillouin scattering. Figure 8.42

Figure 8.42 Theoretical concept of the implementation of complex-valued incoherent filters using stimulated Brillouin scattering (top). Experimental set-up for the demonstration of a two-tap complexvalued filter (left) and a tuneable transfer function with no change in the FSR value (right) (bottom). Reproduced from [103]


233

plots the principle of operation, filter configuration and the main results regarding the tuneability of the filter. A tuneable pump and Stokes waves are employed to provide a tuneable RF phase shift between the optical carrier and the RF subcarrier as shown in the upper-right part of Figure 8.42. Achievable RF phase shift is obtained upon detection and beating between the optical carrier and the subcarrier. As shown in the middle-right part of the figure, a complete 360 degree phase shift is achievable and thus the location of the filter zero can be rotated to any direction in the complex plane. As a consequence, in the case of a two-tap notch filter, the notch position can be tuned without changing the filter FSR parameter as shown in the lower-right part of the figure. The technique has been extended recently to the implementation of multiple-tap filters [104].

8.7 Epilogue and Final Remarks We have provided a comprehensive review of the fundamentals, applications, past and recent progress and current state of the art of photonic filters for the processing of RF and microwave signals. To complete this treatment a significant reference list with the most relevant references published so far in the subject over the last 25 years is included as well. These references are intended to provide the reader with the possibility of completing the technical details of the concepts that have been presented here. Obviously, as in any book chapter, the space limitation limits the degree of detail with which we can treat the subject, therefore we apologize in advance if relevant work from other researchers may have been omitted. Future directions in this field should be directed towards the implementation of compact, stable, tuneable and reconfigurable devices featuring high Q values (over 5000), single resonance filters and integrated versions of the proposed structures. While this may be a difficult challenge with currently available fibre technologies, novel ones such as integrated optics, photonic crystal devices and fibres may provide the platform towards the achievement of this goal.

Acknowledgements The authors wish to acknowledge the EU funded research projects IST-2001-37435 (LABELS) and IST-2001-32786 (NEFERTITI) under which part of the work reported here is being carried out. The support of the Valencian Government through the PROMETEO 2008/092 program of research excellence is also gratefully acknowledged.

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9 RF and Microwave Photonics in Biomedical Applications Afshin S. Daryoush

9.1 Introduction In the last 20 years the field of microwave photonics has evolved due to unique features of analogue fibre-optic systems and its applications in radio over fibre for telecommunications [1] and optically controlled phased array antennas [2] for military applications, as has been discussed in earlier chapters of this book. Recently, microwave photonics techniques have also been extended to biomedical systems and this chapter presents two distinctive biomedical imaging applications that employ these techniques. (Optics already lends its application to laser Doppler anemometry, optical biopsy and optical molecular imaging, and phase microscopy.) The first application to be discussed is the design and implementation of optical hydrophone for calibration of ultrasound transducers for frequencies up to 100 MHz, which has found applications in sub-millimeter wave imaging and therapeutic applications. The second is the use of broadband modulated near infrared (NIR) light waves for quantifying blood flow and cellular functionality using spectroscopy, which is to be applied to coagulation monitoring and functional imaging with sub-centimetre spatial resolution using photon density waves. Both techniques are first discussed in terms of the fundamental physical interaction of lightwaves with biological tissues and the technical advantages that RF and microwave photonics could bring to conventional imaging modalities.

9.1.1 Introduction to Optical Hydrophone Only a decade ago, the highest ultrasound imaging frequency was of the order of 7 MHz. Today, modern diagnostic machines, particularly those designed for applications such as dermatology, ophthalmology and microsurgery, operate at centre frequencies close to 15 or 20 MHz [3].


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Figure 9.1 High-resolution imaging of biological tissues using short ultrasound pulses with a bandwidth requirement of up to 100 MHz

Also, a majority of the currently available machines has integrated harmonic imaging capability that can provide diagnostic images at twice the fundamental frequency and hence increase the resolution twofold. However, ultrasound probes need to be calibrated in the measurement bandwidth extending to at least eight times the centre frequency of the imaging transducer [4, 5]. This frequency limit has been introduced to account for nonlinear propagation phenomena, which lead to distortion of the pressure–time waveform launched into the examined tissue. Assuming the centre frequency of the imaging array to be about 12 MHz, this would require the sensitivity of the hydrophone probe to be determined in the vicinity of 100 MHz [6] (Figure 9.1). In order to acquire and reproduce faithfully the pressure–time waveforms, and also to determine accurately the key acoustic parameters of the characterized acoustic field, the active element of the probe has to be considerably smaller in comparison with the cross sections of the acoustic beam profiles measured; alternatively, tedious spatial averaging correction models have to be used [4, 7, 8]. In order to ensure half-wavelength sampling that is needed to eliminate spatial averaging effects, the pressure-sensitive portion of the probe needs to be about 8 mm to faithfully reproduce the field at 100 MHz (assuming plane waves). Unfortunately, the physical dimensions of available ultrasound probes typically have diameters of 500 mm [4–6, 9]. The smallest available probe has a diameter of approximately 80 mm and this is still an order of magnitude too large for 100 MHz measurements. The development of fibre-optic (FO) probes that are specifically designed to increase sensitivity to ultrasound waves with a diameter of about 8 microns to minimize the spatial averaging error up to 100 MHz is discussed. In Section 9.2, various principles of sensing acoustic waves using interaction of acoustic energy with intensity, phase and frequency of lightwaves in the FO probes are briefly outlined, and emphasis is given to the intensity detection technique. Theoretical calculations of the laser source output power and acoustic pressure amplitude needed to ensure a minimum acceptable signal-to-noise ratio are presented, and an experimental evaluation of a custom-designed down-tapered gold-coated FO probe, which meets bandwidths of up to 100 MHz, is also explored.

9.1.2 Introduction to Optical Spectroscopy using NIR Near infrared (NIR) spectroscopy is a new, noninvasive technique to analyse living tissue in terms of absorption and reduced scattering coefficients, which could provide information about disease-related functional and structural changes [10–12]. Three main categories of NIR spectroscopy are time domain, frequency domain and continuous wave (CW) measurement techniques [13]. The frequency-domain method has attracted interest from the biomedical

RF and Microwave Photonics in Biomedical Applications

241

Figure 9.2 Concept of diffused photon near-infrared spectroscopy in biological tissue depicting: (a) optical absorption coefficient of oxygenated and de-oxygenated haemoglobin (Oxy-Hb and Deoxy-Hb) and water in near-infrared region; (b) impact of modulation frequency on tissue penetration depth and structure of banana-shaped photon scattering in tissue

research field for decades due to its low component cost, ease in separating absorption and scattering parameters, and potential for real-time imaging. In frequency-domain photon migration (FDPM) methods, diffuse photon density waves (PDW) are generated when light is modulated by radio frequency signals, which propagates with a wavelength of several millimetres to centimetres depending on the modulation frequency. Amplitude and phase information of the diffuse photon density waves are used to map the optical absorption and scattering properties of the medium. These optical properties in turn are used to obtain haemaglobin concentration, blood volume and ‘absolute’ oxygen saturation [14, 15]. There are several advantages to multi-frequency instruments compared with single-frequency instruments. Since most tissues have a layered structure and because photon penetration depth is less at a higher frequency due to a higher loss (cf. Figure 9.2), by sweeping the modulation frequency one can have information for all layers in a single measurement. This approach is very important in clinical measurements, where it is preferable to make a single measurement and obtain as much information as possible, due to the calibration challenges. The development of specialized optical systems with modulation capability of up to 3 GHz has also been demonstrated and spectroscopic information is conducted for both solid and liquid phantoms. Moreover, the accuracy of the broadband extraction process is compared to the single-frequency extraction for phantom resembling breast tissue, where the results of this extraction are extended to future clinical imaging.

9.2 Approaches to Fibre-optic Based Acoustic Pressure Sensors Fibre optics has been used in underwater acoustic sensing for a long time and is now being extended to biomedical applications. Optical fibres have the following advantages over

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conventional acoustic sensing/imaging techniques: (i) immunity to electromagnetic interference; (ii) small sensing area; (iii) small physical dimensions and low weight; (iv) large bandwidth,and (v) high resistance to high temperature, corrosion by chemicals and adverse climatic conditions. This section provides an overview of various fibre-optic sensing schemes which have been used in acoustic sensing applications. An electric wave travelling in a medium in the positive z-direction can be expressed by the basic equation given below: Eðz; tÞ ¼ E0 cosðvt kz þ u0 Þ

ð9:1Þ

where E0 is the electric field amplitude in V/m, v is the angular frequency in rad/s, and u0 is the initial phase in radians. In fibre-optical sensing, the physical phenomenon being sensed interacts with the fibre and changes one or more of the above parameters associated with the electromagnetic field in or around the fibre. Accordingly we can classify acoustic fibre-optic sensors as intensity modulated sensors, frequency/wavelength modulated sensors and phase modulated sensors. After a review of the best reported results, the latest ‘hero’ performance results of intensity detection techniques are discussed by the author in Section 9.3.

9.2.1 Intensity Modulated Sensors Acoustic pressure induces change in the intensity of light passing through an optical fibre. These sensors can be reflection type, transmission type or total internal reflection based. 9.2.1.1 Reflection Type In reflection type sensors, the incident pressure induces a change in the refractive index of the sensing medium surrounding the fibre (Figure 9.3). This leads to a change in reflectance at the fibre–water interface. The intensity of reflected light is thus modulated by incident pressure.

Figure 9.3 Reflection type fibre-optic acoustic sensor with intensity detection [16]. Reprinted from J. E. Parsons, C. A. Cain, J. B. Fowlkes, ‘‘Cost-effective assembly of a basic fiber-optic hydrophone for measurement of high-amplitude therapeutic ultrasound fields,’’ J. Acoust. Soc. Am., vol. 119, pp. 1432–1440, 2006. ( Copyright 2006, American Institute of Physics)


Figure 9.4

243

Schematic of transmission type intensity modulated fibre-optic acoustic sensor [17]

This change in intensity is detected using a photodetector [16] where typically a responsivity of 302 re 1 VmPa and sensitivity of 0.9 MPa has been reported. 9.2.1.2 Transmission Type Another technique is the transmission type approach [17], where two single mode fibres are placed tip-to-tip at a very small separation. An acoustic wave incident on the tip causes motion of the fibres and hence changes the optical coupling efficiency (Figure 9.4). The transmitted light intensity thus varies in accordance with the pressure. A modification of the above approach is the schlieren technique [18], in which the region in between the two fibres is occupied by a grating structure to enhance system sensitivity by monitoring changes in coupling efficiency induced by diaphragm movement. A suitable sensitivity of these hydrophones is demonstrated for deep-sea applications over a frequency range of 100 Hz to 1 kHz. 9.2.1.3 Frustrated Total Internal Reflection Another modification to the above transmission sensor type includes the use of frustrated total internal reflection at the edge of two polished fibres [19]. The fibres are angle polished and placed at an angle such that all the modes undergo total internal reflection at the fibre–air–fibre interface. Any vertical displacement of one of the fibres due to the applied acoustic wave violates the total internal reflection condition and hence changes the amount of light coupled to the other fibre. This sensor type has a bandwidth of 500 Hz. Intensity modulation schemes are simple and are not as affected by phase noise as interferometric schemes. However, they are subject to high losses of optical energy since most is lost in reflection or coupling loss. Thus the sensitivity of these systems is lower. External amplification has to be provided in order to boost sensitivity.

9.2.2 Phase Modulated Sensors The phase of incident light varies with acoustic pressure and can be detected using interferometric techniques. When two coherent light waves which are shifted apart in phase are

244


Figure 9.5 Acoustic pressure sensor using Mach–Zehnder interferometric detection. Reproduced from [20]

superimposed they undergo constructive and destructive interference to form an interference pattern. In the interferometric sensing method, two arms of fibre are used and compared. One arm acts as the reference arm while the other is the sensing arm. Any change in the relative phase or optical path length of the light from the two arms leads to displacement of the interference fringes. Michelsons interferometer, Fabry–Perot interferometers and Mach–Zehnder interferometers (Figure 9.5) have been employed in the past to detect acoustic signals. These phase modulated sensors have been extensively studied and can be classified as either external or internal interferometric phase sensors. 9.2.2.1 External Interferometric Phase Sensors Michelson and Mach–Zehnder interferometers have been extensively used as phase sensors. Application of pressure to the sensing arm leads to changes in the refractive index of the sensing fibre material as well as changes in the physical dimensions of the fibre. This leads to phase shift and subsequently fringe displacement. Sensitivity of 92 kPa/fringe displacement has been reported [20]. This technique is, however, subject to fringe displacement related to temperature-induced fibre index variation, which is of the order of 10 p.p.m./C in silica based fibres [21]. This temperature-induced phase change leads to uncertainty in the measured pressure value and is only useful at frequencies much higher than the rate of thermal fluctuations in the sensing arm. In such sensors, the fibre in the two arms of the interferometer can be free or wrapped around a mandrel (cylinder) of suitable material. Previous studies indicate that higher sensitivity can be obtained by using mandrel fibres [20, 22]. In this case, when a mandrel of low Youngs modulus is subject to pressure, its length changes thus causing stretching or


245

Figure 9.6 Schematic of an optical sensor structure wound on the mandrel hydrophone as a pressure sensor arm of an interferometer. Reproduced from [22]

compression of the fibre wound around it. This leads to changes in refractive index as well as changes in the optical length of the fibre as mentioned above. The sensitivity of such structures depends on mandrel geometry and the properties of the mandrel material. Due to the low photoelastic coefficient of silica, a long length of fibre is needed for improved sensitivity. This, however, leads to poor frequency response. As a solution, embedded single-mode fibre acoustic sensors have been suggested [23], where the fibre is moulded on to the mandrel by using material of appropriate Youngs modulus and coating thickness, as depicted in Figure 9.6. In this case, sensitivity in the range of 328 to 338 dB re 1 V/mPa has been reported over a frequency range of 0.75–10 kHz. It can also be noted that the above phase modulation techniques are subject to random phase fluctuation due to temperature drifts or environmental conditions and hence are limited in performance by phase noise. These temperature drifts can be reduced by using a push–pull configuration and tuneable resonant cavity techniques [24], where a feedback control circuit is employed to maintain the stability of the operating point on the interference pattern. However, a large sensing area of the mandrel fibre sensors leads to poor spatial resolution making them unsuitable for imaging applications. 9.2.2.2 Internal Interferometric Phase Sensors In this case the interferometer is embedded within the fibre itself. Two distinct approaches are discussed next. Fabry–Perot (FP) Interferometers The FP interferometer is one type of structure used for internal interferemetric phase sensors. Previous work includes formation of an FP cavity by using 25 mm thick Parylene film deposited on the edge of a straight-cleaved fibre from which the final 1 mm of jacket has been removed [25]. Partially reflecting mirrors of the resonant structure consist of reflective coatings of aluminum, where experimentally system sensitivity in terms of noise equivalent power (NEP) of 10 kPa over a 25 MHz bandwidth is observed. Fabry–Perot cavity resonators consisting of 10 mm Parylene film surrounded by gold mirrors have been reported [27]. These structures are fabricated at the tip of straight-cleaved and tapered fibres. The reflectivity can be

246


Figure 9.7 Plane-cleaved fibre-optic sensor based on the principle of the FP interferometric technique. Reproduced from [26]

controlled by the gold-coating thickness. Incident acoustic pressure modulates the optical length of the Parylene film as well as the reflectivity of the gold creating an interference pattern (Figure 9.7). The system has a nonflat frequency response of up to 50 MHz and extrapolated sensitivity of 2 kPa. Multi-layer structures These are constructed based on the principle of periodic micro-interferometers as shown in Figure 9.8 [27]. Two high-reflection subsystems, both consisting of several l/4 layers, are connected by a central l/2 spacer layer. The sensor is made of 19 dielectric layers with alternating high–low refractive indices of n ¼ 2.3 (Nb2O5) and n ¼ 1.48 (SiO2). The sensor element has an overall thickness of d ¼ 1.9 mm. The principle of ultrasound measurement is based on the elastic deformation of the multi-layer system by an incident acoustic pressure and the detection of the induced change in optical reflectance, DR. The system is operated at a maximum sensitivity point (the point where the slope of change of reflectance with pressure is N+1

2

(N+1)/2 (N+1)/2

LL

LL LL

Fibre

Iout

ni di

Acoustic pressure

0

I in

2ni di

Figure 9.8 Fibre-optic multilayer hydrophone, i ¼ 1. . ..N, L ¼ low index layer, H ¼ high index layer, p ¼ pressure pulse [27]


247

highest). The transfer function of this sensor shows a resonant peak at a frequency of 24 MHz, which is attributed to possible diffraction effects. In intrinsic FP cavity structures, the operating point has to be stabilized at the maximum slope point on the interference transfer function. Any drift in this operating point due to temperature or other factors can lead to increased noise or a decrease in sensitivity. Due to periodicity, the accurate measurement of differential phase change in phase modulated sensors is difficult and hence such systems are not suited to most applications.

9.2.3 Frequency/Wavelength Modulated Sensors Frequency or wavelength sensing mechanisms are an extension of phase sensitive fibre-optic sensors and a few examples are discussed next. 9.2.3.1 External Bragg Cell Sensor A measuring technique based on acoustically induced frequency modulation of light has been reported in fibre sensors over a frequency range of 100–1200 Hz [28]. This arrangement makes use of an external Bragg cell which shifts the frequency (wavelength) of the laser source by 11 MHz. The unshifted frequency component is incident on the sensing fibre which reacts to acoustically induced strain and change in refractive index. This induces a change in the phase of the optical signal and results in the frequency modulation of the signal. This frequency modulated signal from the fibre sensor and frequency shifted component from the Bragg cell are combined at the frequency discriminator, the output of which is proportional to the incident acoustic pressure. 9.2.3.2 Fibre Bragg Grating Sensor The most common type of wavelength modulated sensor makes use of the fibre Bragg grating (FBG). Detection is based on an acoustically induced change in Bragg wavelength or intensity modulation of light from the grating. When an acoustic wave is incident on an optical fibre with an FBG, both the refractive index and the FBG grating period undergo changes due to elastooptic effects (Figure 9.9) [29]. This change in refractive index in turn causes a shift in the FBG wavelength resulting in wavelength modulation. The bandwidth of these sensors ranges from 0.1–5 MHz.

Figure 9.9 Schematic of a fibre Bragg grating sensor with a required interaction length of at least 600 mm for sufficient sensitivity. Reproduced from [29]

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Figure 9.10 Schematic of an optical hydrophone employing a distributed Bragg reflector fibre sensor. Reproduced from [30] ( 2005 IEEE)

9.2.3.3 Distributed Grating Reflector Another type of sensing technique based on an internal distributed Bragg reflector (DBR) has been reported recently [31]. Detection of this fibre sensor is based on the modulation principle of birefringence induced by the incident acoustic pressure in the fibre laser. Two 1550 nm Er–Yb doped grating structures each of length 10 mm and 3 mm respectively are written inside a single mode fibre (Figure 9.10). The separation distance between the two gratings is about 10 mm and results in a dual polarized signal. Awavelength division multiplexer, along with the photodetector, monitors beat frequency between both the polarization modes. In the presence of an acoustic signal, the change in birefringence modulates the beat frequency and additional sidebands are obtained at the output. The beat frequency serves as an indication of the incident acoustic pressure, while its amplitude indicates the excitation voltage. The minimum detectable pressure level was calculated to be 164 dB re mPa and 158 dB re mPa at 10 and 20 MHz, respectively. Such a sensor can detect ultrasound up to 40 MHz though its sensitivity is relatively poor and its signal-to-noise ratio versus frequency is nonuniform. These types of sensors are localized and have smaller sensing areas as compared to phase modulated schemes. They are also insensitive to random amplitude fluctuations. However, frequency or phase drift due to temperature can affect the performance of such systems. Also, the sensing aperture dimension is of the order of a few millimeters. Hence, they cannot be used for high spatial resolution measurements and also have limited bandwidth.

9.3 Intensity Sensing Principle, Design and Realization Intensity-detection based optical hydrophone uses measurement of the Fresnel reflectance caused by the change in refractive index between the fibre tip and the surrounding fibre medium. The index of refraction of water depends on the acoustic pressure as reported earlier and a resultant reflectance versus acoustic pressure is plotted in Figure 9.11 [26]. Sensitivity of the fibre-optic ultrasound hydrophone probe, S, is calculated from the expression S ¼ V0/p, where, V0 is the output voltage of the ultrasound hydrophone probe for a given acoustic pressure p. With a light source power of 50 mW, the theoretical sensitivity of the fibre-optic probe is calculated to be 4.3 mV/MPa for uncoated fibres. Figure 9.12 shows a typical APD

249

RF and Microwave Photonics in Biomedical Applications -40 -45

∆ R (dB)

-50 -55 -60 -65 -70 -75 0.01

0.1

1

10

Acoustic pressure (MPa)

Figure 9.11

Reflectance change versus acoustic pressure, where a linear relationship is depicted

output power at different acoustic pressure amplitudes and laser source power levels. The 60 dBm plane corresponds to the calculated system noise floor, where it can be seen that at 100 kPa, to achieve an output signal-to-noise ratio of unity, a light source power level of 65 mW is needed. Also, with the level of 200 mW, the minimum detectable acoustic pressure is about 34 kPa.

Figure 9.12 The photodetected output power from an APD as a function of different acoustic pressure amplitudes and light source power levels as reported [26]. The 60 dBm plateau corresponds to the calculated system RIN-dominated noise floor

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As indicated in this reported analysis the achieved response of this fibre hydrophone sensor is not competitive with commercial hydrophones, such as the needle hydrophone with a sensitivity of 40 mV/MPa (i.e. 262 dB re V/mPa). System sensitivity improvements are achieved by coating the fibre tip with gold. Design of optimum gold-coating thickness at the fibre tip is identified through maximization of reflectance sensitivity to acoustic pressure and is described next.

9.3.1 Transmission Line Modelling of Coated Fibres A simplified transmission line model was used to improve the understanding of the impact of fibre coating on the overall sensitivity of the optical hydrophone. Based on this model, the complex reflection coefficient (r) of coated fibre can be expressed as r¼

nd ðnc nw Þ þ ðnw nc n2d Þtanh gd nd ðnc þ nw Þ þ ðnw nc þ n2d Þtanh gd

ð9:2Þ

where d is the coating thickness, nd is the complex refractive index of the coating, nw is the refractive index of water, and nc is the refractive index of the fibre core. The complex propagation constant in a lossy gold layer, g, is described in terms of the complex index of refraction of gold, nd, and wavelength, l, as: g ¼ jð

2pðn jkÞ Þ: l

ð9:3Þ

Note that n is the real part of the complex refractive index and k is the extinction coefficient. The effective Fresnel reflectance (R) is given by R ¼ r.r , and the dependence of reflectance on pressure can be found by differentiating the reflectance expression with respect to pressure: dR dr* dr ¼ r: þ r* dP dp dp

ð9:4Þ

dr 2nd ðdnw =dpÞ½nw tanhgd þ nd ðtanhgdÞ2 nc nd nc nw tanhgd ¼ : dp ½nd ðnc þ nw Þ þ ðnc nw þ nd 2 Þtanhgd 2

ð9:5Þ

where

The analysis presented here can be extended to uncoated fibre by considering the coating thickness to be zero in Equation (9.2). Reflectance (R) and variation of the reflection coefficient with pressure, are now given by R¼

ð nc nw Þ 2 ð nc þ nw Þ 2

ð9:6Þ

and dr 2nc ðdnw =dpÞ ¼ : dp ðnc þ nw Þ2

ð9:7Þ

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RF and Microwave Photonics in Biomedical Applications 20 Improvement in sensitivity, (dB)

18

X: 52 Y: 16.15

16

14

12

10

8

6

4

2

0

10-1

100 101 102 Coating thickness, (nm)

103

Figure 9.13 Improvement in sensitivity of a straight cleaved fibre with a thin gold coating. (The classical appproach for modelling that is presented here is not totally accurate for thin films, but it is a good approximation for a general understanding of this problem)

A comparison of the sensitivity of uncoated and coated fibre is presented in Figure 9.13 as a function of coating thickness. In this calculation the complex index of refraction of gold has been assumed to be 0.18 j2.21. Note that the calculation based on this simplified model demonstrates an improvement of as much as 15 dB for a thickness of about 50 nm. Naturally a more accurate model is required for down-tapered coated and uncoated fibres.

9.3.2 Finite Element Model (FEM) for Various Fibre Sensor Designs In order to predict the performance of various fibre tip geometries, FEM simulations have been performed using COMSOL. The physical dimensions of 0.1 mm length and core diameter of 10 mm are considered for straight-cleaved optical fibre. Core and cladding refractive indices of 1.4456 and 1.4378 respectively are used for all fibres. A small tapering angle of 6 is considered for the etched fibre sensor to properly represent anisotropic etching. The FEM modelling of gold-coated fibre is based on a gold-coating thickness of 100 nm with complex index of refraction of 0.18 j0.31. The hybrid mode of HE11 is considered as the dominant mode and the simulated power density profile of the field along the fibre length is depicted in Figure 9.14. All the sensor tips have been immersed in water. The region outside the cladding is considered as an absorbing boundary in order to reduce computation complexity. Simulation results for straight cleaved, down-tapered uncoated and coated fibres have indicated power densities of 46.7, 51.5 and 36.3 dBm/mm2 respectively, with a marked improvement in reflectance for the coated fibre case.

9.3.3 Fabrication of Fibre Sensors The probe sensitivity can be enhanced by increasing the reflected signal power. The fibre tip is etched to the size of 7–10 microns before it is coated with a thin layer of metallic material, such

252


Figure 9.14 FEM simulation of power density distribution along the direction of propagation of HE11 for various sensor designs using COMSOL; (a) straight cleaved fibre with mm cross-sectional diameter, (b) tapered fibre with 7 mm cross-sectional diameter, (c) tapered fibre with gold coating

as gold. The fibre tip is etched to a smaller diameter by wet chemical etching of the fibre, using HF (50% by volume) solution. In this process the fibre being etched is connected to a light source and detector, and the fibre tip is dipped in the HF solution for tip etching, while the back reflected signal is continuously monitored. The etched fibre is then coated with a


253

Figure 9.15 Sensing fibre tip images with 10 magnification: (a) down-tapered gold coated fibre and (b) down-tapered uncoated fibre tip cross-sectional diameter, 7 mm

semitransparent film of gold. The thin gold layer was sputtered on the fibre tip with a Cressington 108 sputtering machine, and the approximate thickness of the gold layer is 50–150 nm for sputtering times of 5–20 s. An optical image of the fabricated coated and uncoated fibres is shown in Figure 9.15.

9.3.4 Experimental Set-up and Results The fibre-optic hydrophone system is constructed with commercially available components using single mode FC/APC connectors. The system block diagram is shown in Figure 9.16, and the system is composed of optical source, optical sensor, acoustic source and optical receiver assemblies, as reported in [31]. The optical source is the 1550 nm distributed feedback (DFB) laser (NEC NX8563LB) with an output power of 2 dBm for Ib ¼ 30 mA. The source is coupled to a 10 dB optical coupler and the output from the 10% coupled arm is sent to the erbium-doped fibre amplifier (NuPhotonics NP2000CORSV303500FCA1) which has an optical gain of 40 dB and output power of up to 30 dBm. The output from the EDFA is divided equally using a 2 2 coupler with a 3 dB coupling factor. One of the optical outputs is immersed in water as reference, while the other output is connected to the optical sensor. The optical sensor is immersed in a water tank and placed at the focal point of a focused acoustic transducer. The acoustic transducer is a one-element transducer (Sonic Concepts H110AS/N 01) with dual band operation at frequencies of 1.6 MHz and 5.0 MHz. It requires a radio frequency (RF) impedance matching network and 50 W over dual bands of 1.41–1.98 MHz and 5.0–5.7 MHz. The transducer has an active diameter of 20 mm and it has a focal length of 34.52 mm. An RF power amplifier provides a maximum pulsed power level of 100 W with 25% duty cycles. The position of the acoustic source and optical hydrophone are controlled by a precision scanning system from Onda Corporation. The system provides precise six-axis positioning and data acquisition from any sensor in the water tank for accurate measurements of acoustic fields. The precision of each axis is repeatable within 12 mm and absolute accuracy of 25 mm over 30 cm. Experiments have been performed using the various optical sensors discussed in Section 9.3.3. The reflected optical energy is collected in a wide band amplified InGaAs detector (Thor Labs PDA 10CF) with a responsivity of 0.95 A/W at 1500 nm and signal bandwidth of 150 MHz. It has a transimpedance gain of 5 kW and noise equivalent power of 12 pW/(Hz)1/2. Comparison

NEC DFB Laser 1550nm NX 8563LB

IN

SMSCA223R P1005FA

10dB coupler

90% OUT

10% OUT

IN

Agilent spectrum analyser E8408A

Nu photonics EDFA NP2000CORSB 303500FCA1 Optical isolator ISILPD55SS9

IN

50% OUT

Sensor fibre

0.76 m

Water tank

50% OUT

Reference fibre

Chip-hope 3 dB coupler SMSCA223RP 5005FA

Figure 9.16 System block diagram [31]

ThorlabsPIN photo-detector PDA10CF

OUT

0.46 m

Not connected at present

Ultrasound transducer

8m 0.3

Power amplifier and matching circuit

Signal generator agilent 3325A


255


of fibre performance using three designed sensors depicted in Figure 9.14 has typically indicated an 11 dB and 13 dB improvement for gold 5 second (about 50 nm thick) coated fibre over straight cleaved and uncoated down-tapered etched fibre sensors, which corroborates the simulated predictions from FEM modelling. The measured reflected optical signals at different EDFA power levels indicate a 2 dB variation for every dB variation of optical power. The noise floor level also increases at the same rate, which indicates that the receiver noise is dominated by amplified relative intensity noise (RIN) of laser source. Using common mode rejection of a balun as a power combiner, the amplified RIN noise is cancelled by 14 dB leading to a shotnoise dominated noise floor of the detection system [32]. The measured optimum gain responsivity for 25 dBm optical power is measured as 245 re 1 V/mPa with average sensitivity as low as 150 Pa. Comparison of time domain pressure response of this optical hydrophone with commercially available needle hydrophones is depicted in Figure 9.17, where a modulating tone burst at frequency of 1.5 MHz is employed. The small active sensing area of 30 dB) of the unwanted sideband [20]. If the microwave frequency response of the SSB modulator and the photodetector are calibrated out, the RF component of the photocurrent is given by: iout ðtÞ / Hðv0 ÞHðv0 þ vm Þcosðvm t þ fðv0 þ vm Þ fðv0 ÞÞ; where H(v0 þ vm) and f(v0 þ vm) represent the optical magnitude and phase response of the DUT. Hence by sweeping the modulation frequency vm,while keeping the optical carrier frequency v0 constant, it is possible to measure the magnitude and phase response of the O/O DUT as a function of the optical frequency v0 þ vm. It is stressed that envelope signals are not being used here, and so what is being measured is not the microwave response of the O/O DUT. Rather, this approach is an alternative to the coherent optical network analyser discussed earlier, albeit without provision for polarization effects. In contrast to the coherent optical network analyser, this approach offers much higher resolution because the wavelength sweep is achieved using the microwave source of the VNA rather than a tuneable laser. It is therefore useful for the spectral characterization of fibre Bragg gratings [19]. In order to examine the microwave frequency response of an O/O DUT, we must revert to double sideband modulation and use the envelope approach as described next.

10.2.4 Envelope S-parameters for O/O Components The first attempt at a rigorous definition of S-parameters for O–O components in the microwave IM/DD regime was made by Curtis and Ames [21], and we will mostly base the theory in this section on their analysis. Their starting point was to consider an O/O component residing within an E/E black box (Figure 10.12), the microwave S-matrix of which could be measured with a microwave VNA. In order to ‘de-embed’ the O/O response from the E/E S-parameters, E/O and O/E conversion is required, and test sets as originally proposed by Bowe [22] allow this for both transmission and reflection measurements as shown in Figure 10.13. (These test setups have formed the basis of a family of commercially available lightwave component analysers [22–26].) The key problem is then to relate measured electrical S-parameters from Figure 10.12 to the appropriate S-parameters for the O/O component. In order to do so, travelling-wave variables are defined in terms of the envelope of the intensity-modulated optical signal and the resulting envelope S-parameters then describe how an optical component affects the microwave envelope and not the optical carrier.

Figure 10.12

Black-box representation of a microwave fibre-optic two-port network

Characterization of Microwave Photonic Components

305

Figure 10.13 Basic lightwave component analyser configurations for (a) transmission and (b) reflection measurements of O/O DUTs. Reproduced from [1]

The incident and reflected envelope waves for a fixed optical carrier frequency at the nth optical port of a multi-port optical device are defined as: aOM ¼ Pan m cos vm t þ fOM an n

ð10:7Þ

bOM ¼ Pbn m cos vm t þ fOM bn n

ð10:8Þ

and

respectively. Here m is the modulation index, Pan and Pbn are the average incident and reflected optical powers, while fan and fbn are the corresponding microwave phases. (Alternatively, a

306


definition in terms of optical intensity may be used, since this quantity is directly proportional to optical power.) The reflection envelope S-parameter at the nth port is then given by: SO=O nn ¼

POM bOM OM n bn ¼ exp jðfOM bn fan Þ ; OM OM an Pan

ð10:9Þ

while the envelope S-parameter for transmission from port m to n is: SO=O nm ¼

POM bOM OM n bn ¼ exp jðfOM bn fam Þ ; OM OM am Pam

ð10:10Þ

where use is made of phasor notation in order to be consistent with conventional microwave S-parameters, and all ports are correctly terminated. Having established a convention for O/O S-parameters, these must now be related to the E/E S-parameters of the black box in Figure 10.12. Whereas the optical S-parameters in Equation (10.2) have travelling-wave variables with dimensions of H(optical power), the envelope travelling waves (10.7) and (10.8) are directly proportional to optical power. This is because the test signals for optical S-parameters are electric field variables (E) whereas here we are using optical power (which is proportional to |E2|). In addition, the travelling waves for the E/E case in Equation (10.1) have dimensions of H(electrical power), and can therefore be taken to be proportional to incident or reflected current as appropriate. This is expedient, since the microwave transfer functions for directly modulated3 optical sources and photoreceivers are of the form: hðjvm Þ ¼

pS ðjvm Þ iS ðjvm Þ

ð10:11Þ

Rðjvm Þ ¼

iR ðjvm Þ pR ðjvm Þ

ð10:12Þ

and

where h and R are the source slope efficiency and receiver responsivity respectively. (R is also wavelength dependent.) The source drive current and photocurrent are denoted by iS and iR, while the emitted and received optical power are given by pS and pR. In the discussion that follows, it is taken that the optical source and photoreceiver are matched to 50 W on their electrical ports, and that they also do not present any optical reflections of their own to the O/O DUT. Hence for the transmission measurement set-up, there is no optical back-reflection. One can then relate the E/E travelling waves to O/O envelope travelling waves through ostensibly linear relationships as follows (where the jvm terms have been dropped for notational convenience): aEn aOM ¼ h pffiffiffiffiffi n Z0 3

ð10:13Þ

When considering modulators, one normally considers drive voltage instead of current in the equivalent expression to (10.11). However, this is not a drawback since a travelling power wave can be shown to be given by an expression such as a ¼ vi/HZ0 ¼ iiHZ0 and Equations (10.13), (10.14) and (10.15) still hold for modulators provided they are scaled correctly.

307


bEm pffiffiffiffiffi ¼ R bOM m Z0

ð10:14Þ

bEm bOM ¼ Rh m E an aOM n

ð10:15Þ

whence

Here we have used the following conventions for the electrical travelling waves: pffiffiffiffiffi pffiffiffiffiffi Vni Vmr aEn ¼ pffiffiffiffiffi ¼ Ini Z0 & bEm ¼ pffiffiffiffiffi ¼ Imr Z0 Z0 Z0

ð10:16Þ

If we take Equation (10.15) for the particular case of a two-port and also incorporate the terminating conditions, we obtain the following forward-transmission relationship: bE2 bOM 2 ¼ Rh OM : ð10:17Þ E a1 aE ¼0 a1 aOM ¼0 2

2

Hence: E=E

O=O

jS21 j ¼ jRhjjS21 j:

ð10:18Þ

The Rh term in Equation (10.18) is, in effect, a current transfer function for which linearity, and hence superposition, still hold. In that respect the intervening O/O medium is not an issue in terms of ensuring linearity of the test set-ups in Figure 10.13. Now, if we make a thru O=O connection by omitting the O/O device, this is mathematically equivalent to S21 ¼ 1 and this measurement provides a way of calibrating out the Rh term in Equation (10.18): M0 ¼ jRhj ð10:19Þ E=E where M0 is the value of S21 measured with a calibrated VNA. If we now insert an O/O DUT O=O such as an attenuator for which S21 ¼ A(where A is less than unity) and measure it, we have from Equation (10.18): O=O ð10:20Þ M1 ¼ RhS21 ¼ M0 A E=E where M1 is the measured value of S21 for this DUT. The ratio M1/M0 gives a calibrated value for A. If we compare Equations (10.19) and (10.20), then the optical that has been attenuation E=E introduced is given by:10 log10 A dB. The corresponding value of S21 is reduced by a factor of A, but to obtain the corresponding electrical attenuation in dB we must take: 20 log10 M1 =M0 ¼ 20log10 A from which we conclude that a 1 dB reduction of optical power will lead to a 2 dB reduction of electrical power.

308


In order to avoid the inadvertent addition of optical and electrical dBs in link budget calculations, we can adopt the following decibel notation for microwave and envelope S-parameters [27] Type of component E/E O/O

Definition S-parameter in dB format of bE 20 log10 aE dBe OM 10 log10 baOM dBo.

In this section we have developed a definition for envelope S-parameters, and there are commercial lightwave component analysers that can measure these quantities for O/O twoports. Even so, this should not be taken to mean that we can measure an arbitrary O/O component and be able to unambiguously determine its envelope S-parameters. To be more precise, the measured envelope S-parameters of the DUT may not actually be valid in terms of the physics of the DUT and the lightwave component analyser to which the DUT is connected. The reasons for this will be outlined fully in the next section.

10.2.5 Limiting Assumptions of the Envelope S-parameter Technique The simplest O/O component we will consider is a length L of single-mode fibre. If dispersion can be neglected, the microwave envelope of the light output intensity (Iout ) will be related to the input intensity (Iin ) via [28]: Iout ¼ Iin Ae jbL :

ð10:21Þ

Hence the microwave transfer function can be expressed as: S21 ¼ Ae jbL O=O

ð10:22Þ

where A is constant within the measurement bandwidth (and is < 1) and b is the phase coefficient as given by: vm neff b¼ : ð10:23Þ c Negligible dispersion is assumed, hence the group velocity has the same value as the phase velocity (c/neff). We will also assume that the value of neff matches that of the lightwave component analyser test ports. Equation (10.22) satisfies the conditions for distortionless transmission as required in Vifians work [25], which means that attenuation of the envelopes amplitude will track the attenuation of the optical carrier. Given that attenuation may also be measured with optical power meters (and methods such as cut-back [29]), it appears that using a network analyser approach to obtain the same quantity is extravagant. However, the true value of using modulated optical signals to characterize optical fibres lies in being able to determine the group delay from measurements of the envelope phase shift. The measured group delay can then be used (with the reflection test set) to isolate and locate the cause of different reflections in optical fibres, such as those caused by Fresnel reflections and fibre connectors, as outlined in [25]. Indeed, this approach can be used to determine the differential time delay between modes in multimode fibres. Hence the lightwave component analysis approach potentially yields more insight than an optical time domain reflectometer (OTDR), which suffers from a

309

Characterization of Microwave Photonic Components Table 10.2 Measurements derivable from lightwave S-parameters (after reference [23]); applies to E/E, E/O, O/E and O/O two-ports unless specified otherwise. Transmission

Reflection

Insertion loss/gain Frequency response . Modulation bandwidth . Flatness . Slope responsivity (E/O and O/E) Time domain response . Rise time . Pulse broadening Delay Length Insertion modulation phase Group delay Index of refraction Optical reflection sensitivity (E/O)

Return loss Impedance (electrical) Reflectometry . Electrical (time domain) . Optical (frequency domain) Delay Length

‘deadzone’ due to it using pulses as test signals [30]. In fact, when S-parameter measurements of E/O and O/E components (as discussed later) are also included, a wide variety of other parameters can be derived as indicated in Table 10.2. However, when measuring O–O components with the lightwave component analyser configurations illustrated in Figure 10.13, careful interpretation of the results is required under certain conditions. These conditions relate to issues associated with: (i) linear distortion, (ii) polarization, (iii) optical source coherence and (iv) optical cavity resonances. (i) Linear Distortion If a component exhibits linear distortion, it has an amplitude response that is not constant or a phase response that is not linear, or both. Such a situation arises for filters and by combining optical-fibre delays with directional couplers it is possible to construct an all-optical network which, when interfaced with E–O and O–E transducers will act as a microwave filter [31]. (Chapter 8 discusses this subject in greater depth, and also considers the use of other optical components such as fibre Bragg gratings in order to realize microwave transfer functions.) A simple example of an all-optical filter is the Mach–Zehnder interferometer (Figure 10.14) which consists of two directional couplers, used to split and recombine the signal, separated by two paths whose lengths differ by a unit delay length of Dl. Assuming perfect 3 dB couplers are used, the resulting microwave frequency transfer function is: Hðvm Þ ¼

1 1 þ e jbDl : 4

A measured result for a delay length of 40 cm (corresponding to a time delay of 2 ns and hence a free-spectral range of 0.5 GHz) is shown in Figure 10.14. The periodic, notch-like response is clearly visible. The delay difference is sufficiently large to prevent coherent effects from occurring, and predicted and measured results agree well for this case. Lightwave component analysers are therefore capable of measuring the frequency response of structures with linear distortion provided they meet the additional criteria described below.

310


Figure 10.14 (a) Example of a Mach–Zehnder interferometer and (b) its frequency response (measured using an HP8703A lightwave component analyser). Reproduced from [56] ( 2008 IEEE)

(ii) Polarization In an optical fibre, birefringence can lead to a change in the polarization of the transmitted and reflected signals. Ordinarily, a single photodiode will have little polarization sensitivity, and hence a standard lightwave component analyser is unable to characterize polarization effects. This can only be done by modifying a lightwave component analyser by using polarizing beam splitters to resolve the x and y orthogonal components. Such an instrument has been proposed [27], but it has not been demonstrated, even though there are some potential applications for it. For example, birefringent fibre has been used to implement delay-based all-optical microwave filters [32] and in recent years a number of polarization modulation schemes have been reported. Quoc et al. [33] have also shown that the polarization state of the optical carrier can have a strong influence on the microwave frequency response of all-optical microwave filters based on unbalanced Mach–Zehnder interferometers and recirculating delay lines. In this situation, the envelope S-parameters are no longer applicable because optical coherence in these structures means optical signals add as electric fields instead of intensities. Hence the travelling waves given by Equations (10.7) and (10.8) are not valid and we must instead use modulated Jones vectors. For example, the incident fields in this situation are described by OM a1x Ex pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð10:24Þ 1 þ mcosvm t expðjvo tÞ OM ¼ a1y Ey (iii) Coherence The conditions for linearity and superposition for envelope S-parameters depend on the coherence of the optical source, since this will in turn determine whether optical signals should be added together using an electric field description or optical intensity (equivalently,


311

Figure 10.15 Coherent and incoherent regimes versus laser coherence length/optical path delay difference (after [34])

optical power). For an optical source with a Lorentzian lineshape, we have [34]: VL ðtÞ ¼ hexp j ðwðt þ tÞ wðtÞÞi ¼ expð jtj=tcoh Þ ¼ expð pDnjtjÞ

ð10:25Þ

where tcoh is the coherence length and w represents the randomly varying phase. The shortest path delay difference in the DUT is denoted by t. For comparison, a Gaussian source has:

t2 VG ðtÞ ¼ exp 2 ð10:26Þ 2tcoh and these two line shape functions are plotted in Figure 10.15 in order to illustrate the coherent and incoherent working regimes. In order to illustrate the impact of coherent effects, Quoc et al. terminated the output of a Mach–Zehnder interferometer (MZI) with a mirror (Figure 10.16) and then measured the reflection characteristics with a lightwave component analyser [35]. In this configuration, the MZI behaves like a cascade of two identical MZIs, leaving two possible return paths of delay T, where T is the fibre delay. The existence of coherence effects means that the signals from the two return paths add in terms of fields (not intensities); hence this contribution to the return loss is highly sensitive to environmental influences, such as temperature changes or touching the fibre, because the wavelength of light is very small (of the order of 1 mm). Changes in optical phase on a distance scale with the optical wavelength can be observed, since the electric fields from the different reflection paths add as vectors. In these circumstances, a commercial lightwave component analyser will give widely different results as the external perturbation is varied (Figure 10.16), because it is essentially being used in the wrong mode – it is ‘programmed’ to expect incoherent optical signals. By using the Jones vector formalism (Equation (10.24)) for the optical signals, it has been shown that the perturbation sensitivity of the microwave frequency response in Figure 10.16 can be modelled in terms of power transfer between the two orthogonal states of polarization. It has also been shown that one way of overcoming perturbation sensitivity (or ‘interferometric noise’) is to insert a sufficiently long length of fibre between the source of the reflections so that the multiple reflections are uncorrelated and do not add coherently [36].

312


Figure 10.16 (a) Mach–Zehnder interferometer. This O/O system will act as a microwave filter when connected with E/O and O/E transducers. Paths (ii) and (iii) are nominally identical, which means that they will interfere in a coherent manner. (b) Measured magnitude response of a Mach–Zehnder interferometer; three markedly different traces are obtained for the same structure. Clearly it is not possible to obtain a response that is ‘stable’ due to the impact of environmental changes (e.g. temperature fluctuations) on the measured result. Reproduced from [35] ( 2008 IEEE)

However, it is still necessary to locate the position of the reflections (and their reflection coefficients) to have a completely characterized system [37]. (iv) Optical Cavity Effects Hale and Williams [37] point out that if both the optical source and photoreceiver in the transmission test set (Figure 10.13) have non-zero optical reflection coefficients, a Fabry–Perot resonator will be formed if an optical fibre is inserted between them. This situation is analogous to that considered in Figure 10.9. If the optical test signal is highly coherent, then the resonators frequency response will depend on the cavity length in optical wavelengths. For a length of 1 m, the free spectral range of the resonator will be in the GHz region, making it possible for a sideband or the optical carrier to be filtered out. This will lead to a change in the envelopes shape (something which is ruled out for the distortionless LTI model of the ideal optical fibre as described above) thus leading to erroneous results. In summary, the correct operation of a lightwave component analyser of the type described in [23] and [25] relies on the assumption of incoherent optical signals. In this case, the test


313

signals are described in terms of optical power (or intensity), and we measure the response of O/O components to microwave signals by examining their effect on the microwave envelope. If the DUT has a constant magnitude and linear phase response, it will not distort the envelope passing through it. Given that most microwave photonic components are deployed in intensity modulation/direct detection links, and that most all-optical filters work in the incoherent regime, the use of incoherent optical sources is justified. In addition, unnecessary optical reflections which can create optical cavities are avoided through the use of isolators and antireflection coatings on E/O sources and O/E detectors. Where there is the possibility of multiple paths for optical transmission and reflection, one must ensure that the optical sources coherence length is longer than the shortest optical path difference inside the component being measured. If this is not the case, then a phase relationship will exist amongst the different signal paths and signals will add on an electric-field basis rather than as intensities, rendering the incoherent assumption invalid. In this situation, instruments such as the coherent optical network analyser must be used, along with a Jones vector description for the optical signals. The one advantage here is the ability to determine the impact of changes in polarization.

10.2.6 S-parameter Characterization of E–O and O–E Components Taking the black-box model shown in Figure 10.12, we have already seen that well-established techniques exist for S-parameter characterization of this at the E–/E level. The O/O ‘core’ can also be characterized using the same concept at optical frequencies when coherent optical signals are employed. Moreover, a modified form of S-parameters (envelope S-parameters) was introduced in Section 10.2.4 to characterize the microwave behaviour of O/O components operating in the incoherent regime. When one considers that an analogous technique (modulated S-parameters) has also been recently developed for E/E components [38], it appears from the signal analysis perspective that O/O and E/E components are very similar. This is not surprising, since S-parameters can be viewed as a mathematical description of a linear system, in much the same way that signal-flow graphs have been used to model both microwave systems [16] and alloptical networks [28]. Signal-flow graphs also have applications in linear control theory, and this point is raised because analogue control systems are a good example of systems in which many physically different signals exist – for example, a servo control system will have variables such as angular position, acceleration, voltage and current. All of these variables can be cast in the frequency domain using the Laplace transform, thus allowing transfer functions to be used in which the input and output variables are physically different. In fact, Equations (10.11) and (10.12) (the small-signal transfer functions for lasers and photodiodes) fit this type of description. With this in mind, there is no reason why the flow graphs of an E/E and O/O component cannot be joined together via an intermediate E/O converter as shown in Figure 10.17. The critical question here is whether or not E/O and O/E components can be dealt with in a similar manner to E/E and O/O components by using S-parameters. There is no difficulty with measuring the reflection properties of E/O and O/E components. The S11 and S22 parameters for E/O and O/E two-ports (respectively) correspond to microwave input reflection coefficients which can be measured with a microwave VNA. Similarly, reflection off the optical ports may be readily measured for both modulated and unmodulated light. It is the transmission characteristics (and also the physics) of E/O and O/E components that pose the potential for conceptual difficulty in applying S-parameters. When looking at an

314


Port A

Port B E/E

E/O

O/O

O/E

E/E

(a) S E/O 21

S E/E 21A

S E/E 11A

S E/E 22A

S E/O 11

r E/O 21

S E/O 12

S E/E 12A

O/O

t E/O 21 r E/O 12 t E/O 12

t O/E 21

S 21

r O/E 21

S O/O 12

E/E S21B

S O/E 21

S O22/E

r O/E 12

S E/E 11B

S O/E 12

t O/E 12

S E/E 22B

S E/E 12B

(b) S E/E 21A S E/E 11A

S E/E 22A S E/E 12A

O S E/ 21

S O21/O

O S E/ 11

O/E S 21

S O22/E

(c)

S E/E 21B S E/E 11B

S E/E 22B

S E/E 12B

Figure 10.17 (a) Cascade of E/E, E/O, O/O, O/E and E/E components; (b) signal-flow graph (including optical reflections at the optical ports); (c) reduced-flow graph for a unilateral link with no optical reflections

external modulator, for example, we have a single-frequency microwave input generating an output that contains multiple-frequency terms (when an electric field description is used) as discussed in Section 10.2.3. From this perspective, the component is nonlinear and in effect acts as a frequency upconverter. This precludes the use of conventional S-parameters, since these assume linear time invariant networks [16]. Jargon et al. [39] have defined nonlinear S-parameters for microwave circuits and have also shown how they reduce to linear S-parameters in the absence of nonlinearity, thus showing that this method can handle combinationsof linearandnonlineartwo-ports.This approach could, in principle, be modified to model the E/O conversion between an input microwave signal and an output double sideband modulated optical signal. These changes, however, would be cumbersome since Jones vectors (as in Equation (10.2)) would have to be used in place of voltage travelling waves, and the different frequency components in the matrix would not, strictly speaking, be harmonically related. The problems associated with multiple-frequency content of the electric field are circumvented more simply by assuming incoherent optical signals and using travelling waves based on optical power, as for the envelope S-parameters defined in Section 10.2.4. Using this approach, the S-parameters for an E/O two-port are defined as: # E " E=O E=O E b1 a1 S12 S11 ¼ ð10:27Þ OM E=O E=O bOM a S21 S22 2 2 E=O S11

bE1 ¼ E ¼ input ðmicrowaveÞreflection coefficient ðwith optical port matchedÞ a1 aOM ¼0 2

E=O S21

bOM 2 ¼ E ¼ forward transmission coefficient ðwith optical port matchedÞ a1 aOM ¼0 2

315


E=O S12

bE1 ¼ OM ¼ reverse transmission coefficient ðwith electrical port matchedÞ a2 aE ¼0 1

E=O

S22 ¼

bOM 2 ¼ output ðopticalÞ reflection coefficient ðwith electrical port matchedÞ OM a2 aE ¼0 1

Whereas electrical, optical and envelope S-parameters are all dimensionless, here E=O E=O only S11 and S22 are dimensionless. Given that the electrical and modulated optical pffiffiffiffiffiffiffiffiffiffiffiffiffi travelling waves have dimensions of power and power respectively, the microwave-topffiffiffiffiffiffiffiffiffiffiffiffiffi E=O modulated optical parameter S21 has dimensions of power while the modulated opticalp ffiffiffiffiffiffiffiffiffiffiffiffiffi E=O to-microwave parameter S12 has dimensions of 1/ power, and the corresponding units E=O E=O are W1/2 and W1/2. Some authors elect not to refer to S21 and S12 as S-parameters for this reason [37]. The microwave modulation response of E/O and O/E components is normally referred to as slope responsivity h and responsivity R respectively, and in this case the corresponding units are W/A and A/W. A simple dimensional analysis makes it clear that h and R are not the same as E=O E=O S21 and S12 . The relationship between these pairs of quantities was first formulated by Stockbroeckx et al. [40], using a simple transmission line approach. Taking a directly modulated laser diode as the E/O component, the modulating current is related to the incident and reflected travelling current waves: aE1 bE1 ð1 GE Þ I1 ¼ I1i þ I1r ¼ pffiffiffiffiffi pffiffiffiffiffi ¼ pffiffiffiffiffiIN : Z0 Z0 Z0

ð10:28Þ

Using Equations (10.11) and (10.28) then gives: E=O

S21

E=O h 1 S11 h 1 GEIN pffiffiffiffiffi pffiffiffiffiffi ¼ ¼ : Z0 Z0 aOM ¼0

ð10:29Þ

2

E=O

In practice, laser diodes are unilateral (S12 ¼ 0) and isolators are often used to ensure ¼ 0. However, Stockbroeckx et al. entertain the theoretical possibility of nonzero values for both, and using a similar approach to the derivation of Equation (10.29), the envelope S-matrix for a bilateral laser diode is given by: E=O S22

2

E=O

S11

6 E=O SLD ¼ 6 4 h 1 S11 pffiffiffiffiffi Z0

3 pffiffiffiffiffi E=O hR Z0 1 S22 7 7 5 E=O S22

ð10:30Þ

where hR denotes inverse transmittance [40]. For a general O/E two-port, we have: # OM " O=E O=E OM S11 S12 b1 a1 ¼ ð10:31Þ O=E O=E bE2 aE2 S21 S22

316


Figure 10.18 Bilateral electro-optic network (BEON). Reproduced from [1]

and a similar approach yields the envelope S-matrix for a photodiode [40]: 3 2 O=E RR 1 S22 O=E 6 7 pffiffiffiffiffi S11 7 SPD ¼ 6 Z0 4 pffiffiffiffiffi 5 O=E O=E R Z0 1 S11 S22

ð10:32Þ

Although laser diodes and photodiodes are not bilateral, it is possible to use them to construct bilateral electro-optic networks (BEONs) which permit forward (E–O) and reverse (O–E) transmission, as shown in Figure 10.18. The microwave circulator separates incident and reflected electrical power waves, while the optical directional coupler performs a similar function for lightwaves. It is also possible to use a modulator in place of the laser diode, and an optical circulator instead of the optical coupler. The BEON finds application in fibre radio picocells as a transducer [41], but it has also been used for lightwave measurements. For example, it may be employed in a one-port optical measurement configuration with a ‘black box’ approach as demonstrated in [42]. It has also been proposed as a means of converting the microwave measurement ports of a microwave VNA into optical ports [43]. In this case, one can develop optical techniques that are analogous to two-port microwave calibration and deembedding, and we will look at this in more detail later. One limitation of the BEON is the poor sensitivity due to the low conversion efficiency of its constituent laser diode and photodiode, and simulations show that the inclusion of optical amplification immediately before the photodiode can improve matters. However, the biggest drawback of the BEON is that the microwave circulator ultimately limits the measurement bandwidth. For this reason, the BEON has not been widely adopted for lightwave measurements, and in fact the unilateral nature of E–O and O–E semiconductor devices has influenced the development of lightwave component analysers with ‘unilateral test sets’.

10.3 Lightwave Component Analyser Architectures Having developed a formalism for the small-signal microwave behaviour of optical and optoelectronic two-ports that is based on S-parameters, we now describe instruments for the characterization of these components. In particular, we define a lightwave component analyser as an instrument that can measure microwave S-parameters of E/E components, envelope S-parameters for O/O components, and the small-signal modulation response, electrical and modulated optical reflection coefficients for both E/O and O/E components.


317

10.3.1 First Generation Lightwave Component Analysers Lightwave component analysers (LCAs) have been commercially available since the late 1980s, but their basic architecture and mode of operation remains unchanged. A simplified block diagram of an LCA is shown in Figure 10.19; the instrument has two electrical test ports (E 1 and E 2) and two optical test ports (O1 and O2). By using an appropriate configuration for the microwave switches, this instrument can provide calibrated measurements of E/E, E/O, O/E and O/O components. With the switch S 1 set to position A, the instrument has the configuration of a conventional microwave vector network analyser with a reversible test set (achieved by using the second switch S 2), which allows the application of two-port calibrations (such as TRL [44]). The ports E 1 and E 2 are preceded by reflectometers, which means that incident and reflected travelling waves can be detected, and all four E/E two-port S-parameters can be

Figure 10.19 (a) Conceptual block diagram of a lightwave component analyser; (b) the modification needed to measure reflection coefficients for O/O components. Reproduced from [56] ( 2008 IEEE)

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measured in situ. With the switch S 1 set to position B, it is possible to measure O/O, E/O or O/E components, depending on which test ports are selected. (i) O/O Measurements In this case, the test ports O1 and O2 are selected, and these are preceded by broadband E/O and O/E transducers respectively. In the case of the E/O transducer corresponding to O1 a Mach–Zehnder modulator is often used, while the O/E transducer used for O2 is an amplified photoreceiver. The unilateral nature of both these components means that O1 is an optical output port and O2 is an optical input port, which means that the optical equivalent of two-port calibration is not applicable. When compared with E/E measurements, this is a limitation. If the O=O reverse transmission parameter (S12 ) is required, then the O/O DUT must be physically reversed. Moreover, measurement of the optical reflection parameters requires the addition of an optical directional coupler and a matched optical load as shown in Figure 10.19, and the O/O O=O O=O DUT must again be reversed if both S11 and S22 are required. Hence full two-port characterization of an O/O DUT requires two distinct test set configurations (one for transmission and another for reflection) plus the attendant calibrations, and four connect–disconnect cycles for the DUT. Such an approach is cumbersome, and has led to alternative proposals [45] such as the two-port optical test set to be described in Section 10.3.2. Simple normalization calibration techniques are used for lightwave component analysers in the O/O mode. For transmission calibration, a short length of optical fibre is often used as a through standard. For reflection measurements, the optical equivalent of the offset shorts and matched-load one-port calibration technique was first reported by Curtis and Ames [21], who fabricated their own set of standards. The optical matched load consisted of a fibre terminated in a vial of index-matching gel, and an average return loss of 50 dB was obtained. The offset shorts were constructed by terminating two different lengths of fibre in a mirror. Despite its successful implementation in the optical domain, this approach has the same drawback as its microwave counterpart, namely having to know the S-parameters of the calibration standards. (ii) O/E and E/O Measurements Here, the test ports O1 and E 2 are selected in order to measure the responsivity of an O/E component, which we will take to be unilateral. Further assumptions are that the input does not O=E O=E present any optical reflections (S11 ¼ 0) and that the electrical reflection coefficient (S22 ) is measured with the lightwave component analyser in the E/E mode. With these conditions in place, the O/E set-up can provide measurements of the responsivityRðjvÞwhich in principle O=E can be used to calculate S21 using Equation (10.32). Similarly, for measurement of E/O twoports, we assume unilateral behaviour and zero optical reflection of the device. In this case, the test ports E 1 and O2 are selected in order to measure the slope responsivity hðjvÞ, although from Equation (10.30) it is seen that to obtain this parameter also requires measurement of the input E=O reflection coefficient (S11 ). E=E O=O When compared with the corresponding measurements of S21 and S21 for E/E and O/O components, the greatest challenge for O/E and E/O measurements is calibration. The physical impossibility of constructing a thru connection for either an O/E or E/O component precludes the use of conventional two-port self-calibration routines such as those used for E/E measurements. Consequently, measurements must be referenced to some ‘golden’ standard, typically a reference photoreceiver that has been independently measured with traceable techniques. In this situation, it can be argued that the measurement is being normalized with respect to the


319

reference device in an attempt to obtain the absolute value of the desired parameter, be it responsivity or slope responsivity. However, there are some important cases where this is not necessary, and is indeed undesirable, a case in point being the intrinsic modulation response of laser diodes. Laser diodes may be modelled as the cascade of a parasitic network and the intrinsic device. Equivalent circuit modelling techniques may then be used to model both the parasitics and the intrinsic circuit, with the circuit elements for the latter corresponding directly to parameters in the rate equations [46]. The benefit of this approach is that it allows laser diodes to be incorporated into microwave CAD programs, thereby enabling the design and optimization of matching networks for example. The downside is the need to accurately extract model parameters, which requires DC characterization in addition to S-parameter measurements. For packaged devices, the parameter extraction process can involve a large number of parameters, although the procedure may be simplified by assuming the active region to be a short circuit [47]. However, if one takes the intrinsic region alone, the modulation response is second order, and hence only two parameters – the D and K parameters (corresponding to the damping factor and resonance frequency) – are required to specify the devices performance [2]. Moreover, the intrinsic modulation response is bias dependent whereas the parasitic elements do not vary significantly in value as the bias current is adjusted. Hence the issue of calibration can be circumvented for the special case of laser diode modulation response measurement, by E=O using the bias subtraction method. Here, the S21 parameter is measured at two different bias points (both above threshold), and the response (in dB) of the upper bias point is subtracted from the lower bias point [2]. In this manner, the impact of the laser parasitics is removed, as is the need to calibrate out the response of the photoreceiver in the lightwave component analyser. A typical example of a bias subtraction measurement is shown in Figure 10.20. Here it is seen quite clearly that using bias subtraction leads to removal of parasitic effects and there are clear ‘turning’ points allowing the identification of resonance effects. Despite the effectiveness of the bias subtraction technique for intrinsic laser diode characterization, it is not applicable to other important E/O components such as electroabsorption and Mach–Zehnder modulators, nor is it useful for O/E components. In this latter case, well-established heterodyne measurement techniques exist for the measurement of photodiode and photoreceiver frequency response. When allied with equivalent circuit modelling techniques, it is feasible to deduce both the magnitude and phase response, thereby

Figure 10.20 (a) Typical measured IM response for a DFB laser diode at different bias currents; (b) bias subtraction measurements for the same device

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obtaining RðjvÞ for a given photoreceiver. This is the basis of the so-called factory calibration used for some lightwave component analysers [24]; armed with such a calibration, it is possible to obtain measurements of E/O components that are referenced to the factory calibration data. The same philosophy applies to the use of photoreceivers as transfer standards, the so-called ‘golden standard’ referred to earlier. These may be used for the measurement of not only E/O components, but also other O/E photoreceivers. In this situation, the reference photoreceiver will ideally be a device with linear time-invariant characteristics, high responsivity, low noise and a bandwidth well in excess of the E/O and O/E DUTs that will be measured relative to it. This last requirement is easily achievable, since photodiodes with bandwidths in excess of 500 GHz have been produced [48]. In the discussion that follows, we will assume that a photoreceiver transfer standard is available, and that its responsivity RðjvÞis known in a 50 W system. The heterodyne techniques that are used to determine the responsivity of the transfer standard are described in [37] and are outlined in Appendix 10.B. The measurement theory of both E/O and O/E components using a calibrated reference photoreceiver and microwave vector network analyser is studied in some detail in the seminal paper of Hale et al. [37]. Here, the basic approach is to examine a simple cascade of an E/O and O/E pair that can be measured with a calibrated VNA, and to assume that no optical reflections occur in between them. The resulting S-matrix is: "

E=E

S11 E=E S21

E=E

S12 E=E S22

#

" ¼

E=O

S11 E=O hR 1 S11

0 O=E

S22

# :

ð10:33Þ

O=E

If the responsivity RðjvÞ and electrical reflection coefficient S22 for the reference O/E photoreceiver are known, then the slope responsivity hðjvÞand electrical reflection coefficient E=O S11 for the E/O DUT are readily obtained from Equation (10.33). It is then possible to measure an O/E DUT if this is used to replace the original reference photoreceiver. In this case, the responsivity RðjvÞof the O/E DUT will be related to the responsivity of the reference device via: O=E

RðjvÞ ¼

S21

O=E

RðjvÞ

S21

ð10:34Þ

where the quantities marked with a bar are those of the DUT and all other quantities are taken from Equation (10.33). The use of a reference photoreceiver for the calibration of a lightwave component analyser is also shown in [37].

10.3.2 Second-generation Lightwave Component Analysers One of the key drawbacks of the first generation of lightwave component analysers is the number of different set-ups and calibrations that are required in order to obtain measurements from the full range of lightwave components. This limitation arises partly from the architecture described in Section 10.3.1, but it is also due to the primitive state of O/O standards and the relative difficulty of procuring transfer standards for E/O and O/E measurements when compared to the E/E case. Subsequently, a number of alternative architectures and calibration techniques have been investigated. In many cases, the motivation has been to obtain the O/O,


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E/O and O/E equivalents of the reversible tests and self-calibration procedures that have been available to the microwave network analyser community for some time. (i) The Bilateral Electro-optic Network (BEON) The use of bilateral electro-optic networks for lightwave component analysis was first proposed in [43] as a means of overcoming the architectural limitations of existing instruments. This approach is conceptually simple, and consists of selecting calibration and measurement planes at various points in a cascade of bilateral E/E, O/O and E/O and O/E two-ports as shown in Figure 10.21. The E/O and O/E two-ports are identical to the BEON structure discussed in Section 10.2.6. This cascade is connected to ports 1 and 2 of a microwave VNA. If we assume that the reduced error network model applies, then in this set-up, the E/E networks can be incorporated into the error networks, and calibration between planes P1 and P4 will allow errorcorrected S-parameter measurements of E/E components. It is also argued in [43] that calibration is possible between planes P2 and P3 using the optical equivalent of the selfcalibration techniques developed for microwave measurements [49]. (In this case, the E/O and O/E networks are grouped with their neighbouring E/E networks to form the error networks.) The advantage here is that when compared with the approach of Curtis and Ames [21], the optical standards are easily realizable and their full characteristics need not be known. In general, three standards (labelled O1, O2, and O3 in [43]) are required, and as with the E/E case, they are passive. Only the first standard requires all its S-parameters to be known, and choosing the thru connection is the easiest option. It is also possible in principle to perform E/O and O/E calibrations, by selecting either planes P1 and P3 or planes P2 and P4. If one considers calibration at planes P1 and P3 then the error networks are dissimilar – one is E/E while the other is O/E – and this necessitates E/O standards denoted by EO1, EO2 and EO3. These three standards may be formed by cascading the BEON used for the E/O box in Figure 10.21 with the optical standards O1, O2 and O3 in turn. Provided the S-parameters of the BEON can be determined, this means that the same physical process used for O/O calibration can also be used for E/O calibration. Since all networks are taken to be bilateral, this also allows O/E two-ports to be measured with a calibrated E/O set-up (simply by reversing them before connection to P1 and P3). The one major disadvantage of the E/O calibration is that the BEON is used, and its S-parameters must be found. As part of a calibration process in general, the S11, S22 parameters and the product S12S21 of an error network are determined. This means that during the O/O calibration, it is possible to obtain these parameters for the E/O BEON, and a heterodyne technique can then be used to find S12 and thence S21. With the proviso that a heterodyne technique is used to find the individual forward and reverse transmission parameters of one of the BEONs, it is thus possible to apply an O/O calibration to the cascade in Figure 10.21, and simultaneously to perform either an E/O or O/E calibration procedure. Indeed, it is also possible simultaneously to perform an E/E calibration

Figure 10.21 Generalized fibre-optic link using BEONs for the E/O and O/E two-ports. Reproduced from [43] ( 1991 IEEE)

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relative to planes P1 and P4 if one regards the cascade of O1–O3 with both BEONs as forming a set of E/E standards. (In practice, however, a conventional set of passive E/E standards would be preferred, so this last point is academic.) In this sense, it can be claimed that the techniques described here provide a unified approach to the calibration and measurement of all four types of lightwave two-port. Moreover, the use of a conventional VNA with its ability to perform S-parameter characterization with a single connection of the DUT to the test set means that this approach reduces the number of operator steps compared to first-generation lightwave component analysers. In spite of the conceptual simplicity of the BEON approach, it is limited in its practical usefulness. The electrical circulator used to separate the incident and reflected electrical signals restricts the bandwidth of the two-port, whilst the use of two BEONs leads to two counterpropagating optical stimuli passing through the O/O component, thus creating any number of possible interference scenarios. This includes the generation of laser beat noise. Moreover, the BEON approach is vulnerable to all the effects described in Section 10.2.5 unless adequate precautions are taken, such as effective isolation between the incident and reflected optical signals for the BEONs and ensuring there are no optical reflections due to the interfaces between the O/O network and the BEONs. Optical circulators can be used to ensure the former, while the latter condition requires the use of fibre-based components and physical-contact optical connectors. Finally, it has been argued [50] that for the E/O and O/E calibrations, the effect of the BEON is not removed from the normalized error network and could result in subsequent measurement results being scaled. The performance of the BEON has been simulated and measured, but it has only been applied to a one-port optical configuration with a ‘black-box approach’, in which it extended one port of a microwave VNA to the optical domain. Prior to its connection to the VNA, the S-parameters of the BEON were measured independently, using a lightwave component analyser. These were then stored in memory and used to de-embed the reflection coefficient of the optical DUT from the measured microwave reflection coefficient provided by the VNA. In essence this system is a one-port reflectometer, and an alternative to the black-box approach is to implement an optical one-port calibration analogous to the microwave techniques described in [51]. A typical one-port measurement using the BEON is shown in Figure 10.22 for a mirror on the end of a fibre patchcord. (ii) The O/O Two-port Test Set If the BEON approach as outlined above were to be implemented successfully, it would offer the scope for full two-port characterization of all lightwave component types. From a practical perspective, this is somewhat excessive for E/O and O/E two-ports such as laser diodes and photodiodes. In the case of a laser diode, the reverse transmission is negligible and if an optical isolator is used, there is no significant reflection from its optical port. What actually matters is E=O E=O the forward modulation response and the input reflection coefficient (i.e. S21 and S11 ). In contrast, there is a need for full two-port characterization of components such as optical amplifiers and optical isolators, in which the forward and reverse characteristics may differ markedly. Similar considerations apply to a number of all-optical structures that have been used to implement microwave filtering. Hence there is some merit in developing two-port test sets and calibration procedures purely for O/O components. The first optical two-port test set was developed by Quoc and Tedjini, by using a pair of directional optical couplers [33]. However, the lack of automation made their approach


323

Figure 10.22 De-embedded measurement results using a BEON and from a HP8703A lightwave component analyser compared with predicted results for: (a) mirror and (b) recirculating delay line terminated in a mirror. Reproduced from [42] ( 1997 IEEE)

cumbersome, and they only investigated a single type of calibration (TMR – thru-matchreflect). This approach was extended and improved by Elamaran et al. [45] through the use of an optical test set architecture similar to that of a microwave VNA, in which dual directional couplers and switches are used to route optical signals to the appropriate ports and then separate incident and reflected signals. The resulting architecture functions as a fully reversible transmission and reflection test set for O–/O DUTs and has a broad bandwidth that is limited only by the modulator and photoreceiver modules. The performance of all the Txy family of calibration techniques was examined for optical fibre-based standards. An extensive experimental comparison between all the techniques showed that the Txy approach provides flatter and more accurate test results (especially for reflection S-parameters) when compared with the normalization and isolation method that is

324


Figure 10.23 (a) O/O test set [1]; (b) measurement of 0.2 dBo optical reflect; (c) measurement of recirculating delay line loop [45]. Reproduced from ( 1999 IEEE)

usually used with first-generation analysers. In particular, the use of attenuation (A) and match (M) standards provide the best broadband performance of all the Txy methods. The other standards include reflects (R), Fresnel reflects whose value is not assumed to be known (F), ‘known’ Fresnel reflects (FK) and symmetrical networks (N). It has also been shown that reflection measurements are more affected by calibration accuracy than transmission measurements. Typical results from the two-port O/O test set are shown in Figure 10.23 for the reflection coefficient magnitude of a 0.2 dBo reflect and the optical transmission magnitude for a recirculating delay line loop. For the reflection measurements, it was found that the TAR and TAF calibration techniques give values very close to the nominal values of the DUTs. When compared with the more basic calibration techniques used by first-generation instruments, the Txy family of self-calibration routines gives far superior results. Hence the reversible O/O test set architecture allows greater measurement accuracy to be achieved when compared to the unilateral test sets used in first-generation lightwave component analysers. (iii) The Bilateral Lightwave Network Analyser The bilateral lightwave network analyser (BLNA) is in essence an instrument that combines the O/O test set architecture described in (ii) above with that of a conventional microwave VNA. Hence the resulting instrument has a pair of electrical test ports (denoted by E 1 and E 2) and a pair of optical ports (denoted by O1 and O2), to which E/E, E/O, O/E and O/O two-ports may be connected. Through the use of microwave and optical switching plus microwave and optical double reflectometers, the instrument follows the bilateral test set approach of microwave


Figure 10.24

325

Block diagram of a bilateral lightwave network analyser

VNAs. In other words, a single connection of the lightwave DUT is made to the appropriate test ports, and all four S-parameters are obtained from a single configuration. This also allows the application of two-port self-calibration techniques for both E/E and O/O two-ports, and these can then be used as the first steps in the calibration for E/O and O/E two-ports (for which a twotier calibration is employed [52]). A block diagram showing the test sets, along with the incident and reflected microwave and modulated optical stimuli, is shown in Figure 10.24. A synthesized sweeper supplies the microwave and optical tests sets via a three-way switch; two positions are used to supply ports E 1 and E 2, while the third position is used to route the modulation signal to an external modulator, before being routed via a two-way optical switch to ports O1 and O2. The incident and reflected signals from the microwave test set are passed (via power combiners) to a frequency converter module for downconversion prior to signal processing. A similar route is followed by incident and reflected signals from the optical test set, although in this case photoreceivers are first used to convert the lightwaves into microwave signals. In order to cut down on the number of components needed to construct the BLNA, power combiner modules are used to combine similar pairs of signals from the microwave and optical test ports. Consequently, some pairings of test ports are not allowed; in this case, neither E 1 and O1 nor E 2 and O2 can be used simultaneously. Table 10.3 specifies the ports to which a particular lightwave two-port should be connected. Using the same pair of ports (E 1 and O2) to measure both E/O and O/E components opens up the possibility of using a single two-port calibration to cover both types of measurement. This is accomplished with a two-tier calibration. In the first tier, the microwave port E 1 is extended with a BEON to form an optical port, labelled O1 in Figure 10.25. An optical Txy calibration

326

Microwave Photonics: Devices and Applications Table 10.3 analyser.

Port configurations for a bilateral lightwave

DUT Type

Port 1

Port 2

E/E E/O O/E O/O

E1 E1 O2 O1

E2 O2 E1 O2

Figure 10.25 Measurement configuration for combined E/O and O/E two-tier calibration. Reproduced from [45] ( 1999 IEEE)

(as described in (ii) above) is then applied between ports O1 and O2. This calibration sees an effective error network at O1 which is the cascade of error network A and the BEON. By treating the BEON as a black box with pre-measured S-parameters, a normalized version of error network A may be obtained, while error network B is determined as outlined in [50], where the relevant formulae for the calibration procedure are derived. A BLNA was demonstrated in [50], and used to measure all four types of lightwave component, namely E/E, E/O, O/E and O/O two-ports. The O/O, E/O and O/E measurements were compared with a commercially available first-generation lightwave component analyser (HP8703A). For the O/O measurements, a thru-attenuate-reflect (TAR) calibration was applied between ports O1 and O2. The optical magnitude measurements shown in Figure 10.26 show that the BLNA is within the uncertainty limits of the optical test set described in [45], as are those for the HP8703A. (The method in [53] was used to calculate the uncertainty limits.)

Figure 10.26 Calibrated optical magnitude measurements (from BLNA) compared with those from a HP 8703A: (a) 0.2 dB reflect, (b) 20 dB attenuator. Reproduced from [50] ( 2000 IEEE)


327

However, the improved reflection magnitude obtained from the BLNA shows its enhanced accuracy compared to the first-generation instrument. E/O and O/E measurements were obtained following a two-tier calibration. Optical thru, attenuate and reflect standards in turn were each cascaded with a BEON. Measurements of a laser diode and photoreceiver performed with the BLNA were found to follow closely those of the commercial instrument, but uncertainty limits could not be determined because the method employed in [53] is not applicable to the E/O and O/E cases.

10.4 Conclusions A review of the field of lightwave network analysis has been given. We have seen that characterizing the various components in a microwave photonic system involves a mix of microwave and modulated optical signals, and this requires the extension of existing techniques and tools (S-parameters and vector network analysers). This chapter has presented a theoretical framework for being able to handle cascades of microwave, optoelectronic and optical components operating in the linear regime. In addition, practical measurement techniques based on lightwave component analysers have been discussed.

Appendix 10.A: Two-port Self-calibration and De-embedding The systematic errors in a network analyser can be incorporated into two error networks with transfer matrices A and B, with D denoting the transfer matrix of the DUT. With reference to this model, measurements M may be obtained using an ideal network analyser (Figure 10.A1). M ¼ ADB: In order to obtain D, the effects of A and B must be removed by de-embedding: D ¼ A 1 MB 1 : De-embedding can be achieved once the network analyser model has been calibrated at the DUT planes. This involves substituting the DUT with a set of calibration standards (which usually number three). In the case of self-calibration procedures, using three or more standards to calibrate out the error networks results in an overdetermined set of equations. This allows one to use redundancy in specifying the calibration standards. In particular, it is not necessary to know the values of all the S-parameters of all the calibration standards. For example, if a thru-connection is used for the first standard (for which the transfer matrix is fully known, it being the identity matrix), one need not know all the S-parameters of the

Figure 10.A1

Two-port model of error networks in a microwave VNA

328


second and third standards. One may then choose from an attenuator (A), matched load (M) or a transmission line (L) for the second standard; in the case of the A standard, the only requirement is that S11 ¼ S22 ¼ 0. This flexibility extends to the third standard, where one may choose from either a pair of one-port reflects (R) or a symmetrical two-port network (N). In the case of the reflect standard, the actual value of the reflection coefficient need not be known.

Appendix 10.B Heterodyne Characterization of Photodiodes It is physically impossible to fabricate a thru standard for E/O and O/E components, and this is a significant disadvantage when compared to E/E and O/O measurements. This means, for example, that the two-port self-calibration techniques used for O/O components cannot be replicated for E/O measurements if one is to use a bilateral lightwave network analyser. Instead, a two-tier calibration is required in which passive optical standards are cascaded with a bilateral E=O E=O electro-optic network. The requirement is that the transmission parameters (S21 and S12 ) of this network are known. In the case of a first-generation lightwave component analyser, similar considerations apply: to measure an E/O component, for example, a so-called factory calibration of the instruments photoreceiver is required [36]. Subsequent E/O and O/E measurements are then referenced to this data. In order to have some success with E/O and O–/E measurements using a lightwave component E=O analyser, there must be some independent means of measuring the S21 parameter of a photoreceiver. The photoreceiver can then be integral to the lightwave component analyser [23], or used as an external transfer standard [54]. Although time-domain techniques exist for the measurement of a photoreceivers frequency response [5], the method which has been mostly used by lightwave component analyser manufacturers is the heterodyne technique [54, 55]. A greatly simplified diagram of a heterodyne set-up is shown in Figure 10.B1. The light from two lasers (Nd:YAG devices are usually used) is combined and is then incident on the

Figure 10.B1 Block diagram of heterodyne measurement concept


329

photoreceiver being measured. In this case, we consider the photoreceiver to simply consist of a photodiode for the sake of simplicity. The mathematical details of the heterodyning process are available in Chapter 4, but we will summarize the salient formulae here. We assume that the lasers emit perfectly monochromatic waves that have identical polarizations and are mode matched, hence the complex electric field incident on the photodiode will be: EðtÞ ¼ E1 expðjv1 t þ f1 Þ þ E2 expðjv2 t þ f2 Þ where we assume that the lasers have different frequencies and phases. Since the incident optical intensity (and therefore power) will be proportional to the square of the electric field magnitude, we find that the resulting photocurrent will contain a DC term and also a term that varies with the difference frequency v1–v2, provided this difference is sufficiently small to be within the microwave frequency range. Hence the photocurrent is given by: pffiffiffiffiffiffiffiffiffiffi iP ðf Þ ¼ R ð0ÞfP1 þ P2 g þ 2 P1 P2 Rðf Þcos ½ð2pftÞ þ fðf Þ ¼ IDC þ irf where 2pf ¼ v1 v2, R(f) is the frequency-dependent responsivity of the photodiode, f(f) is the phase delay due to the photodiode and the connecting cable, and P1 and P2 are the optical powers delivered by the two lasers. These last two quantities will be proportional to the square of the electric field magnitudes for the individual lasers. The mean square photocurrent is: hiP2 ðf Þi ¼ R2 ð0ÞfP1 þ P2 g2 þ 2P1 P2 R2 ðf Þ 2 ¼ hIDC i þ hirf2 i If the lasers emit approximately the same optical power level (i.e. P1 P2), then: 1 2P1 P2 ðP1 þ P2 Þ2 2 and the normalized frequency response can then be obtained: 2Prf 2 hIDC iRL

hirf2 iRL 2 2hIDC iRL 2P1 P2 R2 ðf ÞRL ¼ 1ðP þ P Þ2 R2 ð0ÞR 1 2 L 2 R2 ðf Þ 2 R ð0Þ

¼1

Acknowledgements The author is grateful to his former colleagues at the University of Leeds, in particular Bala Elamaran and Roger Pollard, for their work on lightwave analysis research. He also thanks Agilent Technologies for having partly funded this work.

330


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Index ABCD transfer matrix 70, 81 acoustic pressure sensors 241–8, 256 ADCs see analogue-to-digital converters ALMA project 27–8, 86, 105 amplified spontaneous emission (ASE) 176, 203, 206, 209, 228–9 analogue microwave fibre-optic links 133–67 attenuation 140, 142, 156 design options 140–64 detection 143–5 dispersion 143 dynamic range 137–9, 154, 159, 161–4 gain performance 135, 139, 155 input/output port interfaces 150–3 intrinsic fibre-optic links 133–4, 153–64 modulation 146–50 nonlinearity 142, 161–3 optical fibres 141–3 optical wavelength 140–1 performance/limitations 134–40, 153–64 RF microwave signals 133–4, 141, 147, 162–4 signal-to-noise performance 135–7, 154, 156–61 analogue-to-digital converters (ADCs) 7, 30, 195 APDs see avalanche photodiodes array waveguide grating (AWG) 193, 212–16 ASE see amplified spontaneous emission attenuation analogue microwave fibre-optic links 140, 142, 156 characterization of components 293 limits 8–9

Auston switches 114–16 available gain 137 avalanche photodiodes (APDs) 22 AWG see arrayed waveguide grating backward wave cancellation (BWC) 77–81 backward wave oscillators (BWO) 118 backwards isolation 139 ballistic deflection transistors (BDTs) 125 base station architectures 169–74, 176–81, 183–7 baseband over fibre 31–2, 178–9, 180 BCL see bipolar cascade lasers BDTs see ballistic deflection transistors Beer–Lambert law 257–60 BEONs see bilateral electro-optic networks BER see bit-error rates biased photoconductive emitters 114–16 bilateral electro-optic networks (BEONs) 316, 321–3, 325–7 bilateral lightwave network analysers (BLNAs) 324–7 biomedical applications 239–89 broadband NIR systems 270–86 extraction of phantom optical parameters 282–6 fibre-optic acoustic pressure sensors 241–8 haemoglobin oxygenation 241, 257–61, 272–3 intralipid experiments 277, 278–82 mammography 262–4 near infrared spectroscopy 240–1, 257–86 optical hydrophones 239–40, 241–56


334 bipolar cascade lasers (BCL) 61, 62–4 bit-error rates (BER) 8, 179–81, 291 BLNAs see bilateral lightwave network analysers Bloch effect 122 Brillouin scattering 142, 203, 232–3 broadband antenna-coupled THz transmitters 105–6 extraction 282–6 frequency domain systems 270–2 NIR systems 270–86 THz signal generation 112–16 BSCCO superconductor 123 BWC see backward wave cancellation BWO see backward wave oscillators cable television (CATV) 139–41, 164 carrier density 47–9 carrier-to-noise ratio (CNR) 175, 177, 208–9 cascade laser optical links 61–4 CATV see cable television CDMA see code division multiple access cellular communications 169 characterization of components 291–332 analyser architectures 316–27 bilateral electro-optic networks 316, 321–3, 325–7 bilateral lightwave network analysers 324–7 coherence length 292, 310–12 E/E components 291–4, 296–7, 304, 306, 308–9, 316–29 E/O converters 294–6, 309, 313–29 envelope S-parameters 302, 304–13 first generation LCAs 317–20 heterodyning 328–9 lightwave component analysis 296–329 limiting assumptions 308–13 linear distortion 309–10 modulated light 293–4, 301–4 O/E converters 294–6, 309, 313–29 O/O components 291–4, 296, 301–13, 316–29 optical cavity effects 312–13 photodiodes 328–9 polarization 292, 310 principles 291–5 S-parameters 291, 296–301, 313–16 second generation LCAs 320–7 two-port self-calibration and de-embedding 327–8 two-port test sets 322–4

Index

chirp characterization of components 302 intensity modulation 11, 13–14, 16 microwave photonic signal processing 200, 217–18, 221–3 chromatic dispersion 143, 293–4 CMRR see common mode rejection ratio CNR see carrier-to-noise ratio coaxial cables 9–10 code division multiple access (CDMA) 195 coherence length 292, 310–12 coherent detection 11, 143–5 coherent operation regimes 199 common mode rejection ratio (CMRR) 74 composite triple beat (CTB) 139 continuous wave (CW) lasers analogue microwave fibre-optic links 141, 143, 147–9, 155 biomedical applications 240, 257–61, 266 microwave photonic signal processing 204–5 THz signal generation 117 coplanar strips (CPS) 74, 79 coplanar waveguide (CPW) transmission lines 73 cross-phase modulation (XPM) 203 CTB see composite triple beat CW see continuous wave DAN see distributed antenna systems DAST crystals 113 DBR see distributed Bragg reflectors DBRTD see double barrier resonant tunnelling diodes DE-MZM see dual-electrode Mach–Zehnder modulators DFB see distributed feedback DFG see difference frequency generation DHBT see double heterojunction bipolar transistors difference frequency generation (DFG) 116–18 differential detection 226 direct detection 10–11, 143–5 direct modulation 41–65 analogue microwave fibre-optic links 146–7, 152 bipolar cascade lasers 61, 62–4 cascade laser optical links 61–4 high-speed lasers 51–3 optical link gain 49–51 performance/limitations 41–3

Index

principles 10–11, 12–15, 18–19 RF photonic links 58–61 RF signal strength 49–51 semiconductor lasers 43–9 signal bandwidth 51–3 signal distortion 41–2, 53–8 spurious free dynamic range 53–8 dispersion 143, 293–4 dispersion-induced power fading 25 dispersion-shifted single-mode fibres 141 distributed antenna systems (DAN) 31 distributed Bragg reflectors (DBR) 44–5, 248 distributed feedback (DFB) lasers analogue microwave fibre-optic links 143, 147 biomedical applications 253 characterization of components 295, 319 direct modulation 44–6, 59 fibre radio technology 174 microwave photonic signal processing 209 photonic oscillators 102 principles 14–15 doped-fibre lasers 147 double barrier resonant tunnelling diodes (DBRTD) 120 double heterojunction bipolar transistors (DHBT) 124–5 drift-diffusion model 93–7 dual-electrode Mach–Zehnder modulators (DE-MZM) 175–6 dynamic range see spurious-free dynamic range E/E see electrical-electrical E/O see electrical-to-optical EAMs see electro-absorption modulators EDFAs see erbium-doped fibre amplifiers edge-coupling 23, 93 electrical-electrical (E/E) components 291–4, 296–7, 304, 306, 308–9, 316–29 electrical telegraphs 3 electrical-to-optical (E/O) converters applications 26 architectures 10–11 characterization of components 294–6, 309, 313–29 device technology 12–20 fibre radio technology 172 microwave photonic signal processing 203–4 O/O components 25–6 properties 7–10

335 electro-absorption modulators (EAMs) 20 analogue microwave fibre-optic links 148 fibre radio technology 184, 186 microwave photonic signal processing 204, 207 electro-optic (EO) crystals 113–14, 117–18 electro-optical modulators (EOMs) 161, 204–5, 207, 229–32 electromagnetic interference (EMI) 191 electromagnetic spectrum 4 electronic bottleneck 191 EM see external modulation EMI see electromagnetic interference envelope S-parameters 302, 304–13 EO see electro-optic EOMs see electro-optical modulators erbium solid-state/fibre lasers 113 erbium-doped fibre amplifiers (EDFAs) analogue microwave fibre-optic links 141 microwave photonic signal processing 199, 203, 206, 209, 214, 228–9 principles 25–6 THz signal generation 102 external Bragg cell sensors 247 external interferometric phase sensors 244–5, 256 external modulation (EM) 11, 16–20, 146–8, 153, 158, 203 Fabry–Perot (FP) lasers analogue microwave fibre-optic links 143, 146, 148 fibre radio technology 174 interferometers 245–7 principles 14–15 resonators 44–5 far-infrared lasers 112 FBGs see fibre Bragg gratings FDLFs see fibre delay line filters FDPM see frequency domain photon migration FELs see free-electron lasers FETs see field effect transistors FGDLFs see fibre grating delay line filters fibre Bragg gratings (FBGs) biomedical applications 247–8 fibre radio technology 182 microwave photonic signal processing 193, 200, 214, 216–25, 228–9 fibre delay line filters (FDLFs) 210–16

336 fibre grating delay line filters (FGDLFs) 211, 216–25 fibre networks 27 fibre radio technology 169–90 base station architectures 169–74, 176–81, 183–7 baseband over fibre 178–9, 180 enabling technologies 173–81 evolution of radio networks 170 IF over fibre 176–8, 180 optical fibre distribution schemes 170–3 performance/limitations 184–7 RF over fibre 173–6, 180 signal transport schemes 173–81 trade-offs 179–81 wavelength division multiplexing 171–2, 181–4 fibre-optic (FO) acoustic pressure sensors 241–8 frequency/wavelength modulated 247–8 intensity modulated 242–3 performance/limitations 256 phase modulated 243–7 fibre-optic (FO) links see analogue microwave fibre-optic links fibre-optic (FO) probes 240 fibre-to-the-home (FTTH) 5, 41 field effect transistors (FETs) 125–6 filter reconfiguration 200–1, 202, 222–3 filter tuneability 200, 202, 222–3 finite element model (FEM) 251–2, 255 finite impulse recursive (FIR) 30, 196, 203 first generation LCAs 317–20 five-stage uniform filters 222–3 five-tap transversal filters 229 FO see fibre-optic four-wave mixing (FWM) 203 FP see Fabry–Perot Franz–Keldysh effect 148, 161 free dynamic range see spurious free dynamic range free spectral range (FSR) 198–9, 201–2, 209, 213–14, 218, 220, 233 free-electron lasers (FELs) 112 frequency-dependent scattering matrices 139 frequency domain measurements 240–1, 257, 264–6, 270–2 frequency domain photon migration (FDPM) 241, 270–2 frequency modulated sensors 247–8

Index

Fresnel reflectance 248–56 frustrated total internal reflection 243 FSR see free spectral range FTTH see fibre-to-the-home full-compression dynamic range 137 FWM see four-wave mixing gain performance 135, 139, 155, 203–7 gallium arsenide analogue microwave fibre-optic links 140, 145, 147 direct modulation 54 external modulation 16, 19 photonic oscillators 93, 101–2 terahertz signal generation 115–16, 121, 125 gallium nitride 126 gallium phosphide 113, 118 gallium selenide 113–14 Golay cells 102–3, 105–6 Gunn diodes 119–20 haemoglobin oxygenation 241, 257–61, 272–3 harmonic distortion (HD) 54–6, 59, 207–9 HBT see heterojunction bipolar transistors HBV see heterostructure barrier varactor HD see harmonic distortion HDTV see high definition television HEMT see high electron mobility transistor heterodyning 28, 87–91, 328–9 heterojunction bipolar transistors (HBT) 124–5 heterostructure barrier varactor (HBV) 127–8 HFC see hybrid fibre coax HIC see hybrid integrated circuits high definition television (HDTV) 31 high electron mobility transistor (HEMT) 125–6, 186 high-performance radio LAN (HiperLAN) 194 high-power distributed photodetectors 67–83 high-speed lasers 51–3 HiperLAN see high-performance radio LAN historical development 3–6 hybrid fibre coax (HFC) systems 41, 45 hybrid integrated circuits (HIC) 185 hybrid optoelectronic approach 226–7 I/Q system 266–7 IF over fibre 31–2, 176–8, 180 IIR see infinite impulse recursive IM see intensity modulation IMD see intermodulation distortion

337

Index IMDD see intensity modulation/direct detection IMPATT diodes 119–20 incoherent regimes 197, 199–200, 209–11, 225–7, 310–12 indium gallium arsenide (phosphide) 145 indium phosphide 19, 54, 107, 125 infinite impulse recursive (IIR) 30, 196–8, 203, 219 input/output port interfaces 150–3 intensity modulation/direct detection (IMDD) analogue microwave fibre-optic links 146–52, 157, 163 biological applications 242–3, 264–6 characterization of components 291–2, 296–329 microwave photonic signal processing 203–4 performance/limitations 41, 43 photodetectors 67, 81 principles 10–11, 13 intensity noise 41–2 intensity sensing 248–56 experimental set-up and results 253–6 fibre sensor fabrication 251–3 finite element model 251–2, 255 performance/limitations 256 principles 248–50 transmission line modelling of coated fibres 250–1 interferometers see Mach–Zehnder interferometers intermediate frequency see IF over fibre intermodal dispersion 143 intermodulation distortion (IMD) 42, 54–9, 138, 207–9 internal interferometric phase sensors 245–7 internet protocol (IP) 170 intralipid experiments 277, 278–82 intrinsic fibre-optic links 133–5, 153–64 intrinsic small-signal gain 135, 153–4 IP see internet protocol Josephson plasma sources

123

LANs see local area networks laser diodes architectures 10–11 device technology 12–20 direct modulation 10–11, 12–15, 18–19 external modulation 11, 16–20

intensity modulation response 13 light–current characteristics 12–13 performance/limitations 13–14 types 14–15, 16–20 laser RIN 67–8, 73–4 LCA see lightwave component analysis LCFBGs see linearly chirped fibre Bragg gratings LEDs see light-emitting diodes light–current characteristics 12–13 light-emitting diodes (LEDs) 260–1 lightwave component analysis 296–329 analyser architectures 231, 316–27 bilateral electro-optic networks 316, 321–3, 325–7 bilateral lightwave network analysers 324–7 coherence length 310–12 component categorisation 296 E/E components 296–7, 304, 306, 308–9, 316–29 E/O converters 296, 309, 313–29 envelope S-parameters 302, 304–13 first generation LCAs 317–20 heterodyning 328–9 limiting assumptions 308–13 linear distortion 309–10 modulated light 301–4 O/E converters 296, 309, 313–29 O/O components 296, 301–13, 316–29 optical cavity effects 312–13 photodiodes 328–9 polarization 310 S-parameters 291, 296–301, 313–16 second generation LCAs 320–7 two-port self-calibration and de-embedding 327–8 two-port test sets 322–4 limited spectral period see free spectral range linear distortion 309–10 linear time invariant (LTI) systems 302, 312 linearly chirped fibre Bragg gratings (LCFBGs) 200, 217–18, 221–3 link gain 67–8 link loss 9–10 lithium niobate 16–19, 141, 155, 302 LMDS see local multipoint distribution systems LO see local oscillators local area networks (LANs) 169, 170, 174, 178–9, 187 local multipoint distribution systems (LMDS) 170, 173, 176, 179–81, 187

338 local oscillators (LO) 86, 108–9, 173–4, 177–81 low-biasing technique 158–9 low-cost VCSELs 58–61 LTI see linear time invariant Mach–Zehnder filters 218–21 Mach–Zehnder interferometers (MZI) 244–7 analogue microwave fibre-optic links 148–50, 153, 155, 158–64 characterization of components 309–12 Mach–Zehnder modulators (MZM) characterization of components 302–3, 319 fibre radio technology 175–6 microwave photonic signal processing 229–31 principles 5, 16–20, 23–4 signal processing 29–30 main-to-secondary lobe ratio (MSLR) 200–1 mammography 262–4 MANs see metropolitan area networks MBE see molecular beam epitaxy metal–semiconductor–metal (MSM) photodetectors 69, 75, 92–3, 101 metropolitan area networks (MANs) 171–2 microchip lasers 28 microwave fibre-optic links see analogue microwave fibre-optic links microwave photonic signal processing (MWPSP) 191–237 advantages over RF signal processing 192–3 applications 193–6 coherent operation regimes 199 electrical performance 203–9 fibre delay line filters 210–16 fibre grating delay line filters 211, 216–25 fibre nonlinearities 202–3 filter reconfiguration 200–1, 202 filter tuneability 200, 202 fundamental concepts 196–201 gain performance 203–7 harmonic distortion 207–9 incoherent operation regimes 197, 199–200, 209–11, 225–7 intermodulation distortion 207–9 noise figure 205–7 optical performance 201–3 performance/limitations 192–3, 201–9 principles 29–30 MICs see monolithic integrated circuits

Index

Millimetric Waveguide 3 mismatch gain 50–1, 60 MLLD see mode-locked laser diodes MMF see multimode fibre MMI see multimode interference MMICs see monolithic microwave integrated circuits mode-locked laser diodes (MLLD) 91 molecular beam epitaxy (MBE) 120 molecular lasers 112 monolithic integrated circuits (MICs) 185–7 monolithic microwave integrated circuits (MMICs) 4, 215–16, 227 moving target identification (MTI) 194–5 MQW see multiple quantum well MS-TWDP see multisection travelling wave distributed photodetectors MSLR see main-to-secondary lobe ratio MSM see metal–semiconductor–metal MTI see moving target identification multilayer hydrophones 246–7 multimode fibre (MMF) 178 multimode interference (MMI) 24, 74–5 multiple quantum well (MQW) modulators 20 multiplication 126–8 multisection travelling wave distributed photodetectors (MS-TWDP) 78–81 MWPSP see microwave photonic signal processing MZI see Mach–Zehnder interferometers MZM see Mach–Zehnder modulators narrowband photonic oscillators 106–9 Nd-YAG lasers 117 NDR see negative differential resistance near infrared lasers 116–18 near infrared (NIR) spectroscopy 257–86 broadband systems 270–86 continuous wave measurement 240, 257–61, 266 design considerations 272–8 extraction of phantom optical parameters 282–6 frequency domain measurements 240–1, 257, 264–6, 270–2 I/Q system 266–7 intensity modulated sensors 264–6 intralipid experiments 277, 278–82 phased-array systems 267–70 principles 240–1, 257

Index

time domain measurements 240, 257 time-resolved reflectance spectroscopy 262–4, 266 negative differential resistance (NDR) 119–21 NEP see noise equivalent power NF see noise figure NIR see near infrared noise equivalent power (NEP) 102, 245 noise figure (NF) analogue microwave fibre-optic links 136–7, 156–61 direct modulation 42 microwave photonic signal processing 205–7 RF photonics 67–8 nonlinearity analogue microwave fibre-optic links 142, 161–3 characterization of components 292, 314 microwave photonic signal processing 202–3 see also spurious-free dynamic range notch filters 212–13, 228 O/E see optical-to-electrical O/O see optical-optical OEOs see optoelectronic oscillators OFCGs see optical frequency comb generators OFDM see orthogonal frequency division multiplexing OMD see optical modulation depth OP see optical prefiltering OPO see optical parametric oscillators OPPLs see optical phase locked loops optical amplifiers 211 optical cavity effects 312–13 optical clouds 198–9 optical density 257–60, 277 optical down-conversion 112–18 optical fibres 5, 7, 24–5, 170–3 optical frequency comb generators (OFCGs) 28 optical gain 47–8 optical heterodyning 87–91 optical hydrophones fibre-optic acoustic pressure sensors 241–8 intensity sensing 248–56 performance/limitations 256 principles 239–40 optical link gain 49–51 optical modulation depth (OMD) 53 optical parametric oscillators (OPO) 117 optical phase locked loops (OPPLs) 28

339 optical prefiltering (OP) 196 optical rectification 113–14 optical single sideband generation (OSSB) 16 optical single sideband with carrier (OSSB þ C) 175–7, 179, 181–2, 184 optical time domain reflectometry (OTDR) 291, 308–9 optical-optical (O/O) components characterization 291–4, 296, 301–13, 316–29 principles 7, 24–6 optical-to-electrical (O/E) converters applications 26 characterization of components 294–6, 309, 313–29 device technology 20–4 microwave photonic signal processing 203–4 O/O components 25–6 photodetection 10–11, 21–4 properties 7–10 optoelectronic oscillators (OEOs) 28–9 optoelectronics 5–6 orthogonal frequency division multiplexing (OFDM) 25 OSSB see optical single sideband generation OSSB þ C see optical single sideband with carrier OTDR see optical time domain reflectometry p-Ge lasers 112 p-i-n junctions analogue microwave fibre-optic links 145 drift-diffusion model 93–7 photodetectors 22–3, 69, 73, 75–6 photonic oscillators 92, 93–7 p-n photodetectors 92 PANs see personal area networks parallel optical feed photodetectors 74–7 passive attenuation limit 156 PDW see photon density waves personal area networks (PANs) 169 phase induced intensity noise (PIIN) 207 phase matching 113–14 phase modulated sensors 243–7 phase shift keying 10 phased-array systems 267–70 photoconductive emitters 117 photodetectors analogue microwave fibre-optic links 150–2 backward wave cancellation 77–81 fibre radio technology 174–5 high-power distributed 67–83

340 photodetectors (Continued ) parallel optical feed 74–7 performance/limitations 67–9 photonic oscillators 88–101, 107 principles 10–11, 21–4 RF photonic devices 67–83 transmission line model design tool 70–1 travelling wave 69–70, 74, 77–81 types 69–70 velocity match distributed 69–76, 81 photodiodes architectures 10–11 characterization of components 328–9 device technology 21–4 see also photodetectors photomixing see optical heterodyning photomultiplier tubes (PMT) 267 photon density waves (PDW) 241, 264–7 photonic oscillators (PO) 86–110 drift-diffusion model 93–7 narrowband 106–9 optical heterodyning 87–91 performance/limitations 90–1, 92–3 photodetectors 88–101 THz signal generation 86–110 THz sources 86–8 transmission line model 97–101 travelling wave photodetectors 88, 91, 92–101, 103–9 wideband 102–6 picocells 31 PIIN see phase induced intensity noise PIN junctions see p-i-n junctions plasma wave devices 126 PM see polarization-maintaining PMD see polarization mode dispersion PMT see photomultiplier tubes PN see p-n PO see photonic oscillators Pockels effect 16, 19 polarization 201, 292, 310 polarization mode dispersion (PMD) 143 polarization-maintaining (PM) single-mode fibres 141 positive coefficients 201 PRF see pulse repetition frequency propagation loss 7 pulse broadening 292 pulse repetition frequency (PRF) 194

Index

pulsed lasers 117 pulsed-time scanning mammography 262–4 quantum cascade lasers (QCLs) 86–7, 119, 122 quantum confined Stark effect (QCSE) 20 quantum well lasers (QWL) 44, 49 quantum-confined Stark effect 148, 161 quasi-ballistic electron reflection (Q-BER) 128 radio astronomy 27 radio frequency (RF) analogue microwave fibre-optic links 133–4, 141, 147, 162–4 biomedical applications 253, 267–8, 273–4 characterization of components 304 direct modulation 49–51, 58–61 fibre radio technology 186–7 impedance matching networks 253 photonic devices 67–83 signal processing 191–2, 195, 203–5, 221–6, 232–3 transversal filters 221–4 see also microwave photonic signal processing radio networks see fibre radio technology radio over fibre (RoF) 27, 30–2, 194, 203 Raman scattering 142, 203 reconfigurability 200–1, 202, 222–3 rectangular waveguides 102–5 reflection type sensors 242–3 relative intensity noise (RIN) analogue microwave fibre-optic links 156–61 biomedical applications 255, 271 microwave photonic signal processing 205–7 resonant tunnelling diodes (RTDs) 120–1 RF see radio frequency RF over fibre (RoF) 31–2, 173–6, 180 RIN see relative intensity noise RoF see radio over fibre; RF over fibre RTDs see resonant tunnelling diodes S-parameters 291, 296–301 scanning electron micrography (SEM) 80, 107 scattering matrices 139 scattering transfer parameters 300 SCH see separate confinement heterostructure schlieren technique 243 Schottky diodes 127–8 SCM see subcarrier multiplexed SCML see subcarrier multiplexed label SDE see standard diffusion equation

Index

second generation LCAs 320–7 second-order distortions 41–2, 54, 56–7 self-phase modulation (SPM) 203 SEM see scanning electron micrography semiconductor lasers 5, 43–9 semiconductor optical amplifiers (SOAs) 25–6, 199, 206, 209, 227 separate confinement heterostructure (SCH) 44, 49 SFDR see spurious-free dynamic range signal bandwidth 51–3 signal distortion 41–2, 53–8 signal generation 27–9 signal processing see microwave photonic signal processing signal transport 26–7, 173–81 signal-to-noise ratio (SNR) 22 analogue microwave fibre-optic links 135–7, 154, 156–61 fibre radio technology 177 single-frequency tuneable emission 116–18 single-mode fibres 9–10, 23, 25, 29, 294 single sideband (SSB) modulation 302–4 sinusoidal oscillators 4–5 SIS see superconductor–insulator– superconductor six-tap transversal filters 230 SKA project 27 SLEDs see superlattice electron devices SLMs see spatial light modulators slot antenna-coupled THz transmitters 106–9 SNR see signal-to-noise ratio SOAs see semiconductor optical amplifiers solid-state lasers 147 solid-state oscillators 108–9 source coherence 201 spatial light modulators (SLMs) 216 SPM see self-phase modulation spurious-free dynamic range (SFDR) analogue microwave fibre-optic links 137–9, 154, 159, 161–4 characterization of components 292 direct modulation 42–3, 53–8, 60–1 high-power distributed photodetectors 67–83 microwave photonic signal processing 208–9 RF photonic devices 67–8 SSB see single sideband standard diffusion equation (SDE) 264 stimulated Brillouin scattering 142, 203, 232–3 stimulated Raman scattering 142, 203

341 subcarrier multiplexed label (SCML) 195–6 subcarrier multiplexed (SCM) signals 173–4, 181 superconductor–insulator–superconductor (SIS) mixers 86, 106–9 superconductors 123 superlattice electron devices (SLEDs) 120, 121–2 switched propagation paths 200 tapered fibre Bragg gratings (TFBGs) 225 telegraphs 3 terahertz (THz) signal generation biased photoconductive emitters 114–16 broadband antenna-coupled 105–6 broadband THz generation 112–16 difference frequency generation 116–18 electro-optic crystals 113–14, 117–18 electronic sources 118–28 far-infrared lasers 112 field effect transistors 125–6 free-electron lasers 112 heterojunction bipolar transistors 124–5 Josephson plasma sources 123 laser sources 111–18 molecular lasers 112 multiplication 126–8 narrowband photonic oscillators 106–9 optical down-conversion 112–18 optical heterodyning 87–91 optical rectification 113–14 p-Ge lasers 112 photoconductive emitters 117 photonic oscillators 86–110 plasma wave devices 126 quantum cascade lasers 119, 122 resonant tunnelling diodes 120–1 single-frequency tuneable emission 116–18 slot antenna-coupled 106–9 superlattice electron devices 120, 121–2 three-terminal devices 124–6 THz sources 86–8, 111–29 travelling wave photodetectors 92–101, 103–9 two-terminal devices 119–23 waveguide-coupled 102–5 wideband photonic oscillators 102–6 TFBGs see tapered fibre Bragg gratings third-order distortions 54–9 THz see terahertz Ti-sapphire lasers 113, 115–16

342 time domain measurements 240, 257 time-resolved reflectance spectroscopy (TRS) 262–4, 266 transferred electron devices see Gunn diodes transistor outline (TO) cans 273–6 transit time 124 transmission line model 70–1, 97–101, 250–1 transmission type sensors 243 transversal filters 210–11, 219, 221–7, 229–30 travelling wave photodetectors (TWPDs) drift-diffusion model 93–7 performance/limitations 92–3 photodiodes 23–4 photonic oscillators 88, 91, 92–101, 103–9 RF photonics 69–70, 74, 77–81 terahertz signal generation 92–101, 103–9 transmission line model 97–101 TRS see time-resolved reflectance spectroscopy tuneability 200, 202, 222–3 TUNNETT diodes 119–20 two-port test sets 322–4 two-stage notch filters 212–13, 228 TWPD see travelling wave photodetectors ultrafast lasers 112–16 ultrasound see optical hydrophones uni-travelling-carrier (UTC) photodetectors fibre radio technology 174–5, 186 photodiodes 24, 72 photonic oscillators 92–3 uniform fibre Bragg gratings (UFBGs) 228 universal mobile telecommunications systems (UMTC) 194

Index

vector network analysers (VNAs) 297–8, 303–5, 307, 313, 316, 320–4 velocity match distributed photodetectors (VMDP) 69–76, 81 velocity matching 18 vertical cavity surface emitting lasers (VCSELs) 14–15 analogue microwave fibre-optic links 147 direct modulation 44–5, 50, 58–61 fibre radio technology 178 low-cost 58–61 waveguide photodetectors (WGPD) 69, 76, 93, 102–5 wavelength division multiplexed (WDM) systems characterization of components 299 fibre radio technology 171–2, 181–4 microwave photonic signal processing 223–4 principles 23, 25 wavelength modulated sensors 247–8 wavelength-interleaved multiplexer (WI-MUX) 181 wavelength-interleaved optical add-drop multiplexer (WI-OADM) 181–2, 184 wideband photonic oscillators 102–6 XGM wavelength conversion 227 XPM see cross-phase modulation ytterbium solid-state/fibre lasers 113 zinc telluride 113–14

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