Design and Fabrication of Acousto-optic Devices (Optical Science and Engineering)

DESlGn AND

C.

editor of Russian contributions rny of Aerospace instrumentation

Library of Congress Cataloging-in-Publication Data Design and fabrication of acousto-optic devices edited by Akis P. Goutzoulis, Dennis R. Pape; editor of Russian contributions, Sergei V. Kulakov. p.cm. - (Opticalengineering; v. 41) Includes bibliographical references and index. ISBN 0-8247-8930-X Acoustoopticaldevices--Congresses.2. I. Goutzoulis,Akis P. II. Pape,DennisR. m. Kulakov, V.(SergeiViktorovich) N.Series: Optical engineering (Marcel Dekker, Inc.); v. 41. TA1770.D47 1994 621.36’9--d~20 93-40794 CIP

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Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. MARCEL DEKKER, INC. 270 Madison Avenue, New York, New York

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Current printing (last digit): l 0 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

Series Introduction

The philosophy of the Optical Engineering series is to discuss topics in optical engineering at a level useful to those working in the field or attempting to design subsystemsthat arebased on optical techniques or that have significant optical subsystems. The concept is not to provide detailed monographs on narrow subject areas but to deal with the material at a level that makes it immediately useful to the practicing scientist and engineer. We expect that workersin optical research will also find them extremely valuable. As editor of the series, I am pleased to bring you this book, which is the latest in a number of volumes that relate to acousto-optics: for example Acousto-Optic Signal Processing, edited by Berg and Lee (vol. ElectroOptic and Acousto-Optic Scanning and Deflection, by Gottlieb et al. (vol. Acousto-Optics, by Korpel (vol. and sections of Optical Scanning, by Marshall (vol. 31). Acousto-optics is perhaps a confusing term to the uninitiated, but, in fact, it refers to a well-known subfield of both optics and acoustics. It refers, of course, to theinteraction between light and sound;between light waves and sound waves; between photons and phonons. Perhaps more specifically, it refers to the control and modification of a light beam by means of an acoustic beam. It was LCon Brillouin who first suggested, in the very early that light could be scattered by a sound wave. But, ten years went by before iii

iv these types of effects were demonstrated by Debye and Sears and by Lucas and Biquard. Thus, certain fundamental effects in acousto-optics have been known for some time. However, the surge in applications of these effects has occurred much more recently, brought about in part by the development and application of lasers. Thus, we are now fortunate tohave devices that can use sound to modulate, deflect, refract, and diffract light. This volume in our series is devoted to the design, fabrication, and testing of such devices. I acknowledge and appreciate the work of the editors and authorswho have contributed to this volume. Brian J. Thompson University Rochester Rochester, New York

Preface

Acousto-optic (AO) devices have played a centralrole in the development and recent proliferation of activity in the fields of optical information processing, optical computing, optical communications, and optical sensing. The interaction of light and sound, the A 0 effect, was primarily a subject of academic interest until the invention of the laser in 1960. The need then arose for the modulation and deflection of laser beams. Lightmodulating and -deflecting devices based on theA 0 effect were developed and A 0 technology wasborn. In the late 1960s tunable filter devices which use the A 0 effect to filter polychromatic light were developed. Optical processing arose in the 1970swith the realization that information could be manipulated spatially using optics. Acousto-optic modulator and deflector devices found early application in optical signal processing systems as the means by which time-varying electrical information could be imparted onto light waves in real time. As the use of optics to process image and digital information developed throughout the 1970s and 1980s, A 0 technology matured into thedevice technology of choice for electrical to optical information conversion. More recently,A 0 tunable filter (AOTF) devices have begun to have a major impact on the development of optical sensing and optical communication systems. As thefield of acousto-optics has evolved from having primarily scientific interest to technological significance, the design and fabrication of A 0 devices has evolved into ahighly refined engineering specialty at anumber of industrial firms and technical facilities throughout theworld. The growing importance of these devices for commercial and military applications in the late 1970s and 1980s led to restrictions on publishing specific A 0 design and fabrication details. The large amount of work in this field in the former Soviet Union was, until recently, virtually unknown inthe West.

vi

PREFACE

The book offers, for the first time and in a single volume, a systematic and detailed look at A 0 device design, fabrication, and testing. It includes all the necessary technical information (including proven computer-aided design programs) for the design and manufacture A 0 deflectors, modulators, and AOTFs. It also includes major contributions from authors from the leading institutionof acousto-optic technologyin the former Soviet Union (St. Petersburg State Academy of Aerospace Instrumentation, formerly known as Leningrad Institute of Aviation Instrumentation). This book will be an invaluable aid to a wide audience of readers, including teachers in physicsand engineering at both the undergraduate and graduate levels, students wishing to learn about the practicalities of these devices (providing them with enough information to actually fabricate a device), practicing acousto-optic device designers and fabricators in manufacturing wishing to learn techniques by others, and optical engineers designing and fabricating optical systems wishing to learn how to enhance system performance through device design and fabrication. While other books have been published on acousto-optic theory by electrical engineers and optical signal processing and optical computing architectures and applications by optical engineers, this book fills the gap between theory and application by describing the details of device design and fabrication from the perspective of authors with years of practical experience both in working in A 0 device fabrication facilities and in building practical A 0 devicebased systems. This book consists of seven chapters, written by different authors, and describes the principles of AO, the design of deflectors, modulators, and AOTFs, the design the transducer structure, the fabrication of A 0 devices, and the device testing. The first chapter, “Principles of Acousto-Optics” (by Akis P. Goutzoulis and Victor V. Kludzin), reviews the theory and principles A 0 in order to prepare the readerfor the various device design issues discussed in the following chapters. There are threetypes of A 0 devices (deflectors, modulators, and AOTFs), which can use different types of light and sound interaction. The type A 0 interaction depends on the geometry of the A 0 interaction and theoptical and acoustic properties of the A 0 material. All A 0 interactions are based on the photoelastic effect, and they can be either isotropic or anisotropic depending on the optical properties of the A 0 crystal. The theory, characteristics, and types of the various A 0 interactions are discussed inSection 2. The device performance also depends on the inherent properties of the A 0 material used. In many cases the device requirements call for high diffraction efficiency and large number of resolution spots or time-bandwidth product (TBWP). Such issues are discussed in Section along with techniques for evaluating the potential

PREFACE

vii

TBWP of a given material. In the same section the authors present data for several common A 0 materials measured by scientists of the St. Petersburg State Academy of Aerospace Instrumentation. The diffraction efficiency and the bandwidth of any A 0 device can improve if a phased array rather than a single-element transducer is used. These transducers steer the acoustic wave such that the A 0 Bragg matching condition is satisfied over a wide frequency range. The characteristics, types, and basic design procedure of these transducers are discussed in Section An important requirement in high-performance deflectors and A O F s is large spuriousfree dynamic range. This is often limited either by nonlinear acoustics or by multiple A 0 diffractions when multiple tones are present in the A 0 crystal. The degree of acoustic nonlinearities is determined by both the applied power density and the nonlinearcharacteristics the A 0 crystal. Section 5 contains a simplified analysis of nonlinear acoustics, along with experimental data that will help the reader comprehend the overall problem and its implications. The same section also contains a discussion and a comparison of the mechanisms and thecharacteristics of the spurious thirdorder intermodulation products. Section 6 describes the characteristics of acoustic collimation, which cansignificantlyreduce the acoustic spread due to thefinite transducer aperture,resulting in longer aperture, moreefficient A 0 devices, and multichannel deflectors with greatly reduced acoustic crosstalk. The chapter closes with Section 7, whichdiscusses a simple geometrical technique that can be used to transform pure longitudinal waves into pure shearwaves. The second chapter, “Design of Acousto-Optic Deflectors” (by Dennis R. Pape, Oleg B. Gusev, Sergei V. Kulakov, and Victor V. Molotok), describes the detailed design of A 0 deflectors. Section 2 discusses the characteristics of A 0 deflectors, which include bandwidth, diffraction efficiency, and time aperture, and links these characteristics to thekey system operational parameters in scanning and information-processing applications. Section 3 describes the dependence of deflector efficiency on the chief device design parameters of material and acoustic mode selection and transducer geometry length and height specification. Section discusses various materials issues and their desired characteristics (such as strong A 0 interaction, low acoustic attenuation, low acoustic velocity, and small acoustic curvature), andit develops an A 0 figure of merit that relates the material parameters to theproduct of time aperture andthe squareof the device operating frequency. Based on this analysis a nomograph is produced that aids in materialselection. Section 5 contains a discussion of transducer geometry design guidelines. Four major classes of A 0 interaction geometries are discussed: isotropic, anisotropic, phased array, and anisotropic phased array. For each interaction the optimum transducer

viii

PREFACE

length is determined. In the same section a detailed procedure for optimizing the transducer height is presented along with a discussion on nonrectangular transducerconfigurations. Sections 6 and 7 are concerned with the total A 0 efficiency of the deflector, which depends, among other things, on the degree to which the acoustic energy launched at the transducer remains in the optical illumination aperture. Losses in acoustic energy from acoustic diffraction and attenuation are discussed in those two sections respectively. summary of the overall deflectordesign methodology is presented in Section 8, and is followed by five deflector design examples, which are described in Section 9. These examples include (1) 500-MHz isotropic Gap, (2) 1-GHz anisotropic LiNbO,, 32-MHz opticallyactive anisotropic Te02, 500-MHz phased array longitudinal LiNbO,, and 60-MHz phased array anisotropic slow shear TeOz deflector. For each of the preceding examples the authors provide proven computer programs that are based on the design methodology described earlier and that calculate optimal transducer parameters and the expected diffraction efficiency. In Appendix A, Oleg B. Gusev provides a computer program which combines the overall design methodology with electrical impedance design, that the electrical impedance-matching network can be modified interactively with the bandshape to achieve a desired frequency-dependent A 0 diffraction efficiency response. The third chapter, “Design of Acousto-Optic Modulators’’ by Richard V. Johnson), elucidates design principles for A 0 modulators. The first section reviews the major markets A for0 modulators in order to determine the performance measures that are most critical for practical applications. In Section 2 the author describes the fundamental principles and characteristics of modulators, which include the typical modulator head, drive electronics, optical diffraction characteristics, intensity modulation and transfer function, temporal response, and limits to which the incidentlight beam can be focused. Section contains derivations for calculating the RF power requirements of the modulator and a discussion on modulator materials and figures of merit. The requirementsof the incident light source for best modulator operation arereviewed in Section In thesame section the static contrast ratio is calculated for a lowest order T E M , Gaussian profile laser beam. A simple model the modulator’s temporal response isgivenin Section where a single-parameter measure of modulator performance is defined with respect to risetime,and a numerical algorithm is presented for calculating the modulator response to an arbitrary video signal. The effects of transducer length on the modulator performance, including diffraction efficiency, optical beam profile distortion, and degradation in temporal response, are described in Section 6. A typical mod-

PREFACE

ix

ulator design strategy is then. described in Section 7. Such a strategy, involving arbitration between conflicting performance requirements, embodies conventional modulator design wisdom as well as techniques for obtaining even more performance from a modulator. The closing section contains a review of four different approaches for maximizing the performance of a laser scanning system using an A 0 modulator. The fourth chapter, “Acousto-Optic Tunable Filters” (by Milton Gottlieb), provides a comprehensive review of the theory, operation, design, and fabrication of AOTFs along with the description of several AOTF applications. Section 2 discusses the theory and operation of AOTFs. This includes collinear AOTFs and the required crystal symmetries, noncollinear AOTFs and theircharacteristics such as phase-matching conditions, passband, calculation of their angular aperture, and etendue. The same section contains a discussion on the features and advantages of AOTFs such as their agility and internal modulation. Section 3 discusses the materials and A 0 interactions that are appropriate for AOTFs. A general design procedure for both collinear and noncollinear AOTFs is also described along with configurations for separating the diffracted and-undiffracted optical beams and techniques for suppressing the sidelobes and improving and imaging through the AOTF. In Section the author presents a review of the AOTF fabrication procedure, and he emphasizes several fabrication issues that are unique for AOTFs. Section 5 deals with a multitude of AOTF-based systems and applications. These systems include laser cavity tuning, spectrometry, spectropolarimetry, astronomical spectrophotometry, fluorescence spectroscopy, spectral imaging, semiconductor laser tuning for communications, fiberoptic wavelength multiplexing, and coherence detection. For each application the author describes the specifications and characteristics of the AOTF used and provides actual experimental data. The final section contains a brief description of waveguide AOTFs. The fifth chapter,“Transducer Design” (by Akis P. Goutzoulisand William R. Beaudet),addresses the design and theinterfacing of the transducer structure that launches the acoustic wave into the A 0 device. A typical transducer structureconsists of a metal top electrode, a piezoelectric crystal, and one (or more) metal bonding layer that attaches the piezoelectric crystal to the A 0 substrate and is used as the bottom electrode. The performance of the A 0 device-as measured by its bandwidth, impedance, conversion efficiency, and VSWR-depends largely on the characteristics of the transducer structure used. These characteristics are determined by, among other things, the number, composition, dimensions, and natural properties (e.g., mechanical impedance) of the various layers and

PREFACE of the A 0 substrate. Section 2 contains a comprehensive analysis of the transducer structure.The analysis of the various bonding layers is presented via equivalent circuits through the use of a transmission line equivalent matrix analysis to predict the device electrical impedance and transducer conversion efficiency. The effects of the various layers in simple transducer configurations are also described along with techniques that allow broadband operation with minimum conversion loss. The same section also contains a discussion of the various materials issues, where the emphasis is on bonding materials because they dramatically affect the amount of acoustic energy transferredfrom the transducer into the A 0 substrate. InAppendix B, Akis P. Goutzoulis presents a proven computer program based on the analysis presented in Section 2. They use this program in conjunction with three design examples covering the 20-40 MHz, MHz, and1.352.7 GHz frequency ranges, in order to show the use of the design methodology as well as of the program itself, for thestudy and analysis ofsimple and complex transducer structures. Actual experimental results are also presented in order toshow the agreement between theory andexperiment. The final section completes the transducer design by describing the electrical matching and power delivery networks. Impedance-matching techniques appropriate for simple transducers structures, phased array transducers, and multichannel devices are presented alongwith actual data obtained from prototype devices. The sixth chapter, “Acousto-Optic Device Manufacturing” (by Vjacheslav G. Nefedov and Dennis R. Pape), discusses techniques and procedures for fabricating A 0 devices. Section 2 discusses the manufacturing of the A 0 device optical window block. A brief description of typical crystal growth techniques is presented followed by procedures for crystal orientation, sawing of the optical window block, surface polishing, and optical antireflection coating. Section 3 discusses in detail the manufacturing of the piezoelectric transducer and several issues associated with internal stresses. The section begins with a description of thin-film transducer fabrication, including ZnO deposition technology, sputtering configurations, ZnO film characteristics, film quality, and several issues related to thedeposition parameters. This is followed by a discussion of the ZnO transducer performance and characteristics. The second part of Section 3 deals with the platelet transducer fabrication. This includes transducer bonding techniques (such as adhesive bonding, thermocompression bonding, cold vacuum compression bonding and optical contact bonding) ,platelet transducer reduction (such as mechanical reduction and ion milling), and top electrode definition. This chapter closes with a discussion of the final device assembly. This consists the impedance-matching network, wiring bonding, acoustic absorber, and device housing.

PREFACE

xi

The last chapter, “Testing of Acousto-Optic Devices” (by Akis P. Goutzoulis, Milton Gottlieb, and Dennis R. Pape), addresses the testing of the various types of A 0 devices. Device testing is the step thatfollows the device fabrication, and its main purpose is to determine the degree to which the design goals have been achieved. The detailed testing of experimental A 0 devices, which is based on new designs or fabrication techniques, is often of crucial importance because it may reveal performance issues and/or effects not previously estimated or even known. Similarly, testing is important for characterizing new A 0 materials and estimating their performance when used in conjunction with specific device designs and applications. Since all A 0 devices involve electric, acoustic, and optical parameters, the tests must cover allthree domains to the degree necessary dictated by the device type and the application. Tests common to all types of A 0 devices involve (1) the acoustic pulse echo, which shows the transducer bond quality, (2) the Schlieren imaging, which showsthe quality and characteristics of the propagating acoustic field, (3) the electric impedance, reflection loss, and VSWR, the optical scattering, which determines the quality of the A 0 crystal used, and (5) the acoustic attenuation of the A 0 crystal. Section 2 covers the tests appropriate for deflectors, which include frequency response, diffraction efficiency, third-order intermodulation products, single- and two-tone dynamic range, and the TBWP. Section discusses the additional tests necessary for multichannel deflectors, which include channel-to-channel performance uniformity, channelto-channel isolation, and the channel-to-channel phase and time uniformity of the input signal. Section 4 describes the modulator tests, which include risetime, modulation bandwidth, modulation transfer function, and the modulation contrast ratio. In Section 5 the authorsdiscuss the AOTFtests, which include the determination of the tuning relation, optical bandwidth, spectral resolution, the out-of-band transmission, the RF power dependence of transmission, polarization rejection ratio, spectral dependence of the spatial separation of the various orders, angular aperture or field of view, and the spatial resolution of spectral images. This book is an outgrowth of an international conference on A 0 held in the former Soviet Union in Leningrad (now St. Petersburg) in the summer of 1990. Western scientists learned for the first time many details about the development of A 0 technology in the former Soviet Union at this meeting. Drs. Goutzoulis and Pape met the conference organizer Professor Kulakov and his colleagues from the Leningrad Institute of Aviation Instrumentation (now the St. Petersburg State Academy of Aerospace Instrumentation). From this initial meeting the idea for a book that would describe the practical details of A 0 device design and fabrication was suggested by Professor Kulakov. The editors andcontributors are indebted

xii

PREFACE

to the manyscientistsandengineersin the United States,Russia,and throughout the world who have contributed to the development and our understanding technology.

Akis P. Goutzoulis Dennis R. Pape Sergei V . Kulakov

Contents

Series Introduction

iii

Preface

V

Contributors Principles of Acousto-Optics Akis P. Goutzoulis and Victor V . Kludzin Design of Acousto-Optic Deflectors Dennis R. Pape, Oleg B. Gusev, Sergei V . Kulakov, and Victor V . Molotok

xv 1

69

Design of Acousto-Optic Modulators Richard V . Johnson

123

Acousto-Optic Tunable Filters Milton S. Gottlieb

197

Transducer Design Akis P. Goutzoulis and William R . Beaudet

285

Acousto-Optic Device Manufacturing Vjacheslav G. Nefedov and Dennis R. Pape

339

Testing of Acousto-Optic Devices Akis P. Goutzoulis, Milton S. Gottlieb, and Dennis R. Pape

403

xiii

xiv

CONTENTS

Appendix A: Computer-Aided Design Program for Acowto-Optic Deflectors Oleg B. Gwev Appendix B: A Computer Program for the Analysis and Design of Transducer Structures Akis P. Goutzoulis

479

Index

485

Contributors

William Milton

Beaudet Harris Corporation, Melbourne, Florida Gottlieb Westinghouse Scienceand Technology Center, Pitts-

burgh, Pennsylvania Akis P. Goutzoulis Westinghouse Science and Technology Center, Pit&

burgh, Pennsylvania Oleg B.Gusev St. Petersburg State Academy tation, St. Petersburg, Russia Richard V. Johnson

Aerospace Znstrumen-

Crystal Technology, Inc., Palo Alto, California

St.PetersburgState mentation, St. Petersburg, Russia

Academy

Aerospace Znstru-

Sergei V. Kulakov

St. PetersburgState Academy mentation, St. Petersburg, Russia

Aerospace Znstru-

Victor V. Molotok St. Petersburg State Academy

Aerospace Znstru-

VictorV.Kludzin

mentation, St. Petersburg, Russia Vjacheslav G. Nefedov St. Petersburg State Academy strumentation, St. Petersburg, Russia Dennis

Aerospace Zn-

Pape Photonic System Zncorporated, Melbourne, Florida

xv

This Page Intentionally Left Blank

Principles of Acousto-Optics Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

St. Petersburg State Academy of Aerospace Instrumentation St. Petersburg, Russia

INTRODUCTION The objective of this chapter is to review the theory of acousto-optics (AO) in order to prepare the reader for the various device design issues discussed in the following chapters. In general, there are three types of A 0 devices (deflectors, modulators, and tunable filters or AOTFs), each of which can use different types of light and sound interactions. The type of the A 0 interaction is determined by the light-sound geometry and the optical and acoustic properties of the A 0 material. All A 0 .interactions are based on the photoelastic effect, and they can be either isotropic or anisotropic, depending on the optical properties of the A 0 crystal. Isotropic A 0 interactions do not change the polarization of the optical beam, and they can result in either multiple or single diffracted optical beams (or orders). The multiple-order isotropic diffraction is called Raman-Nath, and because of its low diffraction efficiency it is not frequently used inpractical devices. The single-order isotropic diffraction is called Bragg; it is much more efficient and thereforeit is widely used inpractical devices. Anisotropic A 0 interactions change the polarization of the optical beam, and they result in a single diffracted order. They offer higher efficiencies and larger acoustic and optical bandwidths than the isotropic A 0 interactions. Most highperformance deflectors and AOTFs are actually based on anisotropic interactions. The theory, characteristics, and types of A 0 interactions are

l

2

KLUDZIN

AND

GOUTZOULIS

reviewed in Section 2. For each interaction we discuss the mathematical formulation and we derive expressions for the diffraction efficiency and the AO. Such expressions are used routinely in the device design. Aside fromthe actual A 0 interaction employed, the device performance also depends on the inherent properties of the A 0 material used. In general, different properties are required by different devices, however, in almost all cases the requirements call for high diffraction efficiency which translates to a specific figure of merit. For deflectors and for some types of AOTFs an important material-related parameter is the number of resolution spots or time-bandwidth product (TBWP). This parameter is affected mostly by acoustic attenuation, although in certain cases the crystal length may also be the limiting factor. In Section 3 we briefly discuss the A 0 material properties, and we describe techniques for evaluating the potential TBWP of a given material. For several common A 0 materials we present data which have been measured by scientists of the St. Petersburg State Academy of Aerospace Instrumentation (St. Petersburg, Russia) over the last several years. The diffraction efficiency and the bandwidth of any A 0 device can be improved if a phased array rather than a single-element transducer is used. Such transducers steer the acoustic wave such that the A 0 interaction geometry is satisfied over a wide frequency range. For a given acoustic frequency the phased array transducer radiates a greater amountof acoustic power in the desired direction, thereby increasing the overall diffraction efficiency. The characteristics, types, and the basic design procedure of these transducers are discussed in Section 4. An important requirement in high-performance deflectors and AOTFs is large spurious-free dynamic range. This is often limited by either nonlinear acoustics or by multiple A 0 diffractions when multiple tones are present in the A 0 crystal. The degree of acoustic nonlinearities is determined by both the applied power density and the nonlinear characteristics of the A 0 crystal. In Section 5 we present a simplified analysis of the nonlinear acoustics, along with their effects and properties, andwe present experimental data which willhelp the readercomprehend the overall problem and its implications. In the same section we also discuss and compare the mechanisms and the characteristics of the spurious third-order intermodulation products. These types of spurious signals are of interest because they appear within the octave bandwidth of the A 0 device, and therefore they decrease the overall dynamic range. Two important acoustic properties which are very useful in various A 0 devices are the acoustic collimation and the acoustic mode conversion. Acoustic collimation can significantly reduce the acoustic spread due to the finite transducer aperture, and it results in longer aperture, more ef-

PRINCIPLES OF ACOUSTO-OPTICS

3

ficient A 0 devices as well as multichannel deflectors with greatly reduced acoustic crosstalk. The characteristics and the advantages of acoustic collimation are discussed in Section 6 along with examples of acoustically anisotropic A 0 materials which support it. Acoustic wave transformation refers to a simple geometrical technique which can be used to transform pure longitudinal waves into pure shearwaves. In Section 7 we discuss the basics of this acoustic property, and we describe a simple procedure for the design of an acoustic mode converter.

2 ACOUSTO-OPTICINTERACTIONS 2.1 Acousto-optic devices are based on the photoelastic or elasto-optic effect [l-61 according to which an acoustic signal applied on an A 0 crystal produces a strain which changes the optical properties of the crystal. The acoustic signal is injected into thecrystal by means of a piezoelectric transducer, and as it propagates it produces regions of compression and rarefraction. When an optical beam passes through the crystal it may be deflected or modulated, and is frequency shifted. The changes in the optical properties of the crystal are the result of the changes in the index of refraction of the crystal produced by the strain.The complete mathematical description of the photoelastic effect depends on thedirectional properties of the A 0 material and requiresa tensor relation between the elastic strain and the photoelastic coefficients, and is

where AB, is the change in the tensor components of the dielectric impermeability, A(l/nz)ijis the change in the (l/n2)ijcomponent of the optical index ellispoid, pijk1 is a fourth-rank photoelastic tensor, and S,, are the strain components. The strain-induced changes in the optical properties of the crystal result from changes in the material index of refraction and may lead to rotation of the light polarization. The optical changes are best studied via the index ellipsoid by dalculating the difference of the ellipsoid equations for the unperturbed and perturbed states. This results in expressions for the change, Anij, in the refractive index, nij, as a function of the photoelastic coefficients and the strain. The form of these expressions is Anij = O.k$pijk&l,

i,j,k,l = 1,2,3

(2)

The crystal symmetry of any particular material determines which of the Pijkr components are nonzero andwh.ich components are related to others.

GOUTZOULIS AND KLUDZIN The coefficientsPijkl are assumed symmetrical withrespect to indices ij and kl, and can be contracted to p,,,,, (m,n = 1, 2, . . . , 6). However, this is not the case for optically anisotropic materials [4] where a microscopic body rotation in the medium disturbs the symmetry of the p o k l tensor, and thus p j j k l is not necessarily equal to p j j l k . In this case Eq. (1) must be slightly modified to account for these effects. detailed treatment of the index ellipsoid procedure can be found in [6] and In practice the term “acousto-optic interaction” refers to the effect of the acoustic wave on an incident optical wave, because in most cases the presence of the optical wave does not change the acoustic properties of the medium. From this point of view, the interaction can be treated as a parametric process, in which the acoustic field changes the refractive index of the medium. Usingthe methods of classical optics, we candescribe the interaction as the diffraction of the optical wave by a periodical phase grating induced by an acoustic wave. The fundamental difference between an ordinary grating and thephase grating generated by the acoustic wave is that the latter is not stationary; it travels with the speed of sound in the medium and its parameters can vary with time. This traveling phase grating Doppler-shifts the optical frequency, and it can be used to deflect, modulate, or filter the optical beam. Devices basedon these properties of the traveling phase grating are called deflectors, modulators, and tunable filters respectively. Examples of such devices are shown in Figs. 1, 2, and respectively. Although the design of these devices varies significantly, the underlying phenomena are the same and is based on isotropic or anisotropic interactions.

2.2 IsotropicAcousto-opticInteractions The characteristics of the diffracted light beams resulting from an interaction can be determinedby solving the wave equation that describes the optical wavepropagation in the A 0 crystal. Raman and Nath [5] analyzed the case of isotropic interactions which occur when the crystal is isotropic. In this case the refractive indices for the incident and the diffracted optical beams are thesame. (Note thatin an anisotropic interaction the refractive indices for the incident and diffracted optical beams are different, and the polarizations of the two beams are orthogonal.) For an isotropic interaction when an acoustic wave propagates along the x axis and a planeoptical beam propagates in the x-z plane at anangle (inside the medium) from the z axis, the wave equation can be written as

1 Example of a TeO, acousto-optic deflector. (Courtesy Technology.)

Crystal

where is the refractive index in the region of the A 0 interaction, is the speed of light, and E is the electric field. When the acoustic wave is planar, sinusoidal traveling wave, n(.x,t) can be described by = n

+ An sin(Ck,t

- K,x)

(4)

where n is the average refractive index of the medium, An is the amplitude of the refractive index change due to the acoustic strain, and K , and Ck, are the wave number and frequency of the acoustic wave, respectively. The solutions of the wave equation cannot beexpressed in analytical form, however, because is periodic in both space and time, the perturbed optical field E can be expanded in a Fourier series:

2 Example a Tl,AsS, acousto-optic modulator.(Courtesy inghouse Electric Corporation.)

West-

where

. r = ki(z cos - x sin

+ mK$

(6)

where Emand are the amplitude and the wave vector of the mth diffracted light beam respectively, and wi and kiare the frequency and the wave number of the incident light respectively. Equations (5) and (6) represent an expansion in plane waves of the output light distribution, which shows that the frequency, of the zkrnth diffracted order will be equal to = oi

* ma,

which means that the optical frequency of the mth diffracted order will be up- or downshifted by an amount equal to the frequency of the mth harmonic of the acoustic signal. Substituting Eqs. into Eq.(3), we obtain a set coupled-wave equations which describe the interaction of optical and acoustic waves in

PRINCIPLES OF ACOUSTO-OPTICS

7

3 Example of a TAS acousto-optic tunable filter. (Courtesy of Westinghouse Electric Corporation.) the medium. These equations were derived by Raman and Nath [5] and can be written as

where U1 =

- ko AnL COS

eo

and ko = 2dA0 is the wave number of the incident optical beam in free space, with A,, being the optical wavelength in free space. The solutions of Eq. (8) describe the electric field of the optical waves in the various diffraction orders. In interpreting these equations we can applybasic coupledmode theory [S] and assume that different optical waves propagate in the crystal and energy exchange takes place between them. If sinusoidal acoustic waves are used, the optical waves can exchange energy only with adjacent waves. In this case the variable u1 can be viewed as the coupling constant between the adjacent waves. The amount of energy transferred

GOUTZOULIS AND KLUDZIN

8

depends on thecoupling constant andthe degree of synchronization of the waves. The factor m2Ka/2ki cos 0, on the right side of Eq. (8) indicates the degree of synchronization. The larger the value of this factor the.less the synchronization (or thelarger the phase difference between the waves) and therefore the less the amount of energy transferred. We can proceed with Eq. (8) by examining A 0 interaction geometries in which an appreciable amount of light can be transferred outof the zero order into the diffracted orders. This can be accomplished by using the Klein and Cook [2] parameter defined as Q

= ki cos 0,

-

21~hoL nA2 cos 0,

where L is the A 0 interaction length along the direction of propagation of light and A is the acoustic wavelength. The parameter Q is appropriate because it measures the differences in phase of the various partial waves due to thedifferent directions of propagation. Using the parameter Q we can write Eq. (8) as

From Eq. (11) we cansee thatan appreciable amount of light is transferred out of the zeroth orderif either orboth coefficients of the right-hand side are small for m = ? 1. This can be accomplished if (1) Q is small and 0, is about OD, or (2) if Q is large and the two terms on the right-hand side of Eq. (11) are equal. When Q 0.3 the A 0 diffraction is called Raman-Nath and results in multiple diffraction orders similar to those produced by a thin diffraction grating. Figure shows the basic geometry of the Raman-Nath interaction and the resulting multiple diffraction orders. In this case light is transferred from the zeroth orderto thefirst order, from the first order to thesecond order, etc. The mth diffracted order is separated from the undiffracted order by an angle Om which can be approximated by

Since Q 0.3, the first term on the right-hand side of Eq. (11)can be neglected, and byusing the boundary conditions E,(O) = E,, and Ern(0)= 0 we obtain the following solutions: E,,,(z) = Eoe-irnXJ,,,

2ui sin X

PRINCIPLES OF ACOUSTO-OPTICS

m=+N

L Qa

Raman-Nath acousto-optic diffraction geometry showing multiple diffracted orders. where X = (K,z tan and J,,, is the Bessel function of the mth order. By setting = L in Eq. and by calculating the productE,(L)E,,,(L)*, where the asterisk denotes thecomplex conjugate, we obtain anexpression for the normalized intensity, Q = Zm/Io, of the mth diffracted order at = L: sin(K,L tan (K,L tan Using the identity J-,,,(u) = (- l)mJ,,,(u)we find from Eq. (14) that the diffraction pattern is symmetricfor all angles of incidence. As Raman and Nath noted, an examination of the output light intensity shows that phase rather than amplitude modulation is possible, the depth of which is measured by the parameterul. This acousticallyinduced phase modulation can be transformed into amplitude modulation via well-known Schlieren imaging techniques. For Q > 7, the acoustic grating is nolonger thin, andthe A 0 interaction becomes sensitive to theangle of the incident optical beam. This diffraction regime is called Bragg and is most widely used in practical applications. Since energy transfer is most effective between optical waves withthe same phase term, thediffracted light willappear predominantly in a single order. Figure 5 shows the basic geometry for the Bragg diffraction and the resulting single diffraction order. The amount light in the.diffraction order

KLUDZIN

10

AND GOUTZOULIS

OPTICAL

"a

L

t "a

A

T I

z

5 Bragg acousto-optic diffraction geometry showinga single diffracted order.

is maximized when the two terms on the right-hand side of Eq. (11) are equal; i.e., when tan Oo = mQ/2KUL.For m = 1 this condition reduces tQ

K, = sin Bo = sin O B = 2ki 2nA where OB is known as the Bragg angle. In practice O B is small, around a few degrees; e.g., for A. = 0.63 km and for an A 0 crystal with sound velocity V = 2 k d s e c and n = 2.5, the Bragg angle inside the crystal for a frequency of l GHz is 3.6". For thesame example the Bragg angle outside the crystal (i.e., n = 1 in Eq. (15)) is 9.1". The Bragg condition given by Eq. (15) can also be derived by considering the Bragg interaction as a collision between photons and phonons [ 9 ] .From this point of view, a photon with energy and momentum hki interacts with a phonon of frequency flu and momentum hK,, where h is Planck's constant, The interaction produces a new photon at frequency and momentum hkd and a phonon at frequency 0, with momentum hK,. Application of the energy and momentum conservation laws yields the fol-

PRINCIPLES OF ACOUSTO-OPTICS

l1

lowing relationships:

where the + or - sign applies when the optical wave is moving against or with the acoustic wave respectively. Equation (16a) shows that the frequency of the diffracted optical beam will be Doppler-shifted, up or down, depending onthe relative direction of the optical and acoustic beams. Since oi>> r R ,(e.g., 1015 Hz versus lo9 Hz respectively), the magnitude of kd is approximately that of ki, i.e., (kd(= Iki(.This is shown graphically in Fig. 6, and since (kdl = (ki(the diffraction triangle is always isosceles. This means that the magnitude of the acoustic wave vector must satisfy lK,l = 21kil sin eB, which reduces to Eq. (15). From Fig. 6 we note that when the Bragg condition is satisfied, the angle between the incident optical beam and the diffracted beam is We also note that the wave vectors lie on one circle because for the isotropic interaction the refractive indices of the incident and the diffracted light beams are equal. For the ideal isotropic Bragg diffraction wecanassume that energy exchange takes place between the incident optical wave Eo and the diffracted optical wave E,. In this case when is close to eB, the set of equations given by Eq. (11) reduces to the following two equations: dE0 U -+-"E,=O 2L

6 Wave vector diagram for isotropic Bragg diffraction.

12

GOUTZOULIS AND KLUDZZN

and dEl dz

U1 -Eo 2L,

"

where =

=

jx2q El

is given by KoL sin 0, - KoL tan 2 cos e, 2

eo

Phariseau [lo] solved Eqs. (17) and (18) andobtained the following solutions:

The normalized intensity of the diffracted beam, I d , can be calculated by setting = L in Eqs.(20)and(21) and calculating the quantity 1 - Eo(L)Eo(L)*,to get

where Zi is the intensity of the incident optical beam. When the Bragg condition is satisfied, eo = BB and thus = 0; the diffracted beam intensity is maximized and Eq. (22) reduces to

It is of interest to compare the normalized diffraction efficiencies for the Raman-Nath (Eq. (14)) and the Bragg (Eq. (23)) regimes. For normal incidence Eq. (14) reduces to ZT = Pm(ul),and since for m = 1 the maximum value of Jl(ul) = 0.58, the maximum normalizeddiffracted beam intensity or maximum diffraction efficiency possible is 33.6%. On the other hand, the Bragg diffraction can result in 100% diffraction efficiency, since for = IT the normalized intensity Id,,, is equal to 1. The limited diffraction efficiency in conjunction with the appearance multiple diffracted orders restricts the usefulness of Raman-Nath devices.

PRINCIPLES OF ACOUSTO-OPTICS

13

The parameter u1can be expressed as a function of practical parameters via the following relationship of the strain S,, and the acoustic power P,

P,

SkJz, LH

=

where is the density of the A 0 crystal, is the acoustic velocity, and H is the height of the acoustic beam. Using the expression for the strain obtained by substituting Eq. into Eq. and substituting the result for An into Eq. (9), we obtain u1 = COS

eo

Substituting Eq. into Eq. we obtain the following expression for the normalized maximum diffracted intensity:

Equation is important because it relates the normalized diffracted beam intensity to the physical and geometrical characteristics of the A 0 device and the input acoustic power P,. In practice the term “diffraction efficiency,” rather than “normalized maximum diffraction intensity” is used, and Eq. is approximated by the expression:

We emphasize that Eq. is valid only for small values of u1 and that is expressed in percent per watt of the applied acoustic power P,. In Eqs. and the quantity

M2

=

n6p2 -

is called the figure of merit and determines the inherent efficiency of the material regardless of the interaction geometry. As Eq. shows, high-efficiency materials must havea high refractive index and a low acoustic velocity. The geometrical characteristics of the A 0 device are given by the ratio LIH. In practice, M2 is used almost exclusively for AOTFs, as well as for scanners and low-bandwidth, high-resolution deflectors. Another parameter of importance forpractical Bragg diffraction-based devices is the 3-dB A 0 bandwidth, Af, defined as the difference between

KLUDZIN

14

AND GOUTZOULIS

the highest and lowest frequencies at which the normalkfed diffracted intensity I d drops by 50%. To calculate Af we first rewrite Eq. (22) as

where sinc = sin(TA)/TA. When ( ~ ~ 1 2 is ) ' small compared to Eq. (29) is well approximated by [9]

Id

in

From Eq. (19)we see that the parameter used in Eq. (30), is proportional to K , and thus to the acoustic frequency. Therefore Eq. (30) shows that the intensity of the diffracted order follows a sinc2-type behavior as the frequency changes. If the acoustic power is constant with frequency, the 3-dB bandwidth will extend up to thefrequencies for which Id = 0.5. This occurs when the argument of the sinc' function is equal to 2 0 . 4 5 ~ .By using Eq. (19) and = 0.45~,.we can write this condition as KaL (sin BB 2 COS eo

-

sin

=

0.45~

By substituting K, = 2 d A , and sin OB = K,/2ki = Ad2nAC, where A, is the center wavelength, and sin eo = Ad2nA, where A # A,, and by using the relations A, = V!fcand A = V/f, we can write Eq. (31) as fJA0

2nV2 COS eo

(f, -

=

0.45

Since the sinc function is symmetric around the center frequency, we can use the definition Af12 = f , - f , solve for Af, and obtain the following expression for the 3-dB bandwidth: COS

Af = 1.8nCR AoLfc

(33)

Observe that Af is inversely proportional to the interaction length L. This is an important point anda consequence of the fact that for a fixed angle of the incident optical beam and a fixed acoustic direction, an isotropic Bragg device will onlyoperate at one particular length of the acoustic wave vector, i.e., at oneacoustic frequency (or alternatively, the diffracted light wave vector kd must be equal to that of the incident light beam ki). If the direction of the diffracted beam is to be changed, we must change both the direction and the magnitude of the acoustic vector. For operationover a range of acoustic frequencies it is necessary to have a spread of the acoustic wave vector directions from the transducer. This is accomplished

PRINCIPLES OF ACOUSTO-OPTICS

15

by using the acoustic diffraction resulting from a transducer of width L . Since the angular spread of the acoustic beam is N L , the larger the device bandwidth Af, the larger the required wave vector spread and, therefore, the smaller the transducer length L . This situation is shown graphically in Figure 7. Note, however, that the diffraction efficiency q (Eq. (27)) is proportional to L, and therefore there is a bandwidth-efficiency trade-off. Equation (33) shows that the bandwidth is proportional to nVL. This gives rise [l31 to a different figure of merit, MI, which is used when the efficiency-bandwidth performance an A 0 device is of interest. M, is appropriate for weak interactions (i.e., q > A, and therefore grating lobes will occur at angles 8' given by

*

sin 8' = sin 8,

* mA S

where m is an integer. Since the complete acoustic pattern is the product of the array and element patterns, the location of the grating lobes and the width of the element lobe are of primary importance in designing an efficient phased array transducer. In general, it is desirable to choose D small enough that the values of sinc[(nD sin 8)/A] are large for values of 8 that satisfy the Bragg angle conditions over the desired bandwidth. The array pattern is then steered as a function of frequency that the element pattern is enhanced by a factor of W . However, since for practical devices S >> A, the array patternwill exhibit multiple symmetric grating lobes. By properly choosing the width of the element lobe, we can weight down all but two of these lobes, that the final acoustic pattern will consist of two main lobes inclined in opposite directions with respect to the array plane. The angles of both acoustic lobes and e,,- for m = + 1 and m = - 1 respectively) vary as the inverse of the acoustic frequency; however, only one of these lobes is used for tracking the desired Bragg angle. The other acoustic lobe is generally undesirable because it consumes acoustic power, and it may result in a second parasitic Bragg diffraction, which in turn consumes a small part of the optical power [45], and it may increase the intermodulation products. Figure 18 shows the geometry of the acoustic lobes and the Bragg interaction, with the arrows showing the change in the direction of the lobes as the frequency increases. To minimize the parasitic Bragg diffraction and thereforeminimize the loss of light, a bevel is usually set at the acoustic face that at the center frequency, fo, the desired lobe propagates parallel to the crystal length. By setting the angle between the device and the input optical beam equal to the Bragg angle (atfo) we perfectly satisfy the Bragg condition for thedesired lobe, whereas we maximize the mismatch for the undesirable lobe, thereby minimizing the parasitic Bragg diffraction. To maximize the performance of the array, we require that 8, tracks the Bragg angle OB. Since in practice 8, is small, we can use the geometry

PRINCIPLES OF ACOUSTO-OPTICS Transducers

k-S-l

Geometry of the acoustic lobes and the Bragg interaction in a planar phased array transducer. The arrows show the change in the direction of the two main acoustic lobes as the frequency increases.

of Figure 17 to calculate 0, in terms 0, = tan 0, =

the phase shift 4 as

4 -

KaS where K, = 2 d A is the acoustic wave number. When 0 = IT,Eq. (70) becomes

e,

=

V -

2fS which shows that the steering angle is inversely proportional to the frequency. Unfortunately, the Bragg angle is a linear function of frequency and therefore steering errors will occur. Assuming that theincident optical beam makes an angle (inside the material) with respect to the plane of the transducer, we can define the steering error A0, as the difference between the total angle of incidence and the Bragg angle:

38

KLUDZIN

AND GOUTZOULIS

From Eq. (72) we find that for AOe = 0, the phase shift per element must satisfy

which shows that the phase shift required for perfect beam steering is a quadratic function of frequency and therefore thephased array will track the Bragg angle only over some frequencyrange. To minimize the steering error we can reason as follows [45]. Assuming that 8, = A/2A0, the total angle between the incident light and the composite acoustic pattern at the center frequency fo is W2A0 + A,,/2S. As the frequency changes, the total angle changes, and in order to make the Bragg angle increment equal to the angular increment of the acoustic wave front we should have

d d A [2A l+L]=O

(74)

Eq. (74) is satisfied at A = A,, when S = which shows that ideal matching exists only atf = fo. For any other frequency f,the steering angle is smaller by - fo)/f0]’. Given that the error is alwaysin one direction, it can be partially corrected by changing Oi such that there are two frequencies, fL and fH, on opposite sides of fo, for which perfect matching occurs. This is demonstrated in Figure 19, which shows the Bragg angle and the phased array steering angle as a function frequency. The maximum error occurs at frequency fi,which is equal to 0.5(fL + fH). If fL and fH are selected that the mismatch is symmetric around the center frequency, the midband mismatch can be compensated by the peak of the element pattern, which is also symmetric around the midband. The result is that the overall bandwidth is flatter than that of a sigle-element device. Procedures for determining the design parameter S and the adjustable parameter Oi as a function of fL and fH have been developed by Xu [7]. Once a set of fL and fH has been selected, the design proceeds with the calculation of S, D , and the optimal number N . Pinnow [46] has shown that the elementwidth D is given by 2cnw1 D =where the adjustable parameterC isdefined such that theargument of the element pattern in Eq. (68) isCT.Cischosensuch that the aperture pattern, sinc2(C7r), whenevaluated atfL and fH is large. Once the optimal

39

PRINCIPLES OF ACOUSTO-OPTICS

f

L

fl

f

”

Frequency

19 Bragg angle andphasedarray steering angle as a function of frequency. At frequencies fL and fH the error is zero, whereas at frequency f, the error is maximum.

D has been selected, the element spacing S can be determined as

The madmum mismatch that occurs at f i can then be determined [47]:

The mismatch at and around the midband results in a reduced efficiency interaction and, therefore,in a dip. Equations (77) and (68) show that since the mismatch effects the array pattern only, the number of elements N must be adjusted so that the resulting ripple is kept within a desired level. For a ripple level of P dB within the passband the optimal number of elements N is [48]

GOUTZOULIS A N D KLUDZIN

40

where the parameter E can be found from the magnitude P , expressed in dB, of the ripple at the midband given by

P

=

10 log

[ ~

si:G7cJ

(79)

Once N is determined the diffraction efficiency performance of the phased array transducer can be calculated. This can be accomplished by first calculating the ratio of the phased array interaction length, N D , to the interaction length Ls of a single-element transducer:

L

ND Ls

=-

The performance advantage, A,, of the phased array transducer with each element driven by 1/N of the total power is then [46]

where in practice the factor T ( O , f ) / wis somewhat less than 1 over the bandwidth of interest. Several planar phased arrays have been reported in the literature with the most notable being an A 0 deflector with a dual phased array structure [49] on X-propagating LiNbO,. In that device, the first array consisted of 31 elements and covered the 1.31-1.93 GHz range, whereas the second array consisted of 52 elements and covered the 1.92-2.60 GHz range. The diffraction efficiency improvement was about 6~ over that of a single element device. In practice, most reported planar phased array A 0 devices with single arrays have achieved efficiency improvements in the 2 x -5 x range for fractional bandwidths up to 50%, the performance being determined by (1) the parasitic acoustic lobe loss of 3 dB, and (2) the restricted number of elements in order to avoid more than 3 dB in-band ripple. In the stepped phased array structure [45] of Fig. 20 each step is driven separately by a transducer attached to its surface. Adjacent transducers are driven 7c radians out of phase via alternating top and bottom connections. The step height is such that at the center frequencyf, the acoustic wave front produced by all the transducers is perpendicular to the x direction. Given that each element is offset by 180" from its neighbor, this can be achieved by setting the step height equal to h = Ro/2,and it results ?n steps with an overall slope of Ro/2S. As the frequency changes, the combined acoustic wave front tilts so that the slope of the resulting wave front is h/2S, and therefore acoustic beam steering is possible. From Fig.

PRINCIPLES OF A CO USTO-OPTICS TRANSDUCERS

i

Figure 20 Stepped phased array piezoelectric transducer geometry.

20 we find that the steering angle 8, is 8, = tan 8,

. r r h KS S

= --

and for h = Ao/2 it becomes 8,

=

[A I]

I2s f

fo

From Eq. (83) we see that the ideal phase shift is, once again, a quadratic function of frequency, and since in practice this is not possible, errors will occur. The errors can be minimized and the array design can be optimized by following a procedure similar to that of the planar array. The stepped array has an advantage over the planar array in that a single acoustic lobe is generated and therefore the acoustic and parasitic optical losses are eliminated. This advantage is similar to the advantage gained by the use of an optical blazed grating which concentrates the diffracted light in a single order. The disadvantage lies in the difficulty of its fabrication, especially at high frequencies (>1 GHz) where A/2 is a few micrometers for most common A 0 materials. Most of the stepped arrays reported to date have 2-10 elements [50]. One of the highest-frequency stepped array transducers ever reported [47] is the N = 3 element array fabricated on PbMoO,, which exhibited a 3-dB bandwidth of 250 MHz covering the 140-

42

KLUDZIN

AND GOUTZOULIS

390 MHz frequency range, with a diffraction efficiency of 8%/100 mW. Chen and Yao have demonstrated a novel quasi-planar phased array with a center frequency of 2 GHz and a bandwidth of 700 MHz. The device was novel because it was fabricated on a planar transducer surface; however, it almost completely eliminated the second parasitic acoustic lobe, i.e. , it almost acted as a stepped array. The quasi-steps were accomplished by using an etched periodic silver substrate and consisted of 20 elements whose incremental phase was The resulting acoustic pattern consisted of a single acoustic lobe which contained about80% of the acoustic power. In closing this section we note that planarphased array transducers can be combined with birefringent phase matching in order to improve the performance of A 0 deflectors [52,52a]. For example [52], a 1.9-3.5 GHz LiNbO, with N = 6 and element spacing twice the size that is used in isotropic designs was demonstrated, with a peak diffraction efficiency of 7%iW at 0.83 pm.

5 ACOUSTO-OPTICNONLlNEARlTlES Acousto-optic devices can produce nonlinear responses which are due to acoustic nonlinearities and/or multiple linear A 0 diffractions. The acoustic nonlinearities occur mainly as a result of crystal lattice anharmonicities and distort the acoustic signal(s). Thus, an initially sinusoidal signal becomes distorted as it propagates, and this distortion is the source of harmonic generation. In general, the nth harmonic grows nonlinearly as a function of distance, it reaches a maximum, and then it decays. The exact form of this behavior depends critically upon the initial level of the signal, the nonlinearity of the crystal, and the acoustic attenuation of the crystal. Because the harmonics appear at frequencies which are integer multiples of the frequency of the original sinusoidal signal, they can be avoided by using an octave bandwidth, and thus their only effect is the depletion of power from the fundamental. However, when two sinusoidal signals at different frequencies fl and fi are propagating in a crystal, not only the harmonics of each but also the sums and differences of these harmonics will be generated. Inpractice, only two of these intermodulationproducts have appreciable levels and lie within the octave bandwidth. These are known as theelastic two-tone third-order intermodulation products (IMPs) and appear at frequencies 2f1 - f2 and 2f2 - fi. Third-order IMPs can also be produced from multiple linear A 0 diffractions and are known as the dynamic third-order IMPs. Light diffracted by the first signal can be rediffracted by the second signal and then rediffracted by the first signal. Both elastic and dynamic IMPS represent unwanted, spurious signals which degrade the spurious-free dynamic range

PRINCIPLES OF ACOUSTO-OPTICS

43

(SFDR) of the A 0 device, and thus they must be carefully analyzed when designing high-performance devices. In this section we discuss the behavior and the effects of the nonlinear responses. We first present a simplified analysisof the acoustic nonlinearities (Section 5.1) in order to give the reader a general understanding of the behavior of the harmonics generated by a sinusoidal acoustic signal as it propagates in an A 0 crystal. This is followed by a discussion of the thirdorder IMPS (Section 5.2) and their effects on the SFDR of an A 0 device.

5.1 AcousticNonlinearities Acoustic nonlinearities are produced when finite-amplitude waves are distorted as they propagate in the A 0 crystal. The spatial dependence of these nonlinearities can be calculated by solving the equation of motion for the simple case of a sinusoidal acoustic wave. To determine the equation of motion we must first relate the stress, T, and strain, S, produced in the A 0 crystal due to the presence of the acoustic field. For small acoustic amplitudes this relationship is linear and is described by Hooke’s law, which in tensor notation can be written as T = where is the elastic stiffness tensor. The tensor relationship can be also be written as Tij = Cijk,&, i,j,k,l = where a repeated index implies a summation over the index and where c+/ are the elastic stiffness constants. A further simplification in this expression is possible by using the abbreviated subscript notation, according to which Hooke’s law can be written as Ti = ci,.Sj,where i, j = 1, 4, 5, 6. (A detailed treatment of Hooke’s law, the transformation properties and theabbreviated subscript notation can be found in [64] and [65].) For large acoustic amplitudes the stress and strain are no longer linearly related, and we must modify Hooke’s law to take into account the higher-order elastic stiffness constants. In this case cijksk

cijklsksl

l+-+-+--* Cij c,

1

where Ti are the components of the stress, Sj are the components of the strain, and C,, c,,, CijkI, . . . are the second, third, fourth, . . . etc., order elastic constants respectively. For a longitudinal sinusoidal wave only the third-order elastic constants, c i j k , are significant and Eq. (84) reduces to

44

where Ir is the acoustic velocity and TNLis the nonlinear part of the stress, which can be calculated from Eq. (85). As mentioned, the acoustic nonlinearities result from the fact that an originally harmonic wave, while it propagates through a nonlinear medium, undergoes waveform distortions. These distortions result in a waveform whose leading-edge slope is much greater than that of the trailing edge and which asymptotically reaches a sawtooth shape. This propagating sinusoidal acoustic signal can be viewed as a sum of harmonics whose parameters depend not only on the nonlinear characteristics of the crystal and the power density at the fundamental, but also on the power absorption coefficients of the harmonics. The exact form of the various harmonics can be analyzed via Eq. (86) by (1) expanding the displacement into spectral components at the fundamental and harmonic frequencies, and (2) separating the terms with equal phase and frequency. This will result in two coupled-wave equations, the solutions of which will fully describe the harmonics as a function of distance, power density, crystal nonlinearities, and acoustic attenuation. ~nfortunatelythe exact derivation of these equations is complicated and lengthy, and therefore it is beyond the scope of this owever, we can present a simplified, approximate analysis [S5] which will give a qualitative understand in^ of the overall harmonic generation process. Let us assume that in the AO crystal there exist an infinite number of harmonics which constantly exchange energy. This process is illustrated graphically in'Fig. 21, in which the arrows connecting the various acoustic modes show the possible paths and directions of the energy exchange. As Fig. 21 shows, the most significant energy exchange occurs from the fundamental acoustic mode S1 to the harmonics s, (m = 2, 3, . . .). reference to Fig. 21 let us consider a thin layer, d x , of the A 0 crystal and write the amplitudes of the harmonics at its boundaries as S , and S, dS,. The increment, dS,, of the fundamental mode is negative and proportional to the instantan~ousvalue of the amplitude S , which is determined by both the acoustic attenuation at the frequency of S , and the depletion due to the energy transferred to the higher harmonics. The increment, dS,, of the higher modes contains both negative and positive components which are due to the acoustic attenuation at the frequency of S, and the pumping of energy from the f~ndamental.This situation can be described by two coupled-wave equations: ~

+

dS1(x) -

dx

- -[a,

+ (3,(S,)]S,(X)

dS2(x) - - -a2Sa(x) dx

+ P,S?(x)

PRINCIPLES OF ACOUSTO-OPTICS

45

Diagramillustrating the generation of acousticharmonicsandthe power exchanges between the harmonics in an crystal.

where &(x), &(x), and al, are the linear strains and the attenuation coefficients of the fundamental and the second harmonic respectively,p,@,) is a factor that depends on the power level of &(x) and denotes the depletion of energy to higher harmonics, and p, is a factor that denotes the depletion of energy from S1 to S,. In Eq. we have used a square-law relationship between the positive incrementsof the second harmonic ( and the fundamental (&(x)). This square-law dependence is determined by the square-law characteristics of the acoustic nonlinearity in Eq. (85). The solutions of Eqs. and can be found by taking into account the boundary conditions Sl(0)= Sl0, S,,,(O) = 0 and the conservation of energy. The solution of Eq. has the form

which shows that the amplitude of the fundamental mode&(x) decreases as a function of distance and is determined by (1) the factor exp[ -alx] which determines the naturalpower dissipation as thewave propagates in the crystal and which is not connected with the nonlinear properties of the medium, and (2) the factor exp[-P,(S,)x] which determines the attenuation resulting from the energy transfer to the higher modes. The second factor is determined by the acoustic nonlinearity of the material and dependson theamplitude of the fundamental mode (note that pl(0) = 0). The nonlinear coefficient PI is inversely proportional to the disconti-

GOUTZOULIS AND KLUDZIN nuity length L,: P1

=

Y' Ld

where is an empirical dimensionless coefficient, and whereLd is defined as the distance at which (without attenuation al) the particle velocity becomes discontinuous, i.e., at Ld the shape of an initially harmonic wave becomes sawtoothed. Note that the numerical value of Ld can be a convenient way to express the deviation from linearity of the A 0 material. The exact value of Ld is [54]

where is a material-dependent nonlinear constant determined by the second- and third-order elastic constants. For example, for longitudinal waves along the [loo] direction in LiNbO,,

Figure 22 shows experimental data taken for the two types of energy loss mechanisms, usinga longitudinal [l111 KRSJ A 0 deflector operating at 200 MHz. The top curve is a straight line, characteristic of the process of acoustic attenuation without any nonlinearity, and it was obtained by using a very low acoustic power density (1 mW/cm2). The lower curve shows the total acoustic loss, including the nonlinear factor Pl(Sl), and was obtained by using a much higher acoustic power density (0.5 W/cm2). Note that thesecond curve changes its asymptote at thepoint x = Io, which occurs when S,(x) is attenuated to thepoint where exp[ -alx] is the dominant factor. Also note that the exact value of Io is determined by the properties of the A 0 material and the input acoustic power density. Knowing the spatial dependence of Sl(x), wecanproceedwith the solution of Eq. (88). This solution is well approximated by

where is the attenuation coefficient at the second harmonic frequency. The coefficient is

PRINCIPLES OF ACOUSTO-OPTICS

47

9

22 Example of the attentuation of the fundamental mode as a function of distance in a KRS-5 crystal for input power densities of 1 mW/cm2 and 0.5 W/cm2. Longitudinal waves were used for propagation along [l111 with an input frequency of 200 MHz. where

and is a measure of the importance of the nonlinearity relative to that of dissipation. We note that the solution given by Eq. (90) is similar to those obtained in [37, 53, and 571. Figure 23 shows an example [37]of the theoretical and experimental spatial dependence of &(x) (curve l), S&) (curve 2), and (curve 3) (it is discussed next), for a longitudinal [OOl] TeO, deflector operating at 500 MHz with an input power density of W/cm2. The data of Fig. 23 are interesting because they show the changes in the power of the harmonics for both the forward-propagating waves (0-13 mm, left half of the plot) and forthe backward-propagating waves after reflection at thecrystal end (15-28mm, right halfof the plot). Note that the secondharmonic is maximized at distance x = I, from the transducer. The exact value of is determined by equalizing the gradients of the amplitude increase and decrease of the second harmonic:

GOUTZOULIS AND KLUDZIN

48

23 Experimental data showing the spatial dependencies of the acoustic modes (Sl, and S,) for longitudinal waves along [OOl] in a TeO, deflector for f = 500 MHz and for an acoustic power density of P,(O)= 4 W/cm2. Curve 1 corresponds to Pl(x), curve 2 corresponds to P2(x), and curve 3 corresponds to P,(x). The part of the plot to the left of the dashed line inthe middle, corresponds to the forward-propagating waves, whereasthe right part corresponds to the backward propagation after reflection at the crystal end.

Equation constant then

shows that does not directly depend on the nonlinear If the medium has considerable attenuation, i.e., if >> pl,

In

=

2a,

whereas if a1=

then

1

=

G

The data of Fig. show that the second harmonic goes through a null and then it increases again. This behavior can be predicted by evaluating Eq. (89) for the forward-moving wave (over x' = 0 to x' = where is the crystal length) and for the reflected moving wave (over x' = to x' = while taking into account the change in the sign of the amplitude of S&) for the reflected wave (for a detailed treatment of this subject see From Fig. we canalso see that theslope of the fundamental (curve 1)is smaller after thereflection, and this occurs because energy isreturning to it from the higher harmonics. This shows that the assumption implied

PRINCIPLES OF ACOUSTO-OPTICS

49

in setting Eqs. (87) and (88) about the nonreciprocity of the nonlinear interaction is not always correct-in a nonlinear interaction the parameters of the high harmonics are determined by the low harmonics, and vice versa. Having described the behavior of the fundamental and the second harmonic, we can now discuss the third harmonic, S3(x). The third harmonic is mainly the result of the cross interaction between the fundamental and the second harmonic, and it can be described by

The solution of Eq. (99) has the form =

yp$S:o[Ae-a3X +

where the coefficient

- Ce-(az+al+BdX

reflects the relationship between

and

(100)

p3, and

An example of the spatial distribution of S3(x) is shown in Figs. 23 and 24. The latter shows the calculated (solid lines) and measured (dots) normalized power of (curve 2) and (curve 3) as a function of distance from the transducer for a 240-MHz longitudinal wave propagating along [loo] in a KRSS deflector and for an input power density of 1.7 W/cm2. Figure 24 shows that there is good agreement between theory and experiment and that thebehavior of S3(x) is similar to &(x); they both increase as a function of distance fromthe transducer untilattenuation losses dominate. The higher harmonics can be analyzed in a similar manner and via the following generalized equation:

We note that, as the previous procedure and Eq. (104) show, in order to find the solution for the mth harmonic we must know the solutions for all the m - 1 harmonics. In general, the form of the higher harmonics is similar to the form of the second and third harmonics, and their overall power is decreasing as the order m is increasing.

GOUTZOULIS A N D KLUDZIN 0

10

20

20

30

40

Figure 24 Theoretical and experimental data for the spatial dependencies of the acoustic harmonics for longitudinal waves propagating along a [loo] KRS-5 A 0 deflector. For this plot f = 240 MHz, P,(O) = 1.7 W/cm2, and it is assumed that p 10, k = 4, (xl = 0.25/cm, and cx(nf) = n2.26(x(f).

-

5.2 Third-Order lntermodulation Products The dynamic IMPS have been analyzed by Hecht [58],who extended the Klein and Cook [2] solution of the optical wave equation to include multiple acoustic waves at different frequencies. This has resulted in an infinite set of coupled-wave equations, which in the Bragg regime are reduced to two because of the significant phase mismatch between higher-order modes. For the case of two input acoustic signals with small amplitudes, Vl and V2, respectively, Hecht’s analytic solution of the intensity, 12,-1,of the diffracted order at 2f1 - f2 reduces to

PRINCIPLES OF ACOUSTO-OPTICS

51

where I , and I2 are the intensities of the principal diffracted modes and V j can be calculated via Eqs. (2) and (9) as

kon3pSiL 4 cos 00 For small-amplitude signals the diffraction efficiency of the principal diffracted modes is proportional to the normalized drive power (V/2)2, and thus for two equal-amplitude signals the intensity 12,- relative to the intensity of the principal diffracted modes reduces to

Equation (107) is important because it shows that the intensity of the dynamic third-order IMPs depends exclusively on the diffraction efficiency of the device, and therefore in the absence of any acoustic nonlinearities the diffraction efficiency is the limiting factor of the SFDR. The elastic IMPs are due to acoustic nonlinearities, and they can be analyzed using either (1) a procedure similar to the one described in Section 5.1 for acoustic harmonic generation, or (2) via the use of Feynman diagram techniques to analyze the various diffraction processes. A solution based on the former approach has been found by Elston and Kellman [59], whereas solutions based on the latter approach have been found by Chang [60] and by Xu [7]. Elston and Kellman solved the acoustic equation of motion (Eq. (86)) by performing the following tasks. They first expanded the strain into its spectral components up to third order, which resulted in 12 frequency components. The resulting strain expression was placed into Eq. (86) and separated into 12 coupled-wave differential equations by collecting terms at the same frequency and phase. The spatial derivatives in each of the 12 equations were then taken while the temporal derivatives were simplified by recognizing that the desired solution is the steady-state solution, which allows the time derivatives to be set equal to zero. The resulting equations were further simplified by expanding the strain at each frequency component into its real and imaginary parts, and subsequently expanding the equations into their real and imaginary parts while selecting the phases so that the IMPs grow from zero. The last step in the analysis is the inclusion of acoustic attenuation into all 12 differential equations. The form of the final 12 equations is similar, with the equation for the 2f2 - fl IMP term written as

52

KLUDZIN GOUTZOULZS AND

where S,,S1, S,, Sl-,are the amplitudes of the strains at frequencies 2f2 - fl, fl, f,, fl - f, respectively, is the acoustic attenuation at frequency 2f2 - fl, and yo is a constant that determines the rate of energy depletion and is given by yo = IcNL1/4pv3, where p is the material density and C,, is a material-dependent nonlinear coefficient. The solution of the final 12 coupled-wave partial differential equations can be performed by a simultaneous numerical solution. Elston and Kellman [59] and Pape [61] have performed such numerical solutions for the cases of [loo] LiNbO, and [OOl] TeOz respectively. Figure 25 is based on the results obtained by Pape and shows the intensity of the various harmonics and IMPs as a function of distance from the transducer. The behavior of the IMPs is similar to the behavior of the second and third harmonics described in the previous section-they increase as a function of distance from the transducer until attenuation losses dominate. Note that in contrast to the dynamic IMPs, the elastic IMPs strongly depend on the distance traveled by the acoustic wave; i.e., the level of the elastic IMPs is a function of the aperture of the A 0 device. Analytical expressions of the elastic IMP intensity were obtained by Chang [60] usingFeynman diagrams (for a detailed treatment of the IMPs via Feynman diagrams see [7]). Chang showed that the intensity of the elastic IMPs depends on the actual process that gives rise to the elastic IMPs. The two most significantprocesses involve (1)a single A 0 diffraction by the acoustically generated IMPs which are due to the second-order acoustic nonlinearity, and (2) successive A 0 diffractions by the second harmonic and the fundamental. The intensities of the resulting IMPs are given by Eqs. (109) and (110) respectively:

c!)

(Wa) n3pL

4,-1

= 1.8

4 - 1

=

n3pL

where P is given by Eq. (92), f is the frequency, T, is the time aperture of the A 0 device, p is the appropriate photoelastic coefficient, and L is the interaction length. We can now compare the relative strength of the dynamic and elastic IMPs via Eqs. (107) and (109)-(110). This comparison is facilitated by introducing [60] a critical interaction length L, defined as L, =

P'.

PRINCIPLES OF ACOUSTO-OPTICS

p p [/p ........................................

........................................................

111 m

m

...................................

...........

/

.................. :... ............. ..............................

....... ......................

...........

\

.....,. ......................

.:

.........................

........................

:

........................

(........................

......

\ 111111111111111111

54

KLUDZIN

AND GOUTZOULIS

By substituting Eq. (111) into Eqs. (109) and (110) we obtain the following relationships:

L,-I

-

(3)

A direct comparison of Eqs. (107) and (112)-(113) shows that (1) when L, is small the dynamic IMPS dominate, (2) when L,IL > 0.58 the IIelastic IMP process dominates, and (3) when LJL > 1.29 the I-elastic IMP process dominates. Figure 26 shows an example [62] of an A 0 deflector in which the elastic IMPS dominate the dynamic IMPs. The data were taken for a longitudinal [loo] Tl,AsS, A 0 deflector with a TBWP of 400. The example of Fig. 26 showsthat for an input power of 5 dBm the elastic IMPs degrade the dynamic IMP-limited SFDR by over 30 dB.

Or---

Input Power (dBm)

26 Example of an deflector in which the elastic IMPS dominate the deflector dynamic IMPs. The data were takenfor a longitudinal [loo] Tl,AsS, with a TBWP of (From

PRINCIPLES OF ACOUSTO-OPTICS

55

In order to minimize the degradation of the SFDR due to acoustic nonlinearities, the interaction length L must chosen to be greater than 1.7 X L,, or, equivalently, wemustminimize L,. Maximizing L isaccomplished by using birefringent diffraction or phased array transducers, whereas minimizing L, is accomplished by choosing materials with low acoustic nonlinear constants and by using small TBWPs. Examples [63] of materials with low L, are longitudinal [l101 GaP and longitudinal [loo] LiNbO,.

6 ACOUSTIC COLLIMATION IN ANISOTROPIC CRYSTALS When sound propagates in an acoustically anisotropic crystal, the propagation direction of the acoustic energy vector (Poynting vector), K,, does not necessarily coincide with the direction of the acoustic phase vector (wave vector) K,. The angle between K, and Kp is called the power flow angle and depends onthe shape of the acoustic wave vector surfaceK,(+,?). The acoustic wave vector surface is called the slowness surface (or the slowness curve in 2-D) and is determined by the inverse of the phase velocity as a function of the propagation direction (determined by the angles and 'U) [M]. The powerflow angle depends on the shape of K,(+,?) because K, isnormal to the tangent to the slowness surface, whereas K, is radial to the slowness surface. Examples of slowness curves are shown in Figs. 27 and 28 for TeO, in the [OOl], [loo] plane and for GaP in the [l,-1,0], [1,1,-21 plane respectively. For isotropic materials the slowness surface is a sphere, and thus the power flow angle is zero. For anisotropic materials, however, the slowness surface can take a variety of shapes, and it can be convex or concave. In general, as the curvature of the slowness surface increases, the spreading of the acoustic energy increases as well. It is therfore desirable to find certain orientations in certain crystals for which the slowness surface curvature is reduced; this will result in an acoustic beam with a significant degree of self-collimation. In these cases, the acoustic beam spread due to acoustic diffraction can be significantlyreduced. (A treatment the properties of the slowness surface and its implications can be found in [65].) For example,the slowness curve for longitudinal waves propagating along the [OOl] direction in TeO, (Fig. 27) curves outward, and this will result in some spreading of the acoustic beam. This is indeed the case, as it can be seen from the Schlieren images of a 10-channel longitudinal TeO, deflector [66] (Fig. 29), for which the acoustic beams propagate along the [OOl] direction, whereas the optical beam propagates along the [OlO] direction (i.e., k, is perpendicular in the plane of Fig. 27). These Schlieren images showthe profiles of some acoustic beams inthe plane perpendicular

+

GOUTZOULIS AND KLUDZIN

2 -

E

3 2

>

gL

-2

; -3 -5

-3

-1

3

Inverse Velocity (s/rn>

27 Slowness curves

TeO,

x10

5 "

propagation in the [OOl], [loo] plane.

to the interaction plane. On the other hand, the slowness curve for shear waves propagating along the [l,- 1,0] direction in GaP (Fig. 28) curves much less, and therefore a significant amount of acoustic focusing is possible. This is indeed thecase as can be seen from the Schlieren images of a 64-channel shear GaP deflector [66] (Fig. for which the acoustic beams propagate along the [l,- 1,0] direction, whereas the optical beam propagates along the [l111 direction (i.e., is perpendicular in the plane of Fig. 28). Figure shows that acoustic focusing has minimized the effects of acoustic diffraction, and therefore adjacent acoustic channels do not overlap, thereby eliminating acoustic crosstalk. we will see, beside the elimination of acoustic crosstalk in multichannel deflectors, acoustic focusing has significantimplications in the design of deflectors because it allows longer time apertures, T,, or higher diffraction efficiencies [67]. In order to estimate the degree of the acoustic collimation, a parameter of anisotropy, has beenused [68-711,which is defined the first coefficient in the power series representationof the slowness surface. For a given material, the anisotropy parameter b is a function the elastic coefficients and is tabulated for the pure mode axis and different crystal

PRINCIPLES OF ACOUSTO-OPTICS

57 1: 2:

[l , l

*

[ l , l ,-21

c

-

:

I

I

-2 Inverse Velocity

I

I

1

2 x10

I

I

"

28 Slowness curves for GaP for propagation in the [l,-1,0], [1,1,-21 plane.

symmetries in It can be shown that the magnitude of the slowness curve in the vicinity of a symmetry axis can be approximated by the power series

+

where is the angular deviation (in radians) of the energy vector Kp from the direction of the pure acoustic axis. In this case, the deviation of Kp causes a (1 - 26)+ deviation in the direction of the phase vector K,. The energy vector deviation affects the near-field distance, which is defined as the distance away from the transducer for which the acoustic beam is collimated (at thatdistance the 4-dB points of the acoustic profile intersect the geometric shadow of the transducer). For an acoustically isotropic medium, the near-field distance, Di, is

+

58

GOUTZOULIS AND KLUDZIN

29 Schlieren images of acoustic beams in a 10-channel longitudinal TeO, deflector: (a) adjacent channels, (b) alternatechannels. For this device the acoustic beam propagates along[OOl], whereas the optical beam propagates alongthe [OlO]. The slowness curve (Fig.27) does not allow acoustic focusing and therefore acoustic diffraction results in overlapping betweenthe acoustic beams of adjacent channels and significant crosstalk. (From

PRINCIPLES OF ACOUSTO-OPTICS 59

30 Schlieren images of a @-channel shear GaP deflector which utilizes acoustic focusing to reduce acoustic crosstalk between channels. In this device the acoustic beam propagates along [l,- 1,0], whereas the optical beam propagates along [lll].The slowness curve (Fig. along [l,- 1,OJallows a significant amount of acoustic focusing which minimizes acoustic diffraction and acoustic crosstalk. (From [67].)

where H is the transducer aperture and A is the acoustic wavelength. For an acoustically anisotropic medium it can be shown that the acoustic diffraction scales by a factor 1 - 26, and thus the near-field distance, D,, becomes

60

GOUTZOULIS AND KLUDZIN

Equation (116) implies that if the A 0 time aperture is limited by acoustic diffraction in the plane perpendicular to the A 0 interaction plane, a considerable improvement of (1 - 2b)" is possible by properly selecting the direction of sound propagation. For the GaP example of Figs. 28 and 30, 1 - 2b = 0.0264 and therefore an improvement of 380, is possible. Values of the parameterb have been computedfor various crystals, and they range from -5.23 (for longitudinal waves propagating along the c axis in Zn) [69] to -0.5 (for fast shear waves propagating along the [l101 in KRS-6)[37]. When b is negative, 1 - 26 is greater than 1, and this indicates that the near field is closer to the transducer than it is for the isotropic case ( b = 0). Examples of the values of b are shown in Table 2 for several collimating directions in crystals of high symmetries. In practice, the value of b can be estimated for any given direction via the SchaeferBergmann patterns [72], which allow the visualization of the slowness curves. The Schaefer-Bergmann pattern of the plane perpendicular to the A 0 intersection plane can be obtained by the far-field A 0 diffraction pattern. A clear pattern can be obtained by generating the largest possible number of acoustic reflections at different angles in the plane normal to theoptical wave vector. This can be achieved by using a device with a reflective rear face and in conjunction with a low acoustic frequency. Figure 31 shows a photograph of a typical Schaefer-Bergmannpattern of the [1001, [OlO] plane of a KRS-6 crystal. This crystal belongs to the cubic symmetry and has two interesting propagation directions: (1) the [1001 for a pure longitudinal mode and (2) the [l101 for a fast shear mode. For the longitudinal mode

Table

Self-CollimatedModes in Acousto-Optic Crystals

Acoustic wave direction and Optical Acoustic acoustic vector wave velocity ofCoefficient A 0 material propagation direction PbMoO, NaBi(MoO,), TeO, GaP KRS-6 KRS-5

L, 29" XY L, 26" X Y L [l101 L [l101 Fs [l101 L [io01 FS [l101 L [loo] FS l1101

M2

(X

105 cm/sec) 4.33 4.6 4.46 6.46 4. i 3 2.31 1.3 2.11 1.135 2.08

b

0.35 0.343 0.486 0.277 0.487 0.228 0.5 0.202 0.5 0.437

[X

sec'/g) 2.0 0.5 1.0 44.0 7.0 100.0

-

175.0 -

250.0

PRINCIPLES OF ACOUSTO-OPTICS

61

31 Schaefer-Bergmann diffraction pattern in the [OOl] plane of a KRS6 crystal. The [OlO] and [loo] directions are along the horizontal and the vertical coordinates respectively. (Courtesy St. Petersburg State Academy Aerospace Instrumentation.)

along [lOO], b can be written as [68, 691

the inner cruve of Fig. 31 shows, the slowness curve for longitudinal waves along [loo] is almost flat, and therefore some acoustic collimation is possible. For this case it is easily shown that D, = 1.84Di. Note that the fast shear modealong [l101 has an anisotropy coefficient b which can be adjusted by changing the direction of the optical wave vector in the plane [OOl]. Unfortunately, the exact calculations for the required angular change of the optical wave vector are very complexand lengthy, regardless of the high order of crystal symmetry involved [69]. The collimating property of the acoustic anisotropy implies reduced acoustic power requirements. Thisis because the transducer height H , and thus the height of the acoustic column, can be reduced by a factor of (1 - 2b)0.5.Since the diffraction efficiency is proportional to 1/H,the overall

-

62

KLUDZIN

AND GOUTZOULIS

power efficiency is effectively enhanced by a factor of (1 - 2b)-0.5 (in comparison with the isotropic case, all other parameters being the same). Remember, however, that for a fixed input power this will result in increased acoustic power density, which could increase the acoustic nonlinearities and thereby reduce the dynamic range of the device. Finally, the collimating properties can be used in acoustic beam folding, where the losses due to diffraction spread often limit the overall performance.

7 ACOUSTIC MODE CONVERSION The design of specialized devices may require theuse of acoustic mode converters, which convert longitudinal waves to shear waves, and vice versa. In practice, the most frequent conversion requirement is a highly pure conversion from a longitudinal wave to a shear wave. Frequencyindependent mode conversion can be easily accomplished by taking advantage of the acoustic reflections at a stress-free crystal surface [@, 73, 741. In general, in an elastically isotropic crystal, a longitudinal plane wave incident on a stress-free surface at an angle €lL to the surface normal can give rise to two reflected waves: (1) a longitudinal wave at an angle equal to that of the incident wave and (2) a shear wave at a different angle The amount of acoustic energy transferred to each of the reflected waves varies as a function of the angle of incidence. At a certain angle, the excitation of the longitudinal wavecanbecome zero, and the acoustic energy can be fully transferred to the shear wave. There are two main objectives in the design of an acoustic mode converter: (1) precise orientation of the shear acoustic wave vector along a specific direction, and (2) maximum energy transfer from the longitudinal wave to the shear wave. The first design goal can be discussed with reference to Fig. 32, which shows the geometry of a longitudinal-to-shear mode converter. For an elastically isotropic medium the boundary con-

32 Schematic

a frequency-independentacoustic mode converter

PRINCIPLES OF ACOUSTO-OPTICS dition at the surface means that the total normal component of the stress is zero. Thisimplies that atany point along the surface, the phase variation for all components of the longitudinal and shear waves must be the same. With this in mind and from the geometry of Fig. 32, we find that

K, sin 0L

=

K, sin 0,

(118)

Equation (118) is the familiar Snell's law and shows that in order to propagate a shear wave at an angle 0, the angle of the incident longitudinal wave must satisfy

Note that the angle 0, is frequency independent, and since for all solids V , < V,, the angle of the reflected shear wave is smaller than the angle of the incident longitudinal wave. The second design goal is satisfied when the reflection coefficient, rL, for the longitudinal wave is zero. In an elastically isotropic medium, rL is

[@l rL =

sin 20, sin 20, - (VL/Vs)2cos' 28, sin 20L sin 20, + (V,/V# cos2 20,

which implies that in order for rL = 0, the following equation must be satisfied:

(2) 2

sin 20, sin 20, =

cos2 20,

Equation (121) has solutions when the ratio of the shear and longitudinal wave velocities, V , and V , respectively, satisfies V,/V, > 0.565. Therefore for an elastically isotropic medium both design goals can be satisfied if the angles and 0, satisfy Eqs. (119) and (121). For example, forfused quartz the angles 0, and 0, are 42" and 25" respectively. In general, once the optimum 0L and 0, have been determined, the shear wave can be steered to thedesired direction by properly choosing the crystal cut angle 0,. Note that because of reciprocity, the mode converter also operates in the opposite direction and can convert a shear wave to a longitudinal wave. The analytical design of the mode converter for elastically an anisotropic medium is considerably more difficult. This is because the incident longitudinal wave can now give rise to onelongitudinal and two shear reflected waves [64]. The reflected waves are not always pure shear or pure longitudinal, and thus three possible polarizations can be coupled at the reflecting surface. All these must be taken into account when designing the converter, and this generally requires extensive numerical computations.

64

GO UTZO ULIS AND KL UDZIN

Acoustic mode converters have several uses, mainly in high-frequency A 0 devices. In these devices, it is generally preferable to use longitudinalwave transducers because in solids V , < V,. This implies larger half-wave transducer thickness and lower static capacitance. Furthermore, since the radiation resistance ratio, R,/R,, of the longitudinal and shear waves is determined by

where [VL/VSlfand [VL/VSlm are the velocity ratios for the piezoelectric transducer and the transforming medium respectively, a higher radiation resistance is possible. Therefore the acoustic mode conversion technique can also be used as anefficient method for wideband impedance matching between the piezoelectric transducer and the driving electronics. Mode converters may alsobe useful in increasing the tolerance of crystal orientation. For example, propagation of shear waves along the [l101 direction in TeO, without significantwalkoff requires that the crystal is oriented with extreme accuracy (e.g., This is because the high elastic anisotropy in TeO, (and similarly inthe crystals Hg2CI, and Hg2Br2) leads to a significant difference between the energy and phase velocities. Since a good x-ray from an etched surface can provide an orientation to an accuracy of -OS", the potential for a walkoff of several degrees exists if only x-ray orientation is used. When a mode converter is used, any possible misorientation of the reflecting face can be compensated by correcting the angle 0,. This may be achieved withlarger tolerances (than the direct crystal orientation) if the crystal exhibits less elastic anisotropy for longitudinal waves along the KL direction. Mode converters can also be used in collinear devices, where they may provide significant flexibility inthe overall design given the collinear propagation light and sound, and the need for optically transparent transducer structures.

ACKNOWLEDGMENTS The authors would like to thank V. Kulakov for the English translation of the work ofProfessor V. Kludzin which was written originally inRussian, and Dr. D. Pape of Photonic Systems Inc., for providing the Schlieren images of the TeO, and GaP multichannel deflectors. A. Goutzoulis would like to thank Dr. M. Gottlieb and Dr. K. Yao for helpful discussions.

P ~ I ~ C I OF P ~ACOUSTO-OPTICS ~ S

65

1. Rytov, S, M., Diffraction of light by ultrasonic waves, Trans. SUAcad. Sci. Ser. Phys., No. 2 , 222-259 (1937) (in Russian). 2. Klein, W. R., and Cook, €3. D., Unified approach to ultrasonic light diffraction, I E E E Trans., SU-14, 123-134 (1967). 3. €3alakshiy,V. J., Parygin, V. N., and Chirkov, L. E., The physical principles of acousto-optics, Radio i Sviaz, Moscow, USSR (1985) (in Russian). 4. Nelson, D. F. , and Lax, M., Theory of the photoelastic interaction, Pkys. Rev. B , 3, 2778-2794 (1971). 5. Raman, C. V. , and Nath, N. S. N. ,The diffraction of light by high frequency sound waves, Parts 1, 2,2A, 406-412, 413-420 (1935); Parts 3-5,3A7 7584, 119-126, 459-465 (1936). 6. Narasimhamurty,T. S. ,Photoelastic and Electru-optic Properties of Crystals, Plenum Press, New York, 1981. 7. Xu, J., and Stroud, R., Acousto-optic Devices: Principles, Design, and A p plications, Wi’tey, New York, 1992. 8. Kogelnik, H. ,Coupled wave theory for thick hologram gratings, Bell System Tech. J . , 48, 2909-2949 (1969). 9. Chang, I. C. , Acousto-optic devices and applications, IEEE Trans. Sonics Ultrasonics, SU-23, 2-22 (1976). 10. Phariseau, P., On the diffraction of light by progressive ultrasonic waves, Proc. Indian Acad. Sci., 44A, 165-170 (1956). 11. Smith, T. M. , and Korpel, A. , Measurement of light-sound interaction efficiency in solids, I E E E J . Quantum Electron., QE-1 , 283-284 (1965). 12. Gordon, E. I., A review of acousto-optical deflection and modulation devices, Proc. I E E E , 54, 1391-1401 (1966). 13. Gordon, E. I. , Figure of merit for acousto-optical deflection and modulation devices, IEEE J . Quantum Electron. , QE-2 , 104- 105 (1966). 14. Dixon, R. W., Photoelastic properties of selected materials and their rele-

15, 16. 17. 18. 19.

20.

vance for applications to acoustic light modulators and scanners, J . Appl. Phys., 38, 5149-5153 (1967). Harris, S. E., and Wallace, R. W., Acousto-optic tunable filter, J . Opt. SOC. Am. , 59, 744-747 (1969). Dixon, €3. W., Acoustic diffraction of light in anisotropic media, I E E E J . Quantum Electron. , QE-3, 85-93 (1967). Nieh, S. T. K. , and Harris, S. E. , Aperture-bandwidth characteristics of the acousto-optic filter, J . Opt. SOC.Am. , 62, 672-676 (1972). Chang, I. C., and Hecht, D. L., Characteristics of acousto-optic devices for signal processors, Opt. Eng. , 21 , 76-81 (1982). Hecht ,D. L. ,Variable bandshapes in birefringent acousto-optical diffraction in LiNbO,, in Annual Meeting of the Optical Society of America, Tuscon, Arizona, Oct. 1976. Abstract: J . Opt. SOC.Am., 66, 1094 (1976). Hecht, D. L., and Petrie, G. W., Angle tuned axial birefringent acoustooptic deflectorsin TeO,, in Annual Meeting of the Optical Society of America, 1980. Abstract: J . Opt. SOC.Am., 70, 1611 (1980).

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AND GOUTZOULIS

21. Chang, I. C., Designofwidebandacousto-opticBraggcells, Proc. SPIE, 352, 34 (1982). 22. Elston, G., Optically and acousticallyrotated slow shear Bragg cells in TeO,, Proc. SPIE, 936, 95-101 (1988). 23. Warner, A., White, D. L., and Bonner, W. A., Acousto-optic light deflectors using optical activity in paratellurite, J . Appl. Phys., 43, 4489-4495 (1972). 24. Hsu,H., andKavage, W., StimulatedBrillouinscatteringinanisotropic media and observation of phonons, Phys. Lett., 15, 207 (1965). 25. Bagshaw, J. M., and Willats,T. E., Aspects of the performance of broadband anisotropic Bragg cells, GEC J . Res., 3, 256-260 (1985). 26. Demidov, A. Ja., Zadorin, A. S., and Pugovkin,A. V., Wideband abnormal light diffractionby hypersound inthe crystal LiNbOS,in Acousto-optic Methods and Technology for Information Processing, LETI, Leningrad, USSR, 1980, pp. 106-111 (in Russian). 27. Uchida, N., andNiizeki,N.,Acousto-opticdeflectionmaterialsandtechniques, Proc. IEEE, 61, 1073-1092 (1973). 28. Chang, I. C., Selection of materials for acousto-optic devices, Opt. Eng., 24, 132-137 (1985). 29. Elston, G . , Amano, M.,and Lucero, J., Materialtradeoff for wideband Bragg cells, Proc. SPIE, 567, 150-158 (1985). 30. Goutzoulis, A. P., and Gottlieb, M., Characteristics and desienof mercurous halideBraggcellsforopticalsignalprocessing, Opt. Eng., 27,157-163 (1988). 31. Woodruff, T. O., and Ehrenreich, H., Absorption of sound in insulators, Phys. Rev., 123, 1553-1559 (1961). 32. Pomerantz, M., Ultrasonic attenuation by phonons in insulators, in Proceedings of the IEEE Ultrasonics Symposium, Oct. 4-7, 1972, pp. 479-485. IEEE Catalog Number: 72CH0708-8SU. 33. Bolef, D., in Physical Acoustics, (W. P. Mason, ed.), Vol. IV, Part Academic Press, New York, 1966, p. 113. 34. Spencer, E. G., Lenzo, P. V., and Ballman, A. A., Dielectric materials for electro-optic, elasto-optic, and ultrasonic device applications, Proc. IEEE, 55,2074-2108 (1967). 35. Chang, I. C., High performance wideband Bragg cells, in 1988 IEEE Ultrasonics Symposium, 1988, pp. 435-439. 36. Hecht, D. L., Spectrum analysis using acousto-optic devices,Opt. Eng., 461-466 (1977). 37. Gusev, 0. B., and Kludzin, V. V., Acousto-optic measurements, Leningrad State University, USSR, 1987 (in Russian). 38. Young, E., and Yao, S-K., Design considerationsfor acousto-optic devices, Proc. IEEE, 69,54-64 (1981). 39. Goutzoulis, A. P., Gottlieb, M., and Singh, N. B., High performance acoustooptic materials: Hg,CI, and PbBr,, presented at the SPIE Symposium on Optical Signal Processing, Vol. 1704, Paper 22, Orlando, FL, April 20-24, 1992.

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Wenkoff,M. P., and Katchky,M., An improved read-intechniquefor optical delay line correlators, Appl. Opt., 9, Gottlieb, M., Conroy, J. J., and Foster, T., Opto-acoustic processing of large time-bandwidth signals, Appl. Opt., 11, Korpel, A., Adler, R., and Desmares, P., An improved ultrasonic light deflection system, presented at the IEEE International Electron Devices Meeting, Paper Washington, DC, October Born, M., and Wolf, E., Principles of Optics, Pergamon Press, Oxford, pp. Radar Handbook, 2nd ed. (M. Skolnik, ed.), Phased array radar antennas, in Cheston, T., and Frank, J., McGraw-Hill, New York, pp. Korpel, A., Adler,R., Desmares, P., and Watson, W., A television display using acoustic deflection and modulation of coherent light, Appl. Opt., 5, Pinnow, D. A., Acousto-optic light deflection: design considerations for firstorder beam steering techniques, IEEE Trans. Sonics Ultrasonics,SU-18, Yao, S. K., and Young, E. H., Two hundred MHz bandwidth step-array acousto-optic beam deflector, Proc. SPIE, Pape, D., Vasilousky, P., and Krainak, M., A high performance apodized phased array Bragg cell, Proc. SPIE, 789, Delaney, M. J., and Yao, S. K., Widebandacousto-opticBraggcell, in Proceedings of the IEEE Ultrasonics Symposium, pp. Coquin, G. H., Griffin, J. P., and Anderson, L. K., Widebandacoustooptic deflectors using acoustic beamsteering, IEEE Trans, Sonics Ultrasonics, SU-17, Chen, T. S., and Yao, S. K., A novel phasedarray acousto-optic Bragg cell, J . Appl. Phys., Chang, 1. C., Birefringent phased array Bragg cells, in Proceedings of the IEEE Ultrasonics 1985 Symposium, pp. Shah, M. L., and Pape, D. R., Ageneralized theory of phased array Bragg interaction in a birefringent medium and its application to TeO, for intermodulation product reduction, Proc. SPIE, 1704, Richardson, B. A., Thompson, R. R., andWilkinson,C. D. W.,Finite amplitude acoustic waves in dielectric crystals, J . Acoust. Soc. Am., 44, Breazeale, M., and Ford, J., Ultrasonic studies of the nonlinear behavior of solids, J. Appl. Phys., Kludzin, V., St. Petersburg State Academy of Aerospace Instrumentation, to appear. Gedroits, A. A., and Krasilnikov, V. A., Finite amplitude elastic wavesin solids and deviations from Hook’s law, Sov. Phys. JETP, (in Russian).

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GOUTZOULIS AND KLUDZIN Torguet, R., and Bridoux, E., Etude theorique et experimentale de la generation harmonique acoustique dans le molybdate de plomb, Rev. Phys. Appl., Hecht, D. L., Multifrequency acousto-optical diffraction,IEEE Trans. Sonics Ultrasonics, SU-24, Elston, G., and Kellman,P., The effects of acoustic nonlinearities in acoustoUltrasonics Symposium, optic signal processing systems, inIEEE pp. Chang, I. C., Multifrequency acousto-opticinteraction in Bragg cells,Proc. SPIE, Pape, D. R., Acousto-optic Bragg cell intermodulation product, in IEEE Ultrasonic Symposium, pp. Goutzoulis, A. P.,Davies, D. K., and Gottlieb, M., Thallium arsenic sulfide (Tl,AsS,) Bragg cells for acousto-optic spectrum analysis, Opt. Comm., 57, Amano, M., Elston, G., and Lucero, J., Materials for large time aperture Bragg cell, Proc. SPIE, Auld, B. A., Acoustic Fields and Waves in Solids, Vols. I, 11, Wiley, New York, Rosenbaum, J. F., Bulk Acoustic Wave Theory and Devices, Artech House, Norwood, MA, Pape, D., Multi-channel Bragg cells: design, performance, and applications, Opt. Eng., Hecht, D. L., and Petrie, G. M., Acousto-optic diffraction from acoustic anisotropic shear modes in Gap, in IEEE Ultrasonic Symposium, pp. Papadakis, E. P., Diffraction of ultrasound in elastically anisotropic NaCl and in some other materials, J. Acousr. Soc. A m . , Papadakis, E. P., Diffraction of sound radiatinginto an elastically anisotropic medium, J . Acoust. Soc. A m . , Papadakis, E. P.,Ultrasonic diffractionloss and phase change in anisotropic materials, J . Acoucst. Soc. A m . , Cohen, M. G . , Optical study of ultrasonic diffraction and focusing in anisotropic media, J . Appl. Phys., Schaefer, C. L., and Bergmann, L., Uber neue Beugungserscheinungen an Schwingenden Kristallen, Naturwissenschaften, 22, Kino, G. C., Acoustic Waves: Devices, Imaging, and Analog Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, Dieulesaint, E., and Royer, D., Ondes Elastiques duns les Solides, Mason et C, Paris,

2 Design of Acousto-Optic Deflectors Dennis R. Pape Photonic Systems Incorporated Melbourne, Florida

Oleg 6. Gusev, Sergei V. Kulakov, and Victor V. Molotok St. Petersburg State Academy of Aerospace Instrumentation St. Petersburg, Russia

INTRODUCTION The acousto-optic (AO) deflector deviceis one the major practical applications of the interaction of light and sound in a crystalline material. A 0 deflectors are principally used in optical scanning and information processing applications. A 0 deflectors are superior to mechanical scanners in applications where high-speed and/or nonmechanical scanning is required. In optical information processing applications an A 0 deflector can be used as a spatial light modulator (SLM) for imparting electrical information onto an optical beam. The real-time operation the A 0 deflector coupled with the high fidelity with which it transfers electrical information to the optical domain usually makes it superior to otherSLM technologies in most practical optical processing applications. It is the SLM device of choice when signal information is to be processed. An A 0 deflector device, shown in Fig. 1, consists of a piezoelectric transducer mechanically bonded to a transparent crystalline material. An R F signal input to the transducer through an RF matching network is converted to a sound wave which travels through the A 0 crystal. The traveling sound wave forms a phase grating which diffracts an optical beam incident on thedevice. An A 0 deflector is created by designing the device that themajority of the diffracted light from a collimated incident optical beam appears in a single order whose spatial position is linearly propor69

70

PAPE ET AL. Undiff racted Light

Piezoelectric

Incident Light Acousto-optic Bragg cell.

Diffracted Optical Plane Wave

Plane wave 2 Acousto-optic Bragg interaction.

tional to thefrequency of the input RF signal. In such an arrangement the deflector is said to beoperating in the Bragg regime, and the deflector is commonly referred to as a Bragg cell. In Chapter 1 the Bragg interaction is described from a theoretical viewpoint with references to the primary literature. In this chapter we describe the interaction from a geometrical viewpoint in phase space which unifies the various interaction geometries into asingle framework and aids in the practical design of a deflector. The Bragg interaction is conveniently described using a phase (or momentum) space representation as shown in Fig. 2. Conservation of momentum in the interaction requires that the momentum vector of the diffracted optical plane wave kd, be equal to the vector sum of the momentum vectors of the incident optical plane wave ki, and the acoustic

uency

h

71

DESIGN OF ACOUSTO-OPTIC DEFLECTORS plane wave, K (directed normal to the transducer):

A 0 Bragg matching is a consequence of momentum conservation, where the magnitude of the acoustic momentum vector, K , is

where the angle between the incident optical beam and the acoustic beam is the Bragg angle (inside the A 0 crystal):

-

B -

h 0

2nA

Here n is the index of refraction of the A 0 medium, h, is the free-space optical wavelength, A is the acoustic wavelength, k = k, = kt = n2n/ho, and K = 2 d A . When the A 0 deflector is illuminated at the Bragg angle, the angle €lD between the undiffracted and diffracted optical beams exiting the cell is equal to twice the Bragg angle:

where A = v/f. Thus, the diffraction angle is proportional to the input RF frequency. Using this fundamental A 0 interaction phenomena, a wide range of practical A 0 deflectors has been designed and fabricated throughout the world over the past 20 years. The typical range of characteristics of these deflectors is shown in Table 1. The primary crystalline materials for A 0 deflectors include lithium niobate (LiNbO,),galliumphosphide (Gap), tellurium dioxide (TeO,), lead molybdate (PbMoO,), and fused silica. Table 1 Acousto-opticDeflector OperatingCharacteristics Characteristic Center Bandwidth Diffraction Time aperture Number of resolvable spots resolution Frequency Optical Maximumpower FW operating

Specificatio MHz-2

MHz

kHz-80

'

40 MHz-5 GHz 10 GHz 1-80%iW 0.05-100 psec 25-5000 20 0.3-10.6 pm

1w

PAPE ET AL. The design of an A 0 deflector entails a careful balance among requirements for bandwidth, diffraction efficiency, and time aperture. The bandwidth of the deflector, which, from Eq. (4), determines the total angular deflection of the Bragg cell, is clearly a primary A 0 deflector performance parameter. Diffraction efficiency, the efficiency with which the device diffracts light, clearly can determine the practical utility of a device in a particular application. Time aperture or,in spatial terms, the width of the optical aperture, as we shall discuss, is a fundamental measure of the frequency resolution of the device and, incombination withthe bandwidth, determines the number of resolvable deflector spots. These characteristics are discussed in Section 2, where they are linked to the key system operational parameters in scanning and information processing applications. The efficiency of an A 0 deflector is a function of the strength of the A 0 interaction in the device crystalline material as well as the degree to which the acoustic wave vectors are momentum-matched to the incident optical wave vector over the operatingbandwidth of the device. In Section we show the dependence of A 0 deflector efficiency on the chief device design parameters of material andacoustic mode selection and transducer geometry length and height specification. The group of materials useful for A 0 Bragg cells is those that exhibit strong A 0 interaction, low acoustic attenuation, low acoustic velocity, and small acoustic curvature. In Section we develop an A 0 material figure of merit that relates these material parameters to the product of the time aperture and the squareof the device operating frequency. A nomogram is produced which aids in material selection. Transducer geometry design guidelines are described in Section The degree to which the acoustic wave vectors are momentum-matched to the incident optical wave vector over the operating bandwidth of the device is dependent onthe length of the transducer and thespecific interaction geometry employed in the device design. In Section 5.1 we discussthe four major classes of A 0 interaction geometries: isotropic, anisotropic, phased array, and anisotropic phased array and the determination of the optimal transducer length within each class. The transducer height determines the angular extent of the acoustic plane waves in the direction orthogonal to both the acoustic and optical propagation directions. The height is optimized that the majority of the acoustic energy remains confined to the optical illumination aperture of the device. In Section 5.2 we discuss optimization of the transducer height as well as consider nonrectangular transducer configurations. The total efficiency of an A 0 deflector is, of course, entirely dependent on the degree to which the acoustic energy launched at the transducer remains inthe optical illumination aperture. Losses inacoustic energy from

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

73

acoustic diffractian and attenuation degradethe efficiency of the deflector and are discussed in Sections 6 and 7, respectively. In Section 8 we summarize the design procedure for an A 0 deflector. In Section 9 we describe specific examples of A 0 deflector designs with the aid of computer design programs which encode the design equations developed in the previous sections. The design methodology described here is one in which the design of the A 0 deflector results in the material selection, interaction geometry, and acoustic mode and orientation selection, and transducer geometry specification. The specific design of the transducer, including material selection, composition, and the electrical impedance matching network are designed separately (and discussed in Chapter In Appendix A we provide a design program from the Petersburg State Academy Aerospace Instrumentation which combines these two designs into a single program. In this way the bandshape of the electrical impedance-matching network can be modified interactively withthe A 0 bandshape to achieve a desired frequencydependent A 0 deflector diffraction efficiency response.

The main performance parameters of an A 0 deflector are shown in Table 2. The key performance parameters of an A 0 deflector for a particular optical system application usually are diffraction efficiency, bandwidth, and time aperture. These characteristics are intimately connected, and it is the goal of an A 0 deflector design to optimize one or more the characteristics given specific performance requirements and A 0 material constraints. The diffraction efficiency of a deflector is usually expressed in units of %/W and is defined as the ratio of the percentage the incident optical beam which is diffracted (Id/Zi)to the applied RF power P, (expressed in Table 2 Acousto-opticDeflectorParameters

Characteristic Center frequency Bandwidth Diffraction efficiency Time aperture Time-bandwidth product

Parameter fc

Af ~D.E.

TB = rAf

RF input power

P

Optical wavelength (free space)

x,

PAPE ET AL.

74

watts). The diffraction efficiency of an deflector is dependent on both device frequency and time aperture. The totaldiffraction efficiency can be expressed as T(D.E.(f,.)

=

(5)

sin2

where (6) where is the efficiency, which ismaterial and transducer geometry dependent, q D is the efficiency lossassociated with the diffraction of acoustic energy outside the illumination aperture of the device, is the efficiency lossassociated with acoustic attenuation in the deflector, and is the loss associated with converting electric energy into acoustic energy at the transducer. The term isapproximately equal to the total diffraction efficiency when the efficiency is small. graph versus frequency showsthe bandshape the device and provides a visual display the chief performance parameters of the deflector. The bulk of this deflector which yields a uniform chapter deals with the design of an maximized 7)D.E.(f,T) over a specific frequency range and time aperture. The diffraction efficiency is an important optical system parameter because it determines theoptical throughput power of the system. Constraints placed on the optical power at the illumination source as well as the RF power at the deflector will ultimately dictate the usefulness of a particular deflector with a given diffraction efficiency. The bandwidth and time aperture of the deflector are also primary optical system application performance parameters, bothindividually and as a product-the time-bandwidth product. For a scanning application, the key system features are number resolvable spots andresponse time. The number of resolvable spots N of an deflector is the ratio of the total optical beam deflection angle A0 to the divergence angle A+ of the optical beam exiting the deflector: q(f9.1

=

7)A07)07)a7)TRAN

7)D.E.

The total optical beam deflection angle for an input RF signal containing a range of frequencies Af is, from Eq. (4), h0 Af A0 = -

The optical beam divergence angle is

A+

A0 nD

DESIGN ACOUSTO-OPTIC OF DEFLECTORS

75

where the exact equality is dependent upon the nature of the illumination optical beam. (For example, a Gaussian optical beam has a divergence angle (4/7r)(A&D).) The number of resolvable spots is then

where = D/v is the transit time of the acoustic wave across the optical aperture D of the device. The number of resolvable spots is thus the timebandwidth product of the deflector, TB. Since optical deflection is a result of the transit of the acoustic wave across the optical beam, the speed with which the deflector can access random positions is UT. For signal processing applications, the key systemfeatures, forspectrum analysis, bandwidth and frequency resolution and, for correlation, bandwidth and number of taps. Frequency resolution is just the ratio of the total bandwidth to the number of resolvable frequencies (spots): fres

=

Af

=

1

while for correlator applications, where the A 0 deflector acts as an optically tapped delay line, the number of taps is just N, the time-bandwidth product. Given the system application, and the associated specifications for the A 0 deflector efficiency, bandwidth, and time aperture,the process of A 0 deflector device design can begin.

EFFICIENCY The efficiency with which an A 0 device deflects light, is a product of the strength of the A 0 interaction in the device crystalline material, q M , and the degree to which the acoustic wave vector is momentum-matched to the incident optical wave vector. The strength of the A 0 interaction can be found through a coupledmode analysis (see Chapter 1 and [l])in which the A 0 interaction is described by an electric field wave equation where the index of refraction includes the acoustically induced index perturbation. The strength (for an isotropic interaction) is

76

ET

PAPE

AL.

where Po is the acoustic power at the transducer, L is the path length of the optical beam in the acoustic sound field, H is the height of the acoustic sound field, and OB,= is the Bragg angle at thefrequency (nominally center) of the device where momentumis exactly matched, andM zis an figure of merit dependint only on material parameters. The degree to which the acoustic wave vector is momentum-matched to the incident optical wave vector can be determined by examining the intensity distribution of acoustic plane waves from a finite-length transducer. The intensity of the angular spectrum of acoustic plane waves exiting the transducer of length L is

Exact Bragg matching, for a fixed Bragg angle, occurs only for the one acoustic wave vector directed normal to the transducer which satisfies the momentum-matching condition expressed in Eq. (1). The distribution of acoustic plane waves resulting from the finite-length transducer, however, allows Bragg matching to occur over a range of acoustic wave vectors directed the normal to the transducer. phase-space representation of this matching is shown in Fig. 3(a) for an isotropic Bragg interaction (other typesof Bragg interactions will be discussed in Section 5 ) . Here the optical wave vectors are confined to theoptical normal surface. The range

(a)

3 Acousto-opticinteraction: (a) plane-wave distribution and(b) resulting bandshape.

DESIGN O F ACOUSTO-OPTIC DEFLECTORS

77

of the component of the acoustic plane waves normal to the center frequency wave vector K is AKz = K -h 2 where is the angular range of the acoustic plane waves. Since 26y is equal tothe angular spread of diffracted optical wave vectors, the frequency dependence the intensity I d of the diffracted optical beam is

Id

=

sin(AKzL/2) AKzL/2

(

Io

)

The resulting A 0 bandshape is shown in Fig. 3(b). 'The product of the strength of the A 0 interaction and the intensity distribution is the A 0 diffraction efficiency defined as the ratio of the intensity of the diffracted optical beam to the intensity of the undiffracted optical beam: =

k? M2PoL sin(AKzL/2) 8 cos2 O&-I( AKzL/2

)

In the next section we describe a means of selecting A 0 materials which will maximize diffraction efficiency. 4 ACOUSTO-OPTICMATERIALSELECTION In the expression for the total deflector diffraction efficiency (Eq. (5)) all of the explicit material-dependent parametershave been grouped together into the A 0 efficiency (Eq. (16)) as an A 0 figure of merit M2. For an isotropic A 0 interaction, M2 is (see Chapter 1 and [2]):

n6p2

M, = where n is the A 0 material refractive index, p is the effective photoelastic coefficient, is the density of the A 0 material, and v is the acoustic velocity. The expression for diffraction efficiency, however, also contains terms which implicitlyincorporate material-dependent parameters. Inparticular, is dependent upon the material acoustic attenuation factor, L, when optimized, is dependent on material index of refraction and acoustic velocity, and H,when optimized, is dependent on acoustic curvature aswell as acoustic velocity. In order to compare different materials for optimum

78

PAPE ET AL.

A 0 deflector performance it is useful to separate thematerial-dependent terms from L , and H and incorporate them intoa new figure of merit. The loss in efficiency associated with acoustic attenuation, qa is a result of the absorption of power in the acoustic beam as it traverses the optical aperture of the deflector. The power in the acoustic beam P&) is reduced exponentially away from the transducer (in the acoustic propagation direction x ) as P,(x) = Poe-2”

(18)

where Po is the power at the transducer and a is the material attenuation constant measured in units of neperslcm. For almost all of the common A 0 materials the attenuation constant is a function the square of the acoustic frequency. The attenuation constant can be rewritten as ff ‘=

ffof

(19)

where is the frequency-independent attenuation coefficient usually measured in units of neperslcm-G**. The average acoustic power inside a deflector of width D (= is then

The relative loss associated with acoustic attenuation is then

which contains the material-dependent attenuation constant cq,. The length of the acoustic sound field, L , determines the regime in which the A 0 interaction occurs (Raman-Nath or Bragg). This length is dependent on acoustic wavelength (and hence acoustic velocity) and material index of refraction. L can be characterized by the Klein-Cook parameter Q [l](see Chapter l) as L =

QnAz cos 27rh0

where A, is the acoustic wavelength at the center frequency of the device operating bandwidth (A, = and where Q < 0.3 forRaman-Nath diffraction and Q > 7 for Bragg diffraction. Equation (22) shows the dependence of L on n and The transducer height determines the angular extent of the acoustic plane waves exiting the transducer in the vertical direction (orthogonal to both the acoustic and optical propagation directions). Near the transducer

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

79

the acoustic field remains approximately collimated. The height of the transducer is designed that the time apertureof the device is within the collimated region, thus minimizing the amount of acoustic energy outside of the optical illumination region. The intensity of the angular spectrum of acoustic plane waves exiting a rectangular transducer of height H in the vertical direction is sin(TPH/A(l - 2b) aPHIA(1 - 2b) where the acoustic curvature factor 11 - 2b( is a measure of the acoustic anisotropy of the material [4]. An isotropic material has an acoustic curvature of l and hence a b value of 0. For materials with an acoustic curvature 11 - 2bl > (= .5 THEN N=lNT(TRANUD)+l ELSEIF (TRANUD)/2 lNT((TRANUD)/2) < .5 THEN N=IN~(TRANUD) END I F TRANL=D*N ~ R A N H = V E ~ S Q R ( ( T A ~ * A S-2"B))IFCENTER) S(1 PRINT "TRANSDUCER LENGTH IS', TRANL PRINT "TRANSDUCER ELEMENT LENGTH IS",W PRINT "TRANSDUCER CENTER-TO-CENTERSPACING Is", D PRINT "NUMBER OF TRANSDUCER ELEMENTS Is",N PRINT "TRANSDUCER HEIGHT IS", TRANH PRINT "ILLUMINATIONANGLE IS", BRAGGC BRAGGC=.0516 FSTART=FCENTER-(3"BW/4) FSTOP=FCENTER+(~BW~4) FRES=BW/30 FOR F=FSTART TO FSTOP STEP FRES XF=LAMgF/(2'VEL*INDEXl) BRAGGF=AlN((XF)/SQR(1-XFA2)) GAM=BRAGGF-BFWGGC IF GAM=O THEN GAMslE-32 K=2"P I"F/VEL BETA=(K"W/2)*SIN(GAM) ALP HA=(K" 012)" (SIN(GAM)-SIN( P I/(K"D))) IF ALPHA=O THEN ALPHA=IE-32 ETAAO=((K1"2"P"M2"TRANL)/(8"TRANH"(COS(BRAGGC~)"2)~~( 1/NA2)*((2/P1)"2) "((SIN(BETA)/BETA)"2)"( (SIN( N*ALPHA)/SIN(ALPHA))"2) ETAALPH=( 1*EXP(-ALPHAL*((((F)/l E+09))"2)*TAU*lOOOOOO~)) /(ALPHAL"( ((( F)/1E+09))"2)*TAU* 1OOOOOOi) ETA=ETAAO"ETAALPH lTEN=SlN(SQR(ETA))A2 RITE # l , F/lOOOOOO&,lTEN*lOOO NEXT CLOSE #1 END

-

-

Anisotropic phased array Bragg cell design program-TeO,

example.

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

119

the tangential matchingfrequency (BRAGGC)using Eq. (61), the nominal transducer length L (TRANL) using Eq. (65), and the nominal transducer center-to-center spacing D (D) using Eq. (66). The length of each element “(W)isfoundusing WID = 0.742 (see the subsection “Phased Array Interaction”). The total number of phased array elements N (N) is then calculated using Eq. (60). The program then finds the optimum transducer height H (TRANH) using Eq. (25). The program then calculates the value of (DELKZ) using Eq. (42). Within the same program loop the A 0 efficiency (ETAAO) is calculated using Eq. (16), where the sinc term is modified using Eq. (62), and the loss associated with acoustic attenuation (ETAALPH) is calculated using Eq. (79). Finally the diffraction efficiency ITEN is calculated using Eq. (80). In this design we assume there is no diffraction loss (i.e., q D = 1) and no conversion loss at the transducer (%RAN

=

Figure 32 shows a plot of the bandshape for this deflector calculated by the program in Fig. 31. A center frequency of about 85 MHz is predicted,

120

PAPE ET AL.

Phased array TeOz deflector. (Photo courtesy Incorporated.)

Photonic Systems

and a 3-dB bandwidth of about 57 MHz is predicted. The high acoustic attenuation in this material is responsible for the low right-diffractionefficiency peak. The transducer geometry parameters calculated by the program are L = 1.7 mm, N = elements, D = pm, W = pm, H = 3.37 pm, Oi = mrad. The illumination angle was lowered to mrad to achieve a more symmetrical 3-dB bandshape. The device has a peak efficiency of 44%/W. Figure 33 shows an example of a phased array TeO, deflector designed using these parameters which achieved a peak diffraction efficiency of 30%/W.

ACKNOWLEDGMENTS The authors would like to thank V. S. Kulakov for the English translation of the work of Gusev, Kulakov, and Molotok, which waswritten originally in Russian. D. R. Pape wishes to acknowledge stimulating conversations with A. Bardos and B. Beaudet of Harris Corporation and M. Shah of M W Electronics, Inc. concerning the design of A 0 deflector devices.

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1. Klein, W. R., and Cook, B. D., Unified approach to ultrasonic light diffraction, IEEE Trans. Sonics Ultrasonics, SU-14, 123-134 (1967). 2. Smith, T. M., and Korpel, A., Measurement of light-sound interactions efficiency in solids, IEEE J . Quantum Electron., QE-I , 283-284 (1965). 3. Auld, B., Acoustic Fields and Waves in Solids, Krieger, Malabar, F L Y 1990, Chap. 3. 4. Papadakis, E., Diffraction of ultrasound radiating into an elastically anisotropic medium, J. Acoust. Soc. Am. , 36,414-422 (1964). 5. Dixon R. W., Photoelasticproperties of selected materialsand their relevance for applications to acoustic light modulators and scanners, J . Appl. Phys., 38, 5149-5153 (1967). 6. Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J . Quantum Electron., QE-3, 85-93 (1967). 7. Warner, A. W., White,D. L., and Bonner, W. A., Acousto-opticlight deflectors using optical activity in paratellurite, J . Appl. Phys., 43,44894494 (1972). 8. Gordon, E.I., A review of acoustooptical deflection and modulation devices, Proc. IEEE, 54, 1391-1400 (1966). 9. Hecht, E.,Optics, Addison Wesley, Reading, MA, 1987, Chap. 10. 10. Shah, M. L., and Pape, D. R., A generalized theory of phased array Bragg interaction in a birefringent medium and its application to TeO, for intermodulation product reduction, Proc. SPIE, Advancesin Optical Information Processing V,1704, 210-220 (1992). 11. Cook, B. D., Cavanagh, E., and Darby, H. D., A numerical procedure for calculating the integrated acoustooptic effect, IEEE Trans. Sonics Ultrasonics, SU-27, 202-2206 (1980). 12. Hams, F. J., On the use of windows for harmonic analysis with the discrete Fourier transform, Proc. IEEE, 66, 51-83 (1978). Opt. Eng. ,25,30313. Bademian, L., Parallel channel acousto-optic modulation, 308 (1966). 14. Pape, D. R.,Wasilousky, P. A., and Krainak, M., A high performance phased array Bragg cell, Proc. SPIE, 789, Optical Technology for Microwave Applications 111, 116-126 (1987). 15. Cohen, M. G., Optical study of ultrasonic diffraction and focusing in anisotropic media, J. Appl. Phys., 38, 3821-3828 (1967). 16. Maydan, D., Acoustooptical pulse modulators, IEEE Trans., VQ-6, 15-24 (1970). 17. Zadorin, A. and Sharangovich, S. N., The calculation of the frequency band of an acousto-optic modulator with a cylindrical piezotransducer, Izv. SSSR, Radioelektron., 28, 76-78 (1985). (Russian) 18. Pape, D. R., Multichannel Bragg cells: Design, performance, and applications. ODt. Ena.. 31. 2148-2158 (1992).

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Hecht, D. L.,and Petrie, G. W., Acousto-optic diffractionfromacoustic anisotropic modes in gallium phosphide, Proceedings of the I980 IEEE Ultrasonics Symposium, pp. Beaudet, W. R.,Popek, M., and Pape, D. R., Advances inmultichannel Bragg cell technology, Proc.SPIE,Advances in Optical Information Processing IZ, 639, Fox, A. J., Thermal design for germanium acoustooptic modulators, Appl. Opt., 26, 22. Elston, G., Optically and acoustically rotated slow shear Bragg cells in TeO,, Proc. SPIE 936, Advances in Optical Information Processing, Xu, J., and Stroud, R.,Acousto-OpticDevices, Wiley, New York, Chap. 6.

Design of Acousto-Optic Modulators Richard V. Johnson Crystal Technology, Inc. Palo Alto, California

INTRODUCTION 1.1 BriefHistoryand Scope Acousto-optic component technologies have evolved naturally out of fundamental scientific research into ultrasonics. Among the most powerful tools for studying ultrasonic propagation, absorption, scattering, and reflection phenomena are optimal imaging techniques, especially schlieren imaging. The schlieren images have suggested the concept of an optical modulator in which light intensity can be controlled by an electronic drive signal. Some of the earliest efforts at fabricating acousto-optic modulators were initiated over 50 years ago, long before the invention of the laser. Interested readers are directed to thebook by Bergmann for a more complete description.of this early work [l]. One of the earliest uses of an acousto-optic modulator in an electrooptic system was for large screen projection of television images in theaters, developed in thelate by the Scophony Laboratory in London [l-41. Even by today’s standards, this scanner stands as one of the most subtle and sophisticated electro-optic systems ever developed. The Scophony scanner is one of the few systems to take full advantage of the acousto-optic modulator’s scrolling spatial light modulation behavior. The Scophony scanner architecture was a key enabling concept to maximize

JOHNSON light energythroughput to theimage plane, asthe original light source was a spatially incoherent arc lamp. we shall see in Section 4, an acoustooptic Bragg cell performs by far the best as a temporal “point” modulator when an incident light beam has the highest possible spatial coherence. Hence, significant market applications for acousto-optic technology had to wait until the invention of the laser in the early By the time lasers wereinvented, key manufacturing processes for acoustooptic components had already been refined to a very high level. The reason was a fortuitous synergy between acousto-optic component manufacturing processes and ultrasonic delay line manufacturing processes. Ultrasonic delay lines were a major market during this period some years ago. Both component categories require piezoelectric transducer plates to be bonded to a polished flat surface,under high pressure in a vacuum chamber. (See discussionin Chapter Bothcomponent categories require the transducer to be ground and polished to final thickness, thereby defining the centerfrequency of the transducer response bandwidth.Both categories require electronic impedance matching circuits to couple RF energy efficiently from 50-ohm instrumentation to a generally non-50 ohm, reactive, dispersive transducer element. Indeed, the onlymanufacturing process required for acousto-optic components which hadnot already been realized with ultrasonic delay lines is a high-quality antireflection coating on the two optical windows. This coating technology already existed from other sources. Acousto-optic modulators can be batch-processed for significant reduction of manufacturing costs (Fig. a result, acousto-optic component technology and markets have evolved dramatically over the past years, as witnessed by the subjects contained within this book The scope of this chapter is to elucidate design principles for acoustooptic modulators Section reviews major markets for the modulator to determinewhich performance measuresare most critical for practical applications. The fundamental operatingconcepts of a modulator are detailed in Section 2, devoid of mathematical complexities, in preparation for detailed analyses contained in Sections The RF drive power and materials requirements for an intensity modulator are studied in Section Requirements of the incident light source for best modulator operation are reviewed inSection 4, and static contrast ratio is calculated for a lowestorder TE% Gaussian profile laser beam. simple model of modulator temporal response is given in Section 5, a single parameter measure of modulator performance isdefined with respect to risetime, and a numerical algorithm is detailed for calculating modulator response to any arbitrary video signal V(t). The finite thickness the sound field, defined by the transducer length L, affects a number of modulator performance parameters, including light diffraction efficiency, optical beam profile distortion,

DESIGN OF ACOUSTO-OPTIC MODULATORS

125

Photograph of typical acousto-optic modulators.These modulators can be batch processed for low manufacturing costs.

JOHNSON

126

and in extreme cases, a degradation in temporal response, as described in Section 6 . Identifying an optimum modulator design involves arbitrating between conflicting performance requirements. A candidate modulator design strategy is listed in Section 7. This design strategy embodies conventional modulator design wisdom, but clever system designers have invented a number of techniques for obtaining even more performance from a modulator. In Section 8, we review four different approaches for maximizing the performance of a laser scanning system using an acousto-optic modulator. Section 9 concludes this chapter.

1.2 Current Modulator Markets partial list of today’s markets for intensity modulators is given in Table 1. By far the largest market share is for laser scanning systems for applications as diverse as reprographics, medical imaging, or VLSI mask generation. A second major market share is for Q-switching of lasers for machining, materials processing, and medical and dental procedures. A market segment primarily for metrology and LIDAR employs intensity modulators for their ability to Doppler-shift the temporal frequency of a laser beam. Finally, a small but rapidly growing market is developing for Table

Acousto-opticModulatorMarkets

Laser scanning: 2D Imaging Reprographics Nonimpact printing Color separation Laser typesetters Medical x-ray digitizing and reconstruction Large screen television displays Laser plotters Laser-based VLSI mask maker Ablation imaging Laser scanning, other categories Printed circuit board inspection Laser optical disk mastering systems Measuring dopant levels of silicon wafers AOQS for pulse laser operation Laser machining and material processing Medical surgery procedures Dental procedures Laser heterodynemetrology OTDR switching

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optical time-domain reflectometry (OTDR) instruments for diagnostic inspection of installed fiberoptic networks. We will explore representative examples of each of these market categories in turn. Laser Scanning Systems typical laser scanner system is shown in Fig. 2 [17-201. It consists of a high-radiance laser light source, an intensity modulator, a scanning means for sweeping the laser light across a photoreceptor surface (such as the rotating polygon mirror shown in the figure), and suitable lenses and mirrors forfocusing and directing the laser light. drum or a belt, notshown in this figure, provides motion along the orthogonal image direction that subsequent scan lines are properly registered in sequence to form an image. A key design parameter is the smallest image area which can be formed by a scanner (a picture element, or pixel), whichgoverns the resolution required of the optics and the data rate required of the intensity modulator. match the visual acuity of most human observers, ascanner resolution suitable for most text-based business documents is 300 pixels

,

I"d

2 Schematic diagram key optical components.

a flying spot laser scanning system, showing the

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128

per inch, whereas graphics or half-tone images require higher resolutions for best image quality. Let us calculate typical modulation bandwidth requirements of the modulator in a laser scanning application. The modulation bandwidth is governed by the scanner resolution, the scan rate in terms of how many copies per second, the area of the copy being scanned, and an efficiency factor which considers scanner retrace and electronic housekeeping requirements. Consider first a comparatively low performance scanner. Assuming a resolution of 300 pixels per inch, an 8.5-by-11-inch document, a scan rate of a document a second, and an active scan time to total scan time efficiency of this implies a video data rate (8.5"

X

ll")/document X

X

(300pixels/inch)2

1 document/sec = 10.5 megapixeldsec 80%

This can be converted into a maximum bandwidth requirement fm for the intensity modulator using the expression 1Hz =

(2)

pixels/sec

which for the example considered above corresponds to a modulation bandwidth of MHz. This is a very modest performance requirement for an acousto-optic modulator. Let us bracket typical scanner requirementsby considering a much higher performance system, a scanner with 600 pixels/inchresolution, copies/ sec throughput rate, and again an 80% active scan duty cycle. The modulator data rate for this application is fM =

=

(8.5"

X

ll")/document

X

(600 pixels/inch)2

X

(1 W 2 pixeldsec) MHz

X

document/sec 80% (3)

This approaches the upperlimit of bandwidth which an acoustooptic modulator can comfortably deliver with high light diffraction efficiency. Another critical performance parameter needed to specify the modulator is the risetime, which determines fidelity of the temporal modulation, as discussed in Section 5. A fast risetime enables modulator output which closely tracks the input video signal; conversely, a slow risetime causes considerable blurring of the output signal. In a laser scanning system, the

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129

finite dimension of the scan spot also serves to blur the final exposure record, and indeedis usuallythe dominantblurring mechanism. One measure of modulator and scanner fidelity is the dynamic contrast ratio in response to a square pulse video signal train. A powerfulmethod foranalyzingscanner performance isthe modulation transfer function (MTF), i.e., the contrast ratio response (in terms of modulation depth) to a sinusoidal video signal. This analysis easily combines response degradation effects due to the finite scan spot dimension and the finite modulator response time. All scanner architectures exhibit a fundamental cutoff frequency Alp/#

fcutoff

=

V-n

due to thewave nature of light, in which F/# is the flnumber of the scan beam incident upon the final image plane, andV,, is the speed with which the scan spot sweeps across this image plane. For a flying spot scanner, the MTF contribution due to the finite sizeof the scan spot alone, independent of the modulator temporal response contribution, results in a steady monotonic response falloff, froma peak response at the lowest spatial frequencies to response cutoff at fmtOft. According to conventional flying spot scanner design, any modulator frequency response rolloff exacerbatesthe total scanner MTF rolloff. Hence conventional scanner design philosophy is to choose a modulator risetime as short possible, within cost constraints. In Section 8 we consider an alternativescanner architecture, the Scophony scanner, which exhibitsoutstanding MTF by exploitingthescrollingspatialmodulation characteristic of the acousto-optic modulator. Q-Switched Lasers A number of applications, such as laser machining, medical and dental surgery processes, and certain scientific research experiments benefit from a laser which emits short discrete pulses of very high peak power, rather than a cw laser of much lower power. A standard approach forachieving high pulse powers is Q-switching A number of alternative techniques exist for Q-switching. For example, electro-optic Pockels cell Q-switches (EOQS) are most useful for very high gain lasers and very short pulse modulation requirements (e.g., laser target designators) which cantolerate higher levels of optical loss. Acousto-optic modulators are most suitable for low-gain cw-pumpedor repetitively pumped lasers which demand lowest possible cavity losses to achieve peak power. These components are referred to as acousto-optic Q-switches (AOQS); see Fig. for a typical laser cavity configuration and Fig. for a photograph of a typical Q-switch. increase the laser cavity loss, an RF signal is applied to the AOQS.

130

JOHNSON

%-1” a

E

LASER CAV TY M RROR

DEFLECTED LIGHT

-/ DEFLECTED L

LASER CAV I TY ACOUSTO-OPTIC MIRROR 0-SW ITCH

Schematic diagram of a laser cavity with an acousto-optic Q-switch for generating short laser pulseswith high peak powers.

Photograph of a typical acousto-optic Q-switch. This unit requires 70 W of RF drive power and requires water cooling.

This allows the internal optical power to build up tovery high levels. The RF is then turned for a short period of time, which suddenly lowers the cavity loss, and allows a very large laser pulse to build up in the cavity. After this pulse has built up and left the laser cavity, the RF can be turned on again and the process repeated at pulse rates as high as 1 kHz.

DESIGN OF ACOUSTO-OPTIC MODULATORS

131

Compared with EOQS, AOQS exhibit very low optical insertion loss (

U

z

W

l” U


n2, and will be determined by the value of tlA. In addition, it will be different for the TE and TM modes for any given value of t l X . The momentum, or propagation vector of the guided beam, is defined as p = 2.~n,~f/A,,, exactly as the k vector is defined for unguided light wavepropagation. Of great significance for A 0 interactions in optical waveguides is the observation that anisotropic interactions may occur even in waveguide media that are isotropic. The anisotropy arises from the modal dependence of since TE and TM modes will have different values of neH.Also, the magnitude of the effective birefringence, neff(TE) - neff(TM),can be chosen by varying the guide layer thickness. In addition, the effective photoelastic coefficients for guidedwave interactions will be more complex than those for bulk wave. Con-

GOTTLIEB

280

sequently, there is a relaxation of the crystal symmetry requirements for useful anisotropic-based devices, such as the AOTF. The acoustic wave for the integrated optic AOTF is generated by an acoustic surface wave (ASW) transducer which is fabricated on the guide surface. The substrate must be a suitable piezoelectric material, such as LiNbO,, and the transducer must be of the interdigital type which efficiently generates theASW. The energy in the guided light waveis confined to the thin guide layer region and it is readily apparent that the acoustic energy must also be confined to the same guide layer region in order for the interaction to be efficient. This occurs very naturally with ASW, for which the strain amplitude will be large only to a depth on the order of an acoustic wavelength. For a well-designed integrated optic A 0 device, the overlap between the optical and the acoustic fields will be near unity. The guide layer is formed on the LiNb03 surface by the process of indiffusion of Ti to a depth of several micrometers. This slightly alters the refractive indices of the substrate to form the light guide. Light can be coupled into theguiding layer by several methods, themost commonbeing the edge coupler, which introduces the light via an optical fiber or a lens to focus the external beam at the edge of the guide. A schematic of an integrated optic AOTF is shown in Fig. in which the incident light beam and theASW are made to propagatecollinearly. The required phasematching condition for the collinear AOTJ? in the waveguide is =

+ KASW

(81).

where the acoustic wave vector K will couple theTE and TM optical modes. The input light is made pure TE by means of the integrated optic mode selector at the input edge. The mode selector is an appropriately designed metal/dielectric layer deposited on the surface. For optical wavelengths that satisfy the phase-matching condition of Eq. (81) there will be a con-

z

50 Integrated optic LiNbO, AOTF.

ACOUSTO-OPTIC TUNABLE

FILTERS

281

version of the TE mode to a TM mode, i.e., a rotation of the plane polarization. The collinearly propagating light beams pass under another optical mode selector at the opposite edgeof the waveguide. This second mode selector is chosen to pass TM modes only, that only the phasematched wavelength istransmitted to theedge the waveguide, where it is coupled out, either by another fiber or collected by a lens. Complete mode conversion of the light has been achieved with only 8 mwof RF power, about 250 times less than the bulk-wave counterpart. Design and fabrication improvements can further improve the power requirements, channel crosstalk, and the number of wavelengths that can be supported.

REFERENCES Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J . Quant. Electron. QE-3, Harris, E., and Wallace, R. W., Acousto-optic tunable filter, J . Opt. Soc.

Am., Nieh, T. K., and Harris, E., Aperture-bandwidthcharacteristics of the Am., acousto-optic filter, J. Opt. Nye, J. F., Physical properties of crystals, Oxford: Clarendon Press, Yano, T., and Watanabe, A., Acousto-optic TeO, tunable filter using far off-axis anisotropic Bragg diffraction,Appl. Opt., Chang, I. C.,Analysis of the noncollinear acousto-optic filter, Electron. Lett., Chang, I. C. ,Tunable acousto-optic filters: an overview, Opt. Eng., ( Salcedo, J. R., Phase-matching in acousto-optic filters. I: Uniaxial crystals, submitted. Dwelle, R., and Katzka, P., Large field of view AOTFs, Proc. SPZE, 753, Voloshinov, V. B., and Mironov, 0. V., Wide aperture acousto-optic filter for the mid-IR range, Opt. Spectrosc. (USSR), Melamed, N. T., and Gottlieb, M., A comparison of various dispersive devices, Westinghouse Research Report No. 85-1Cl-OPREP-R1, Melamed, N. T., The etendueof a filter and of a filter spectrometer, Westinghouse Research Memo No. 85-1Cl-OPREP-M1, Gottlieb, M., Goutzoulis, A. P., and Singh, N. B., Fabrication and characterization of mercurous chloride acousto-optic devices, Appl. Opt., Gottlieb, M., and Singh,N. B., Growth, characterization and device design: thallium phosphorous selenide crystals, in Growth and Characterization Acousto-Optic Materials (N.B. Singhand D. Todd, eds.), Trans. Tech. Publ., Zurich, pp.

GOTTLIEB Gottlieb, M., and Kun, Z., Temporal response of high resolution acoustooptic tunable filters, Appl. Opt., Murphy, J., and Gad, M., Aversatile program for computing and displaying the bulk acoustic wave properties of anisotropic crystals, Proceedings of the IEEE Ultrasonics Symposium, pp. Sovero, E. A., and Khoshnevisan, M., A generalized method for designing acousto-optic tunable filters, Proceedings of the IEEE Ultrasonics Symposium, pp. Chang, I. C., Katzka, P., Jacob, J., and Estrin, Programmable acoustooptic filter, Proceedings of the IEEE Ultrasonics Symposium, pp. Pinnow, D., Abrams, R. L., Lotspeich, J. F., Henderson, D., Stephens, R., and Walker, C., An electro-optic tunable filter, Appl. Phys. Lett., Belikov, I. B., Buimistryvk, G., Voloshinov, V., Magdich, L., Mitkin, M., and Parygin, V., Acousto-optic image filtering, Sov. Tech. Phys. Lett., Suhre, D. R., Gottlieb, M., Taylor, L. H., and Melamed, N. resolution of imaging noncollineartunable filters, Opt. Eng.,

T., Spatial

Harris, E., Nieh, T. K., and Feigelson, R. S., CaMoO, electronically tunable filter, Appl. Phys. Lett., Taylor, D. J., Harris, E., Nieh, T. K., and Hansch, T. W., Electronic tuning of a dye laser using the acousto-optic filter, Appl. Phys. Lett., Denes, L. J., Gottlieb, M., Singh, N. B., Suhre, D. R., Buhay, H., and Conroy, J. J., Rapid tuning mechanism for CO, lasers, Proc. SPIE, Shipp, W. S., Biggins, J., and Wade, C., Performance characteristics of an electronically tunable acousto-optic filter for fast scanning spectrophotometry, Rev. Sci. Instrum., Hallikainen, J., Parkkinen, J., and Jaaskelainen, T., Acousto-optic color spectrometer, Rev. Sci. Instrum., Bardash, M., and Wolga, G. J., Acousto-optic spectrometer system used to monitor combustion processes, Appl. Opt., Hatano, M., Nozowa, T., Murakami, T., and Yamamoto, T., New type of rapid scanning circular dichroism spectropolarimeterusing an acoustic optical filter, Rev. Sci. Instrum., Bates, B., Halliwell, D., and Findlay, D., Astronomical spectrophotometry with an acousto-optic filter spectrometer, Appl. Opt., Watson, R. B., Rappaport, A., and Frederick, E. E., Imaging spectrometer study of Jupiter and Saturn, Icurus, Lansing Taylor, D., Salmon, Edward, and Jacobson, Ken, A Practical Guide to Light Microscopy for Biologists, University Science Books, to be published.

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Kurtz, I., Dwelle, R., and Katzka, P., Rapid scanning fluorescence spectroscopy using and acousto-optictunable filter, Rev. Sci. Instrum., Lambert, J., Chao, T., Yu, and Cheng, L., Acousto-optic tunable filter (AOTF) for imaging spectrometerfor NASA applications:Breadboard demonstration, Proc. SPIE, Yu, J., Chao, T. H., and Cheng, L., Acousto-optic tunable filter (AOTF) imaging spectrometer for NASA applications: systems issues, Proc. SPIE, Coquuin, G . A., and Cheung, K. W., Electronically tunable external cavity semiconductor laser, Electron. Len., Cheung, K. W., Liew, C., and Lo, C. N., Experimental demonstration of multiwavelength optical network with microwave subcamers, Electron. Lett., Cheung, K.W., Smith, D. A., Baran, and Hef'ner, B., Multiple channel operation of integrated acousto-optic tunable filter, Electron. Lett., Cheung, K.,Liew, and Lo, C., Simultaneous five wavelength filtering at nm wavelength separation using integrated-optic acousto-optic tunable filter with subcamer detection, Electron. Lett., Chang, I. C., Laser detection utilizing tunable acoustic-optic filters, IEEE J . Quantum. Electron., QE-14,

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5 Transducer Design Akis P. Goutzoulis Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

William

Beaudet

Harris Corporation Melbourne, Florida

1 INTRODUCTION In Chapters 2, 3, and 4, we discussed the device design methodology that includes material selection, interaction geometry, acoustic mode and orientation selection, as well as transducer geometry specification. In this chapter we address the design and the interfacing of the transducer structure which launches the acoustic wave into the acousto-optic (AO) device. typical transducer structure consists of a metal top electrode, a p i e m electric crystal, and one (or more)metal bonding layer which attaches the piezoelectric crystal to the substrate and which is used as a bottom electrode. The performance of the device as measured by its bandwidth, impedance, conversion efficiency, and voltage standing-wave ratio (VSWR) largely depends on thecharacteristics of the transducer structure used. These characteristics are determined, among other things, by the number, composition, dimensions, and natural properties (e.g. ,mechanical impedance) the various layers and the substrate. the complexity of the transducer structure and the device operating frequency increase, the overall transducer behavior becomes more complex, and the number and accuracy the calculations necessary to predict the device performance increase as well. It is therefore desirable that the device designer not only is able to analyze and design such structures, but is also able to efficiently and accurately predict the overall transducer structure performance regardless of the transducer complexity involved. 285

286

BEAUDET

AND GOUTZOULIS

In this chapter we first present a comprehensive analysis of the transducer structure (Section 2). The analysis of the various bonding layers is presented via equivalent circuits through the use of a transmission line equivalent matrix analysis to predict the device electrical impedance and transducer conversion efficiency. We also discuss various performance parameters which canbe employed in order toevaluate the overall transducer design. The effects the various layers in simple transducer configurations are described next along with techniques that allow broadband operation with minimum conversion loss. We then discuss various materials issues, and we emphasizethe materials that can be used as bonding layers because they dramatically affect the amount of acoustic energy transferred from the transducer into the A 0 substrate. Note that several discussions on bonding and transducer materials can also be found in various sections of Chapter 6. However, the objectives of these discussions are related to the various fabricational processes the A 0 devices rather than to efficient the transfer of the acoustic energy from the transducer to the A 0 crystal. In Section we present a computer program which is based on the analysis presented in Section 2. We use this program in conjunction with three design examples covering the MHz, MHz, and GHz frequency ranges, in order toshow the use of the design methodology as well as of the program itself, for the study and analysis of simple and complex transducer structures. When appropriate we present actual experimental results to show the agreement between theory andexperiment. These threedesign examples also serve asgood opportunities for theanalysis and understanding of generic transducer issues such as theeffectiveness acoustic quarter-wave matching. We complete the transducer design by describing the electrical matching and power delivery networks (Section For this purpose we discuss impedance matching techniques appropriate for simple transducers structures, phased array transducers, and multichannel devices. In each case we explain the design philosophy followed in matching the device, we present the network used, and we show the performance improvement achieved in an actual A 0 device. We close this section by noting that in Appendix A we providea design program from the St. Petersburg StateAcademy of Aerospace Instrumentation which combines the overall A 0 deflector design methodology (including A 0 material selection, interaction geometry, acoustic mode propagation, orientation selection and transducer geometry specification) with the transducer design methodology (including transducer material selection, acoustic and electric impedance matching). This “single” program can be used to adjust (interactively) the electric impedance matching network so that in conjunction with the A 0 bandshape, the desired A 0

TRANSDUCER DESIGN

287

1

L Single-port

deviceconfiguration.

deflector frequency response can be achieved. relatively easily, that it can be used for

This program can be modified modulators and AOTFs.

2 TRANSDUCER ANALYSIS The majority of A 0 devices are single-port one-dimensional (l-D) structures and use a piezoelectric transducer to generate bulk acoustic waves which then propagate in the crystal (Fig. 1). A less common A 0 configuration is the one found in two-dimensional A 0 devices, e.g., X-Y deflectors or scanners, and involves two'transducers which are orthogonal to each other. The analysis of either of these A 0 structures is based on the analysis of a single-port l-D multilayered A 0 structure, such as the one shown in Fig. 2. To simplify suchan analysis the following assumptions will be made aboutthe transducer-A0crystal structure: (1) the transducer dimensions are large compared to the acoustic wavelength (A,) in the piezoelectric film, (2) the transducer crystal symmetry is chosen that the transducer is excited in a pure l-D acoustic mode and the generated acoustic wave propagates toward the thickness direction, i.e., into theA 0 crystal, the A 0 crystal has a crystal symmetry that is appropriate for the desired propagation mode, (4) the various electrode andbonding layers

2

- - - -- --- - -

N-l

N tN

-.

9 Multilayered single-port nected to a source.

device structure with the transducer con-

288

BEAUDET

AND GOUTZOULIS

transmit the acoustic power without mode conversion, and (5) the acoustic energy generated by the transducer propagates into the material such that theinitial beam size is defined by the dimensions of the topelectrode. The goal of our analysis isthe derivation of simple, closed-form expressions for the input complex impedance and~fromthis the untuned conversion efficiency of the transducer. Using these expressions, the device designer can then study and optimize the top electrode area, the electrode/ bonding layer thickness, and the acoustic impedance(s). These serve as a best condition starting point for the latter addition of an electrical matching network (covered in Section 4).

2.1 TransducerEquivalentCircuitAnalysis Typical devices use transducer structures that generate planar volume acoustic waves and satisfy the assumptions described earlier. Thesedevices can be analyzed by using the l-D transducer model developed by Mason [l] and extended by Berlincourt [2], Sitting [3-51, and others [6-91. This l-D model was developed in order to predict the input impedance, conversion loss, and bandwidth (BW) characteristics of a multilayered transducer structure such as the oneof Fig. 2. The results of this l-D analysis are summarized by the equivalent circuit shown in Fig. 3. Here the pie-

I I

I I

Equivalent circuit model summarizingthe Mason l-D analysis results.

TRANSDUCER

289

zoelectric film is represented by the Mason equivalent circuit [l],the top and bottom electrode layers are treated as transmission lines, the topelectrode free surface is treated as an acoustic short, and the crystal is represented by an impedance load The term COis the clamped capacitance of the transducer and is given by

where E is the relative dielectric constant, is the dielectric constant of free space, A . is the cross-sectional area of the transducer defined by the dimensions of the top electrode,and to is the thickness of the piezoelectric crystal. Note that COis the capacitance of the transducer when all mechanical vibrations are prevented, i.e., the clamped capacitance. Theelectrical equivalent of the piezoelectric layer acoustic impedance Z , is given by

R. (Ohms) where zo =

=

@* AOZO

is defined as POVO

with p. and V , being the mass density and acoustic wave velocity of the piezoelectric film respectively. The parameter Q, used in Eq. (2) is given by

where h = e/EEO, and e is the piezoelectric stress constant. Equation (2) can also be written as R. (Ohms) =

1 -

(5)

2foC0k2 where f o = Vo/Ao = V0/2t0is the half-wave resonant frequency of the transducer and k is the electromechanical coupling constant. Note that transducers of one orof integer multiples of an acoustic wavelength thickness will not generate an acoustic wave that can propagate into the substrate because there will be phase cancellation of the piezoelectrically induced stress. This implies that the absoluteBW of the transducer canr,otexceed 2f0. In practice, however, careful design is required for low VSWR (e.g., l G&) device designs this inductive component could become significant and the designer would need to include it in the overall design. To calculate the power (PIN) absorbedby Z1 we can apply standard ac circuit analysis on the equivalent circuit of Fig. 6 and find that

where the asterisk denotes complex conjugate. We are interested in the real part of PINbecause it represents the acoustic power that flows into the A 0 crystal. Setting R; = R, + R,, and with reference to Fig. 6 we can describe the voltage V , by

v, = R;V'Z1 + Z1 By substituting Eq. (27) into Eq. (26) and after some simple algebraic calculations we find that the real partof P, is given by Re[P,]

=

(Rg + R,,

IV' I2Ra + R,)' + (X, - l/dJ'

Maximum power willbe delivered to thetransducer undermatched impedance conditions. This occurs when Z1 is real and the radiation resistance matches that of the source, i.e., R, = R, and R , = 0. Underthese conditions we find (from Eq. (28)) that the maximum available power is given by

TRANSDUCER DESIGN

297

Substituting Eqs. (28) and (29) into Eq. (25) we find that the conversion loss is given by

CL (dB) =

log

(R,

+ R,, + R,,)’ +,( X , - ll0C0)~ 4R,Rll

1

For most applications the device is required to have minimum conversion losses, typically better than 3 dB. This implies that the transducer impedance is well matched to the impedance of the source, we will see in Sections 3 and this may not be possible without the use of an external matching network. Note thatin Eq. (30) we can include the effects of the bonding wire inductance (X,) by substituting the term X , - l/oCo by X , + X,, - l / ~ C o . The coefficient l? is defined as the ratio of the voltage reflected back into the source to the voltage incident on the transducer terminals and is determined by the load impedance only. With reference to Fig. 6 we find that the reflection coefficient for the untuned device is given by

r = Z1 + R,,

- Rg 2 1 + R,, + R, From Eq. (31) we see that when 2,+ R,, = R,, the reflection coefficient is zero. However in this case CL is not 0 dB because part of the incident power is dissipated by R,,. To have both CL = dB and r = 0 we require that R, = 0 and 2,= R,. If reflections do occur, at some position along the unmatched transmission line the incident and the reflected waves will add in phase to give a voltage maximum (Emax)and at another position they will add out of phase to give a voltage minimum (Emin).These positions are stationary and give rise to a standing wave. VSWR is a measure of the strength of this standing wave and is defined

where the subscripts “inc” and “ref” refer to the incident and reflected waves respectively. Based on the definitions and VSWR we can easily show that the two measures relate as follows:

and VSWR - 1 = VSWR

+

298

BEAUDET

ANDGOUTZOULIS

Note that the absolute magnitude of r can be used to describe the efficiency of power transmission via the following relationship % Power reflected = Ir12 (35) 100

Typical commercially available A 0 devices have input impedances of 50 fl and VSWR values of 1.5 < VSWR < 2.1 over the full BW of the device. This means that thereflected power is in the 4-12.6% range. Furthermore, most deflectors and modulators have maximum input drive levels of 0.52 W, whereas AOTFs can vary widely from one-half to tens of watts.

2.3 Wideband TransducerConsiderations Having developed closed-form expressions for the impedanceof the transducer we are now able. to study and analyze the effects of the various parameters of the transducer, electrode, and bonding layers. Recall that the transducerconversion loss (Eq. (30)) contains bothelectrical and acoustic components. It would be desirable to separate the effects of the two and study the corresponding responses independently, which can be accomplished if we assume low coupling figures ( k < 0.3). The majority of bulk state-of-the-art A 0 devices use LiNbO, transducers in configurations with k figures in the 0.49-0.68 range (see Section 2.4). It is thus necessary to study the combined effect of the two responses, a task that leads to quite cumbersome analytical expressions which provide little (if any) intuitive insight. The alternative solution is to use a computer program which calculatesthe input impedance, and the corresponding performance figure:, as a function of the impedance and the thickness of the electrode and the bonding layers, and over the frequency range of interest. InSection 3 we describe such a computerprogram which is based on the formulation presented in Section 2, and which can be used to study the effects of the layer parameters. Before we use this program, however, it is worthwhile to briefly examine the effects of the various layers in verysimple transducer configurations. This will help the designer gain some insight in order to succeed in the most difficult task in transducer design, namely broadband operation with minimum conversion loss. In general, when the various layers in the path of the acoustic wave have specific impedances that are different fromZ, and they behave mismatched transmission lineswhich transform the real load into a complex one. The amount of transformation depends on the degree of mismatch, and it usually results in shifted and deformed CL curves which may have significant ripples in the passband. They may also result in sig-

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nificant phase distortion, which fortunately is not a problem for most A 0 device applications. Using Mason’sequivalent circuit Sitting [4] and Meitzler and Sitting [l31 have analyzed the response of simplified acoustic transducer structures for which they assumed R, = l/o,Co. This eliminates the losses obtained with an untuned transducer andmakes the CL shapedepend on the characteristics of the acoustic layers only. For 0.5 < k < 0.7 the main findings of their work can be summarized as follows: (1) When the electrode and the bonding layers are acoustically thin (i.e.,fo/foi C 0.02, wherefoi is the halfwave frequency of the ith layer) broadband operation with minimum conversion loss is generally possible if the transducer and the A 0 crystal characteristics impedances satisfy 0.8 ZAdZo 2.0. (2) When Z, = and the electrodes are acoustically thin, a symmetric wideband response is possible if the bonding layer is a quarter-wavelength thick. (3) Minimum CL is achieved with no adsorbing layer on thesurface of the top (i.e., the surface is air-backed). (4) The top electrode should be kept as thin as possible, because as it gets thicker the overall response shifts toward lower frequencies and significant ripple may appear within the passband. When ZBM matches ZAo there is no effect, however, whenf,lf,,, < 1 the device response shifts toward higher frequencies if ZBM/Z,o C whereas it shifts toward lower frequencies when ZBM/ZAo > 1. (6) When the impedance of the bonding material is an orderof magnitude lowerthan 2,and the 3-dB BWis generally a few percent of the centerfrequency f,. Finally note that when fO/fOBM 0.002 the 3-dB BW increases to 30% ~41. In practice the situation is far more complex since we generally deal with (1) significant mismatches between Z, and ZAo, and (2) transducer structures that consist of several layers. In almost all cases we can use acoustically thin, air-backed top electrodes thereby eliminating unnecessary conversion losses and band shifting. On the otherhand and in direct analogy with microwave and optical antireflection coatingtechniques, broad, symmetric passbands can beachieved via the use of bond layer thicknesses that are multiples of a quarter-wavelength at f,. The objective is to match two media of different characteristic impedances and minimize the reflection coefficient at thevarious interfaces. This can be achieved by choosing the characteristic impedance of any bondinglayer to obtain equalreflection factors to the adjacent layers. Thus, the large reflection arising between mismatched 2, and ZAo is minimized because it is broken up into many small ones. The design of quarter-wave (N4) acoustic transmission line matching is based on its microwave counterpart [15-171, and it has been extensively

-

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applied to transducers of bulk acoustic delay lines [4,6, 14, 18, 1'91. Using the equivalent microwave formulation we can easily show that the characteristic impedance, ZB, of a single N 4 bonding layer designed to match Zo and ZAo is given by

ZB

=

ZB

=

(36) Broader acoustic BW is achieved if the front half of the transducer itself is treated as a N 4 matching layer in addition to the N 4 matching layer bonded to it In this case the characteristic impedance of a single bonding N 4 layer is given by: (37)

Fdr two N 4 bonding layers used in a Z ~ - Z B 1 - Z ~ - Z A oconfiguration, the characteristic impedances are given by zB1

z!n"23,",

(38)

ZA"Zd,",

(39)

and =

In practice it is difficult to achieve adequate dimensional control for multiN 4 configurations, and even more .difficult to identify and use suitable bonding materials with characteristic impedances that satisfy the N 4 configuration requirements. For these reasons most broadband A 0 device 'designs use a single N 4 bonding layer. Two N 4 bonding layers are used when large mismatches exist between Zo and ZAo.. Note that the N4matching scheme creates ripples in the passband which results in increased phase nonlinearities especially for the multi-N4 configurations. On the other hand, if 2,and ZAo are significantly mismatched, the use of a N4bonding layer with a characteristic impedance equaling the geometric mean of the adjacent layers will improve both the passband and the phase distortion. In all cases the BW improvements, the phase response and the dimensional sensitivity of the various N4-matching strategies must be analyzed indetail via the use of a computer program and in conjunction with the available materials choices.

2.4 Transducer,Electrode,andBonding

Materials

..

The transducer material is selected primarily because of its ele-t romechanical coupling performance (i.e., large k ) since most A 0 applications require very efficient A 0 devices. As such the typical material of choice is LiNb0, which has relatively high coupling figures for both shear and longitudinal operation (0.68 and 0.49, respectively), as well as low dissipation loss. LiNbO, is bonded in the form of a thin platelet (-250 Fm)

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and is then reduced to the properthickness via (1) a combination of coarse (3-5 pm) and fine (0.5-5 pm) mechanical polishing (using various grades of diamond compounds) and/or chemical etching, and (2) coarse mechanical polishing followed by ion milling. When optimized [21] both thinning techniques give similar results for transducer thicknesses as low as 0.45 pm. For thinner transducers the ion-milling approach is preferred because it offers higher precision and control. Using ion-milling techniques pm thin transducers for acoustic delay lines operating at 11 GHz have been reported [22]. When the ease of transducer fabrication is of primary importance, the typical material of choice is ZnO which can be deposited to the proper thickness via thin-film deposition techniques, such as vacuum evaporation or sputtering, without the need for adhesive bonding and mechanical polishing. With this technique A 0 devices operating at 10 GHz have been reported [23]. Table 1shows the acoustic properties of LiNbO, and ZnO for various crystal cuts and wave modes. The 36" Y longitudinal (L) and X shear (S) cuts in LiNbO, produce composite modes where the indicated component predominates (for more details see [24] and [25]). Note that aside these two transducer materials, there are many other less popular materials [26281 including CdS, LiIO,, Si02, AlN, PZT-7A, SPN, etc., which may be appropriate for specialized A 0 device applications. Another importantfactor that must be considered in choosing the transducer material is the acoustic and electric impedance matching. The former must be considered in conjunction with the A 0 substrate and thebonding layers used. The latter depends,among other things, on thesize and number of transducers. For example in single, large-area transducers the resulting low impedance at high frequencies makes materials with high dielectric constants unattractive. This can often be mitigated by serially

Table 1 Acoustic Properties of LiNbO, and Material

Mode

Cut

k

Velocity (dsec) ~~~~

LiNbO, LiNbO, LiNbO, LiNbO,

Y

L L S S

Y X

L S Source: Refs.

X

4800

Z (lo9 g/sec-m*)

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connecting multiple transducer sections. This solution is frequently used in AOTFs and deflectors. The choice of the transducer material is also affected by its power-handling capability. Transducer damage occurs if the classical dielectric breakdown field is exceeded. In practice, A 0 devices with 0.5-pm thin LiNbO, transducers and top electrodedimensions of 150 X 100 Fm2 canbe subjectedto CW RF powers of 500 mWwithout damage. In ZnO the critical dielectric breakdown is determined primarily by processing factors. For example, pinholes generated during the evaporation process or pressure applied to the transducer during wire bonding cause transducer failures at RF powers much lower than those determined by the critical dielectric breakdown. For these reasons LiNbO, transducers are generally accepted as having a higher power-handling capability. The choice of the bonding layer may dramatically affect the amount of acoustic energy transferred since the bonding layer provides the molecular contact between the transducer andthe A 0 crystal. Fortunately, the device designer has available a number of electrode and bonding layer materials that the acoustic impedance matching can be optimized. Table 2 shows the velocities and characteristic mechanical impedances of the most useful metals as well as of the epoxy. As Table2 shows, for both the longitudinal and shear waves there is a wide range of bonding layer impedances that cover the 2.86-69.7 X lo9 g/sec-m2 andthe 1.34-37.0 X lo9 g/sec.m2 ranges respectively. These impedance ranges cover those requiredby most combinations of transducer and A 0 substrate materials. However, when it comes to fabrication some of these materials present serious problems during deposition while some others require special handling in order to avoid oxidation and subsequent bond failure. It is thus important that the designer be aware not only the basic acoustic characteristics of these materials but also of the practical implications associated with each material. Unfortunately thereis no single source of information available that fully covers this issue. The following brief discussion indicates some of these issues and is based on the experience of several members of the Westinghouse Science and Technology Center Thin Film Laboratory As a general rule, the thickness of any metal layer should not exceed 5 Fm because the metal becomes stressed and shows a tendency to pull up from the substrate. Thus, the designer must keep the bonding layers as thin as possible as to avoid stresses and insure a good bond. For thermal deposition (the most usual bonding technique for A 0 devices) typical deposition rates are -100 h m i n , with typical deposition systems operating from 10" toTorr. Bonding temperatures in the 400-700°C range are preferred for good adhesion. Aluminum (Al) is a relatively easy and soft material to handle and evaporates at moderatetemperatures atTorr).It wetswell

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M 5 e,

C

n

(v

8 M> 3

9

U

+-

C I

I

, i

! l I

N

8,

(v

8

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to the evaporation sourceand it adheres better thanmost bonding metals, although better adhesion is achieved if it is buffered with chromium. Unfortunately it oxidizes easily, which means that the full bond operation must be performed rather quickly in order to avoid bond contamination. In most cases some type of protection is advisable usually in the form of thin (100-300 A) chromium layers. Chromium (Cr) has excellent adhesive capabilities and thus it is used almost exclusively for the support other metals. It is regularly used as the buffer layer between electrodes and transducer, and between the various bonding layer(s) and the A 0 substrate. However, it doesstress, and films thicker than 300 tend to pull up. It evaporatesat rather moderate temperatures (-837°C at lo-* Torr); however, it may oxidize and thus it should be protected. Copper (Cu) evaporates at about 727°C (at lo-* Torr), however, it is not easily deposited because it has a tendency to move toward the cold ends of the filament and eventually shorts theconnections of the filament. This forces its evaporation via a resistance source (boat) or via E-beam techniques (the lattersignificantly complicates the A 0 device fabrication). In general, it is a violent metal and oxidizes badly although it does not contaminate the depositionsystem. Epoxy resin mixed to a very low viscosity is considered as the simplest and most convenient way to form a bond. Unfortunatelyin most cases the resulting performance is unacceptable. Thisis because it is hard to control its thickness and its parallelism with respect to both the transducerand the A 0 substrate surfaces. Bonding layers as thick as 1 pm are possible but require a high degree of cleanlinesswhen deposited in order to avoid inclusion of dust particles. Furthermore its mechanical impedance may vary as a function of time and it mismatches those of most A 0 substrates and transducer materials. In general,isitnot recommended for broadband devices or for devices above 100 MHz; however, it may be acceptable for low-frequency, narrowband operation. Gold (Au) is an easy material to,work with and oneof the most popular electrode choices. Unfortunately ithas a poor adhesioncapability and thus it needs a buffer layer. Most frequently itis used as top electrode because it adheres well with gold interconnection wires. Note that for longitudinal waves its acoustic impedance is rather high and thus it is a mismatch for most A 0 substrates. Indium (In) is the easiest and softest bonding material and gives good bonds at low temperatures (-487°C atTorr) because of its high ductility. Maximumdeposited thickness should be less than 10 pm because it tends to deform under mechanical polishing. Unfortunately it is very

TRANSDUCER DESIGN lossy and at 1 GHz even small thicknesses (e.g., 1 pm) result in unacceptable loss (-8 dB). Lead(Pb)evaporates at low temperatures (-342°C atTorr) and is considered as a very difficult material to work with for reasons: (1) it oxidizes quickly after the bond is formed and thus it must be protected immediately and effectively, and (2) it is toxicand contaminates the vacuum system, which must be thoroughly cleaned for subsequent operations. The latter implies that we cannot deposit a different metal after lead is evaporated without breaking the vacuum, which is undesirable because it often leads to unacceptable surface contaminationand thus bond failure. Nickel (Ni) is a hard metal thatwets well and evaporatesat rather high temperatures (927°C atTorr).Itpresentsa problem in that it alloys rapidly with the refractorymetals of the depositionsystem. This limits the maximum thickness of the deposited layer to about 500 A. Platinum (Pt) requires a very high evaporation temperature (1292°C at Torr) and in general it is difficult to evaporate. Typical thicknesses are in the tens of Angstroms and thus it is not very useful for most A 0 devices. Much thicker films (-10 pm) can be deposited via sputtering. It does not oxidize easily and it does not adhere well. Silver (Ag) is easy to evaporate (574°C at lo-’ Torr), but it has poor adhesion properties and thus it requires a buffer layer. Note that it is one of the few metals that do not interact with the mercurous halide class of A 0 crystals with which it forms stable bonds. Tin (Sn) is also easy to evaporate (682°C at Torr) but it crystallizes in different phases and this often.results in stressed and cracked A 0 substrates. This is especially true with soft A 0 materials such as Tl,AsS,, which can be split in two if used in small sizes (e.g., 15 10 5 mm3). This problem can be eliminated if a thin layer of a soft metalbuffer (e.g., In) is used between the Sn and the A 0 substrate. Titanium (Ti) oxidizes very easily and it is hard to evaporate (1067°C atTorr).It alloys rapidly with therefractory metals and thus only small thicknesses can be deposited. If necessary, sputtering techniquescan be used to about 2 pm. Thicker films are not advised because it is a high stress metal that tends to “flake-off.” Zinc (Zn) is easy to evaporate (127°C at lo-* Torr) but it is toxic and contaminates the vacuum system. It should be avoided if not absolutely necessary. The previous discussion indicated that the choice of the bonding and electrode materialsmay affect significantly both the overalldevice design and the device fabrication. The adhesion and oxidation properties of the electrode andbonding metals make the use of a thin(100-200 A) Cr layer

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on both surfaces of the transducer as well as the surface of the A 0 crystal almost mandatory. Although for most devices these adhesive layers are (by themselves) acoustically thin, in reality they are parts of the electrodes and bonding layers which may not necessarily be acoustically thin. Thus, it is a good practice to always examine the effects of these extra layers especially if the A 0 device operates above 1 GHz. This is accomplished by calculating the composite impedance for a two-layer top electrode and treating the remaining layers as additional delay layers. Note that for transducer designs where N 4 acoustic matching requires prohibitively large (>5 pm) bonding metal thickness, the bonding metal may be replaced by a thin crystalline platelet of the appropriatethickness. Indeed, at least one such device has been reported where a 66-pm-thick SiO, platelet was used for A/4 matching between a LiNb03 transducer and a TeO, A 0 substrate. The final parameter of interest is the mechanical impedance of the A 0 crystal. This is the one parameter for which the transducer designer has no choice given that the A 0 crystal is usually determined by system considerations and rarely by the transducer design. Table 3 shows the densities, acoustic velocities, and mechanical impedances of most popular A 0 substrates as a function of the acoustic mode. Comparing Tables 1,2, and we conclude that there is a considerable overlap in acoustic impedances between transducers, bonding metals, and A 0 substrates. This implies that transducer Structures with well-matched layers are possible. As we will see this is indeed the case even for materials like TeO, and the mercurous halides (Hg,Cl,,Hg,Br,, and Hg,12) which have impedances (for shear waves along [llo]) of about an order of magnitude lower than LiNb03 transducers.

3 COMPUTER-AIDEDTRANSDUCERDESIGN Due to the large number of parameters involved, the transducer design theory described previously is best used inthe form of a computer program. To the best of our knowledge the first published computer-aided transducer design was developed by Hopp who used it for the design of bulk microwave acoustic delay lines. In Appendix B we show a FORTRAN program which is based on the methodology presented earlier, a more complex version of which has been used at Westinghouse STC for the study and development of a variety of A 0 devices, extending over the 10 MHz-4 GHz frequency range. Most of these designs have been reduced to practical devices successfully. The program is named DESIGN.FOR andit should be used in conjunction with three subroutines TLIMP, TRAIMP, and CONEFF. All programs are self-explanatory and have been

34.0

25.2

00

26.7

27.5

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307

Table 3 Selected A 0 Device Materials Material

Acoustic mode

LiNbO, LiNbO, TiO, Ti02

L [loo] [100]35° L [l101 8030L [loo] 3630L [OOl]

PbMoO, 5960 Fused Silica TeO, 6.0 TeO, GaP GaP GaP GaP Tl,AsS,

L L [OOl] [l101

6460L [l101 L [loo] 6650L [l111 S [l101 L [loo]

Density (g/cm3)

Acoustic velocity (&sec)

Impedance (lo9 g/sec.m2)

4.64 4.64

6570 3600

30.5 16.7

4.23 4.23

7930

33.5

6.95 2.2

6.0 3.72 4.13 24.2 4.13 4.13 4.13

620 5850 4130

6.2 13.3

2150

HgzCl,7.81

[l101

2.71

347

7.31 2

S [l101

2.00

273

m

m

Hg24 Tl,AsSe, 18.6

[l101 L [loo] 2050

7.7 1.96 9.05

Tl,AsS,

L [loo] 2300

6.46

Ge

L [l111

5.33

29.3

17.1

254 14.9 5500

Source: Refs.

written in a simple form which is readily executable with the Microsoft V50 FORTRAN compiler. DESIGN.FOR calculates the transducer input complex impedance and the conversion loss for 200 points over the frequency range specified by the user. The program first calculates the complex impedance (Z2RR + jZ2II) of the top electrode,which can have up to two metal layers. It then calculates the complex impedance of the bottom electrode (Z3RR + jZ3II), whichcanhave up to five metal layers plus the substrate. These complex impedances are calculated via the use of the subroutine TLIMP which calculates the complex impedance of a transmission line according

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to Eq. (6). The program proceeds with the calculation of the complex impedance of the transducer structure (ZTR + jZTI) according to Eq. (19) and via the use of subroutine TRAIMP. ZTR and ZTI are thenused to calculate the transducer conversion loss (CL) viathe subroutine CONEFF and according to Eq. (30). These calculations are repeated 200 times over the frequency range specified by the user. The results are stored in the arrays ZAR (real part of the transducer impedance),ZAI (imaginary part of the transducer impedance), and CLL (conversion loss). The user must supply an appropriatel-D plot subroutine todisplay ZAR, ZAI,and CLL as a function of frequency. DESIGN.FOR can be modified to include additional layers for either the top or bottom electrode according to the design methodology presented in Section 2. DESIGN.FOR can be used to study and analyze simple or complex transducer structures, thereby gaining useful insight in the overall transducer design. Moreover it can be used to study the relative meritsof the various broadband acoustic-matching techniques described in Section 2.3. The overall transducer design philosophy and the use of DESIGN.FOR is best demonstrated via the use of some specific transducer design examples. In the following three sections we present three such examples, and we discuss the material choices made as well as various other issues peculiar each example.

3.1 Design Example 1: 200-400

LiNbOB Transducer on

The first example involves the design of an A 0 deflector which uses a longitudinal LiNbO, 36" Y-cut transducer on T13AsS4A 0 substrate. For this example the 3-dB BW requirement is 200 MHz centered at fo = 300 MHz. The top electrode is required to have a rectangular shape of dimensions L = pm and H = 530 pm. The length L was determined from the A 0 interaction length (at A = 830 nm), whereas the height H was set from acoustic beam height requirements. For this device we will use a Au topelectrode with Cr for good adhesion on both transducerfaces and on the T13AsS4substrate. Thiswill result in a configuration Au-CrLiNb0,-Cr-X-Cr-Tl,AsS4, where X is the unknown bonding layer(s). For the first design iteration, and in order to keep the Au layer acoustically thin, we will set its thickness to 0.2 pm. (We will examine the effects of the top electrode's thickness in more detail later.) Thethickness of all Cr layers will be kept to 100 A, which is a typical thickness for Cr adhesive layers at frequencies below 1 GHz. For this iteration the only unknown data are(1) the transducerthickness to and (2) the bonding layers and their thicknesses. The former can be estimated from to = V0/2f0 = 12.3 pm.

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We note, however, that in practice the transducer must always be thinner because the resonant frequency of the transducer is alwayslower thanf, = V0/2t0.This frequency loading effect is mainlydue to (1) mass loading due to thefinite thickness of the top electrode[S] and (2) k loading [38], which occurs when k # 0, in which case the center frequency of the transducer is given by

($

tan - = For X-cut shear LiNb03 transducers ( k = 0.68) the k loading has a profound effect since it lowers the center frequency to about 77% of that predicted by fo = V0/2t0. On the other hand, for 36" Y-cut longitudinal LiNbO, transducers ( k = 0.49) the k loading lowers the center frequency to about 90% of that predicted by fo = V0/2t0.The practical aspects of the transducer loading have been analyzed in detail by Weinert [39]. The designer can use DESIGN.FOR to study the combined effects of both frequency loading mechanisms. Because of the wide BWrequirement a good initial guess for thebonding layer can be made in conjunction with a single N 4 matching layer. Use of Eq. (36) with = 34.8 lo9 g/sec-m2and Z,, = 13.3 X lo9 g/sec-m2 gives 2, = 21.5 X lo9g/sec-m2.From Table 2, we see that thebest choices are Pb (22.4 lo9 g/sec-m2),Sn (24.6 X lo9 g/sec.m2), and A1 (17.3 lo9 g/sec-m2). Given the oxidation and contamination problems with Pb, it is wise to start our design with the next best choice, namely Sn. The thickness for Sn can be determined from ts, = Vs,/4f0 = 2.77 pm. With these in mindthe initial formof the transducer structure is Au-Cr-LiNb0,Cr-Sn-Cr-Tl,AsS,, and the corresponding thicknesses are 0.2 pm-100 A-12.3 pm-100 A-2.77 pm-100 A. We are now ready to use DESIGN.FOR to optimize the overall structure. We will concentrate on CL since our objective is its minimization over a 3-dB BW of 200 MHz. Running the program for the above data we see that theoverall response is asymmetric and centered around 260 MHz (Fig. 7). Our first goal is to shift the center of the response to 300 MHz, which is accomplished by reducing the transducer thickness. By using successively smaller to values, we arrive at an optimum value of to = 10 pm. As Fig. 7 suggests, as to is reduced from 12.3 to 10 pm, CL shifts to a higher center frequency while at thesame time it becomes more symmetric. If to is reduced to less than 10 pm, CL will become even more symmetric but it will shift to an unacceptably high center frequency. Thus we will keep to = 10 pm and we try to optimize CL by varying the thickness of Sn. This isshowninFig. from whichwe see the following: (1) CL

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300

500

Frequency (MHz)

7 Effects of transducer thickness (to) on the device conversion loss (CL) for a 2.77-pm-thick Sn matching layer for design example 1.

0'

I

I

300

l

I 500

Frequency (MHz)

8 Effects of Sn thickness on the device conversion loss (CL) for a 10pm-thick LiNbO, transducer for design example 1.

31l

SIGN TRANSDUCER

becomes symmetric for ts, = 3.1 pm, (2) as tSn increases the transducer loading changes and CL moves slightly to lower frequencies, and (3) for ts, > 3.1 pm CL becomes asymmetric. We note that the choice ts, = 3.1 pm achieves both a symmetric CL response and a center frequency of 300 MHz, and it is within 10% of the value predicted by ts, = Vs,/4f0. From Fig. 8 we see that a 3.1-pm-thick Sn bonding layer does satisfy the BW requirements. In fact, theresulting 3-dB BW is 250MHz, whereas the 200-MHz BW is achieved with a ripple of 2 0.85 dB, which isacceptable even for very demanding applications. The +0.85-dB 200 MHz performance is achieved with a worst-case CL figure of -3.8 dB. Since these results correspond to a device impedance -25 Cn, significant improvement in CL can be achieved with electric impedance matching. We should now question whether better results can be achieved using the Pb orA1 choices. This is easily accomplished by repeating and optimizing the above procedure for each of these materials. The so-determined optimized results are shown in Fig. 9 for to = 10 pm, and for fPb = 1.8 pm, = 5.3 pm, and ts, = 3.1 pm. As expected, and as Fig. 9 suggests, Pb gives better results than Sn, specifically; a 200-MHz BW with a ripple only &0.45 dB. On the other hand, Sn is superior to A1 which gives a 2 1.25-dB, 200-MHz BW. From these data we conclude that the difference between Pb and Sn is not large enough to justify Pb as the material of

" 0

0 '

300

500

Frequency

9 Optimized device conversion loss (CL) for 1.8-pm Pb, 3.1-pm Sn, and matching layers with 10-pm a LiNbO, transducer for design example

5.3-pm A1 1.

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choice especially when considering the problems associated with it, and therefore Sn is the material of choice. It is worthwhile to compare the performance obtained with Sn and that obtained with ideal N4 matching layers determined from (A) the typical N4 matching microwave formulation (Eq. (36)), (B) the combination of a N4 transducer layer and a single N4 bonding layer (Eq. (37)), and (C) the combination of a N4 transducer layer and two N4 bonding layers (Eqs. (38) and (39)). Such a comparison will give us an idea of how close Sn is to an ideal N4 matching layer. Using Eqs. (36)-(39) we find that the ideal impedances are (A) = 21.5 X lo9 g/sec.m2, (B) 2, = 18.33 X lo9 g/sec.m2, and (C)Z,, = 23.04 lo9 g/sec-m2,and Zm = 15.23 X lo9 g/sec.m2 for the above three N4 matching cases respectively. Assuming that the above ideal impedances correspond to materials with sound velocities of 3000 d s e c , we find that the ideal N4 thicknesses are 2.5 pm. Using DESIGN.FOR in conjunction with the above datawe can optimize the above three ideal scenarios and arrive at thefinal results shown in Fig. 10. Note that in all cases we used to = 10 pm, and that the optimized thicknesses are (A) c, = 2.7 pm, (B) c, = 2.6 pm, and (C)tsl = 2.8 pm and tm = 2.5 pm. In Fig. 10 we also show the CL response obtained with a thin 200-A Cr bond (D). The dataof Fig. 10 suggest that (1) the thin Cr

m;[ -1

-9

.>

S

-2 I

I

I

Frequency (MHz)

Optimized device conversion (CL) for threedifferent types of ideal N 4 layers: (A) Z, = 21.5 lo9 g/sec-m2,(B) Z, = 18.33 lo9 g/sec-mz, (C) Z,, = 23.04 lo9 g/sec.mz and 2, = 15.23 109 g/sec.m2. Curve (D) corresponds to a thin 200-A chromium bond.

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bond has a 3-dB BW of 130 MHz, which is not acceptable, (2) case (A) has a 3-dB BW of 255 MHz and a 0.7-dB, 200-MHz BW, (3) case (B) has a 3-dB BWof234 MHz and a 1.7-dB, 200-MHz BW, and (4) case (C) offers the best performance with a 3-dB BW of 272 MHz and a 0.45-dB BWof 200 MHz. Although in terms ofBW flatness and actual loss all three ideal cases offer better performance than Sn, thebest case (C) advantage is only 1 dB, which means that for all practical purposes Sn gives a nearly ideal performance. The last parameter we need to examine is the thickness of the Au top electrode (cm). Figure 11 shows the CL response for to = 10 pm, C,,= 3.1 pm for cm varying in the 0.1-1 pm range. These curves show that no serious effect occurs for cm N25 (i.e., pm), however, for largercm values CL becomes asymmetric and shifts toward lower frequencies. It is thus a good practice to keep the top electrode acoustically thin that we have one less parameter to worry about! Note that a similar case can be made for the Cr adhesive layers. To demonstrate the overall design procedure and the value the program DESIGN.FOR, we build an experimental "&ASS, A 0 device according to the results of design example 1. The various layer (measured) thicknesses were TAU= 0.2 pm, all Cr layers were 100-A LiNbO, = 9.7 pm, T,, = 3.0 pm, and the top electrode dimensions were L = 450 pm and H = 500 pm. The CL response of the device without any additional

0 -9

5-

-8

E -7

9

-6

.-

-5

2 >

6c

-2 0

Frequency (MHz)

11 Effect top electrode thickness on the device conversion design example 1.

(CL)

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electric impedance matching is shown in Fig. 12. we can see there is very good agreement with the calculated response, especially if we take into account the slightly thinner transducer and Sn layers. CL is centered at slightly higher frequency; however, it has a very symmetric shape and 'a 3-dB BW of 265 MHz, which is in good agreement with the 250-MHz predicted figure. The actual CL value at the center of the CL curve is at -3.4 dB, whereas the program has predicted -3.8 dB. Note that the dip of the curve is about - 1.1dB fromthe highest peak, whereas DESIGN.FOR had predicted - 1.7 dB. To our experience the results of DESIGN.FOR agree very well with the results obtained from actual devices. Quite often the actual CL is broader and smoother than the calculated one, the CL of the design example 1 being one such example. In practice the control of the transducer and metal layers thickness is such that the actual data agree with those from DESIGN.FOR to about * O S dB.

3.2 Design Example 2: 20-40 MHz LiNbOB Transducer on Hg,CI2 Substrate The second design example involves an anisotropic (birefringent) shear [l101 Hg2Cl, A 0 cell with a 3-dB BWof 20 MHz centered at 30 MHz and a shear LiNbO, X-cut transducer. This is a challenging problem because

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there is a large difference between the impedances of LiNbO, and Hg2C12 (22.6 X 10 g/sec.m2 versus 2.71 X lo9g/sec.mz, respectively). Furthermore the selection of the bond layer material is dictated not only by impedancematching considerations but also by the need to form a bond that will be mechanically strong and stable,and chemically compatible with the Hg2C12 substrate. This latter consideration severely limits the choice of bond materials. It is well known [40, 411 that most metals in contact with Hg2Cl, are not stable and willchemically react. In these cases the metal film becomes severely corroded, whereas the crystal surface becomes greatly pitted and deformed. It is also known that Ag films deposited on Hg,Cl? are stable but do undergo a chemical reaction to form a complex Ag compound. Most other metals subsequently deposited on the Ag are also chemically unstable. One exception is Pb, which in contact with the Ag layer substrate is chemically stable and a bond with good mechanical integrity can be formed by vacuum deposition. The alternative solution in to first cover the Hg2C12substrate with an inert layer and then deposit the desired metal. This solution can be implemented with the combination of MgF, (V = 4200 m/sec and = 12.81 X lo9 g/sec.m2) and In. For this design example we can use DESIGN.FOR to analyze the performance of the above two bond options. For the anisotropic A 0 interaction (at A = 0.6328 pm), the length of the top electrode must be 3.35 mm [35]. Assuming that there is no restriction on the height of the top electrode, we could choose H such that the resulting top electrode area brings the real part of the transducer impedance as close to 50 Cl as possible. This may eliminate the need for an external electric impedance matching network thereby simplifying the overall device fabrication. For both bond options we will use an acoustically thin (0.2 pm) Ag top electrode with an adhesive layer of Cr (100 A) on the top surface of the transducer. Use of the program shows that for the Pb/Ag option the transducer thickness is 70 pm and theoptimum Pb thickness (for N 4 matching) is 8.0 pm. This is a rather thick Pb layer and may result in bond peel-off. To eliminate this risk we can deposit two 4-pm-thick Pb layers with an acoustically thin (100 A) Ag layer between them for better adhesion. Thus, for this option the optimum transducer structure becomes Ag-Cr-LiNb0,Ag-Pb-Ag-Pd-Ag-Hg,Cl,with the following corresponding thicknesses: 0.2 pm-100 A-70 pm-100 A-4.0 pm-100 A-4.0 pm-2000 A. For the In/MgF2 option the transducer thickness is 66 pm, the In layer is 8.1 pm thick and the MgF2layer is 0.2pm thick. For this bond the complete transducer structure is Ag-Cr-LiNb0,-Cr-In-MgF2-Hg2C12 and has the following thicknesses: 0.2 pm-100 A-66 pm-100 A-8.1 pm-2000 A. The resulting, optimized CL responses are shown in Fig. 13. For comparison purposes we also show the CL response for the ideal case of two

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13 Optimized conversion loss (CL) for (a) 8.0-pm thin Pb with 2000 and 70-pm-thick transducer, (b) 8.1 pm thin In with 2000-a thin MgFz and a 66-pm-thick transducer, and (c) two ideal matching layers 25-km-thick with Z,, = 9.1 X lo9 g/sec.mz and Z, = 3.67 X lo9 g/sec-m2 anda66-pm-thick transducer.

25-km-thick N 4 matching layers with Z,, = 9.1 X lo9g/sec-m2and 2, = 3.67 x lo9 g/sec.m2, respectively. Both ideal layers are assumed to have a sound velocity of V = 3000 &sec and are used in conjunction with a 66-pm-thick transducer. The dataof Fig. 13show that theideal bond option offers the broadest and smoothest CL response, with a -0.75-dB average loss over the band interest. In terms practical solutions and for maximum BW, Pb/Ag is the best choice, whereas for.minima1ripple In/MgF2 is preferred. Note that the 1.3-dB ripple the Pb/Ag option can be reduced if we take advantage of the birefringent A 0 bandshape [42] whichcan be used to weight down the two lobes of the CL response. The Pb/Ag bond offers a 3-dB BW 23 MHz, which satisfies the design goal. Furthermore over the 20-40 MHz band the average insertion loss is about 1.5 dB and the average real impedance is 57 CR. The latter could be acceptable for operation with a 50 CR source and it was accomplished by optimizing H . ‘Figure 14 shows the dramatic effect of H on CL for the optimized Pb/Ag bond and for L = 3.35 mm. It can be seen that the H = mm choice results in a minimal-loss, very symmetric CL response. We note, however, that the use rectangular top electrodes (such as the3.35 X 4.0 mm2 electrode of this example) in conjunction with highly acoust-

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Effect of the top electrode height ( H ) on the device conversion loss (CL)for the optimized PbIAg bond design example 2 with L = 3.35 mm.

ically anisotropic A 0 materials (such as Hg2C12or Te02)often results in unacceptable acoustic spread, which places a severe limitation on long aperture A 0 deflectors. This important effectcan be counteracted by the application of apodized electrodes in which the shapeof the top electrode is used to control the spreadingof the acoustic energy. Insuch cases minimization of the acoustic spread shapes the top electrode and may 50-Q impedance. In thesecases matching prevent scaling the total area for of the transducer impedance to 50 Q must be achieved via an external impedance matching network. We have fabricated an experimental Hg2C12device with the optimum layer thicknesses but with a X 3.35 mm2square top electrode.Figure 15 shows the measured CL response which is in very goodagreement with the response predicted via the computer program. Once again the measured CL response has asomewhat broader 3-dB BW (27 MHz versus 23 MHz); however, it has a slightly deeper midband dip. The latter is due mainly to the use of smaller H and secondarily to small mismatches occurring at the Ag-Hg2C12interface. We close this design example by noting the practical implications of the Pb/Ag bond choice. The Pb/Ag structure is very sensitive to oxidation and deterioration and additional features are required for a stable structure. To prevent the exposed Pb film from oxidization, the exposed Pb surface must be protected by a coating of a thin Ag film after the

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Measured conversion loss (CL) of an experimental untuned Hg,Cl, device build according to design example 2. The top electrode dimensions were 3.35 X 3.35 mm2, the Pb layer was 7.0 km thick and the Ag layer 2000 thick. transducer bond has been made. After the LiNbO, transducer is bonded to the Hg2Clz we need to grind and polish the transducer to 70-pm thickness. This is usually done in a water slurry of polishing compound which would allow moistureto bedrawn into the Pblayer between the transducer and the crystal. The Pd bonding layer in contact with the moisture would deteriorate very quickly in this process. This danger can be eliminated by using a thin film of UV light-cured cement around the periphery of the LiNbO, prior to grinding. This forms a seal that keeps moisture from the Pb interface. A diagram showingthe elementsof the resulting rather complex transducer structure is shown in Fig. 16.

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Design Example 3: 1.35-2.7 GHz LiNb03 Transducer on LiNb03 Substrate

The final design example involves a high-frequency anisotropic shear [loo] 35" LiNbO, A 0 deflector centered at 2.0 GHz with a 3-dB BW of 1.35 GHz. For this example the length of the top electrode is equal to the birefringent interaction length, which is 115 pm at 830 nm. Using Eqs. (36)-(39) we find that the impedances for the three ideal N 4 matching options are (1) Z , = 19.43 lo9g/sec-m2,(2) 2, = 18.47 X lo9 g/sec.m2, and (3) Z,, = 19.85 X lo9 g/sec.m2 and Zm = 17.44 lo9 g/sec.mz.

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From Table 2 we see that only Ag and Cu have acceptable impedances, and thus we will use these in conjunction with Au top electrode and 75A-thick adhesive Cr layers. Use of DESIGN.FOR shows that the resulting three optimized transducer structures are (1)Au-Cr-LiNb0,-Cr-Cu-Cr-LiNbO, with thicknesses 750 A-75A-0.58 km-75 81-0.32 pm-75 A, (2) Au-Cr-LiNb0,Cr-Ag-Cr-LiNbO, with thicknesses 750 A-75 A-0.62 pm-75 A-0.36 pm-75 A, and (3) Au-Cr-LiNb0,-Cr-Cu-Ag-Cr-LiNbO, with thicknesses 750 A-75 A-0.62 km-75 A-0.3 pm-0.2 pm-75 A. For all cases the top electrodeheight H is 50 pm and was determined with the objective of maximizing the real electric impedance (10-12 Cl for all cases). Smaller H values will increase the impedance even more, but the resulting top electrode surface will be rather small for bonding the Auconnection wire. The CL responses of the above three structures (Fig. 17) have a 3-dB BW of at least 2 GHz, and thus they all satisfy the design BW goal. The two N4-layer bond does offer the smoothest BW, but it is the most complicated. On the other hand, response the of the Cu structure is very similar with that of the two N4-layer structure and thus it is preferred if Cu is to be used. The response of the Ag bond has the smallest loss(1 dB less than the other options) and a shape that can somewhat correct the midband dip resulting from the wideband anisotropic A 0 interaction. Note that over

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Optimized device conversion (CL) for (a) 0.32-pm thin Cu and 0.58-pm thin transducer, (b) 0.36-pm thin and 0.62-pm thin transducer, and (c) 0.3-pm thin Cu, 0.2-pm thin and 0.55-pm thin transducer.

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the band of interest theaverage real impedances for the three bond options are 10, 11, and 12 R respectively, and thus further impedance matching via an external matching network is required. We emphasize that for high-frequency designs the tolerances of the various thicknesses are very critical and high deposition accuracy is required. This can bedemonstrated in the presentdesign example by varying the thickness of the top electrode. The resulting effect is shown in Fig. 18, where we vary the thickness of the Au layer from to lo00 to 1250 A. It can be seen that this rather small change has a profound effect on the overall response, and it can significantly deteriorate the overall performance. Similar effects can be observed by varying the adhesive Cr layers from to 150 or by varying the transducer thickness by 0.1 pm. 4 ELECTRICAL MATCHING AND POWERDELIVERY The last part of the transducer designinvolves the electrical matching network and the delivery of electrical power to the transducer electrode area. For this problem we must consider the amount and uniformity of the reflected electric power in addition to theconversion loss parameter used in the bond design. The amount of the reflectedpower relates to the efficiency of power transfer, whereas the uniformity of the reflections affects the amountof ripple in the responseof the device as well as its phase linearity. In general, these quantities can be determined by plotting the VSWR as a function of frequency. Figure 19 shows a plot of the loss (in dB) resulting from the reflections as a function of VSWR. The plot of Fig. 19 is based on the formulation discussed in Section 2.2 and described via Eqs. (32)-(35). In practice the VSWR specification is lessthan 2.1, which corresponds to about 0.6 dB of power loss. Tighter VSWR specifications call for lower reflections that are usually based on the driving amplifier response to a nonideal load or response uniformity rather than a lower absolute conversion loss. The design of efficient electrical impedance-matching networks is a wellknown problem in electrical and microwave engineering, and it has been well formulated and analyzed in various previous publications (see, for example, Furthermore there are severalcommercially available, inexpensive, electrical impedance-matching software packages which can efficiently solve very complex impedance-matching problems. The user of these softwarepackages is typicallyrequired to provide the measured complex impedance values of the unmatched device, as well as a set of desired specifications which include the device impedance and VSWR. Based on these data theprogram can calculate variousmatching networks of varying complexity whichsatisfy the desired specifications. (An example of an

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interactive electric impedance-matching network program is contained in the program in the Appendix A, providedby the St. Petersburg State Academy of Aerospace Instrumentation.) Inview of the availability of the formulation, analysis, and computer-aided design solutions, wewill not discuss this problem in detail. Instead, we will provide a qualitative overview emphasizing problems particular to the various types of A 0 transducer structures. 4.1 Simple Two-Element Matching Circuit A simplified electrical equivalent circuit for a typical A 0 device is shown in Fig. 20. For low-frequency devices ( C l GHz) with untuned impedances that result to a few dB of conversion loss, a modest matching network can be produced by resonating the parallel-plate capacitance with a parallel coil and following with a series reactive element to cancel any residual reactance. Figure 21 illustrates this approach with a slow shear TeOzdevice example. The device has a 40-pm-thick shear LiNbO, transducer with a 0.5-pm-thick Au top electrode and an overall active area of 8 mm2. The bond layers from the transducer toward the TeO, substrate consist of a 0.1-pm Au, 1.3-pm Cu, 7.6-pm Sn, 1.3-pm In, and0.1-pm Au. The desired operating frequency extends from 37.5 to 62.5 MHz. The untuned device impedance is shown as curve A on the Smith chart of Fig. 21 (a detailed

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20 Simplified electrical equivalent circuit for typical ducer structures.

A 0 device trans-

explanation of the Smith chart can be found in [45]). shunt inductor of 470 nH translates the impedance along a constant-conductance circle (curve B). series inductance of 96-nH centers the matched impedance, curve C, around the real axis. Figure 22 shows the effect of impedance matching in terms of reflection loss. The untuned loss was less than 2 dB over the passband and the ripple was over 1.5 dB, whereas the tuned conversion loss is no more than 0.5 dB and the ripple has been reduced to under 0.3 dB. The corresponding effect on VSWR is shown in Fig. 23 and itmay be significant for the overall system performance. Fig. 23 shows, the untuned VSWR of 4 is reduced to 2. In general, this simple two-element matching technique very often produces a device useful for laboratory experiments. In the frequency range of a few hundred megahertz to the order of 1 GHz theshunt inductorcan often be implemented right on the device transducer surface with a bond wire shunting the active electrode to ground. photograph of an processor utilizing two slow shear TeO, devices similar to theexample described is shown in Fig. 24.Chip inductors are mounted on printed circuit cards covering the device electrodes. It can be seen that thesimple matching network allowsa compact implementation.

In Chapter 1 we described the advantages of using phased array transducers, one of which is the control of the overall transducer impedance by placing electrodes in series and/orin parallel combinations. Figure 25 shows the electrode configuration used for a longitudinal TeO, operating from 250 to MHz. For this example placing each half of the electrodes in a common busincreases the device impedance, over thatof a single commonarea device, by a factor of 4. For anuncut array half of the elements would connect to theincoming signal and half would connectto thesignal return. For the device of Fig. 25 the original area is cut in half for each segment

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21 (Bottom) Example of a two-element matchingnetworkforaslow shear TeO, deflector covering the MHz range. (Top) Curve A of the Smith chart shows the impedance of the untuned device, curve B shows the effect a 470-nH shunt inductor, and curve C shows,the effect of a series 96-nH inductance.

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Figure 24 processorusing two slow shear TeO, devices similar to that discussed in the example of Figure 21. (Courtesy of Harris Corporation.)

RETURN^ 25 Twelve-electrode phased arraytransducerconfiguration used for a longitudinal TeOz device operating from 250 to 450 MHz.

TRANSDUCER DESIGN and the two segments are electrically connected in series. This must be done as the opposing sides of the bond area operate at a different electrical potential. The equivalent impedance area now consists of four sets of series electrodes, each containing 3 of the total 12 electrode areas. This produces a design area of 1/4 (sections) times 3/12 (elements). The resulting impedance for this configuration is about R which is much more acceptable than the under 1R impedance that would be produced by the full area in parallel, or even the 2.5-R impedance possible withthe uncut phased array. We recall that the transducer design methods presented earlier can be applied to any transducer area given that the resulting impedances are scalable. In practice, however, and in order to view the actual untuned conversion loss, it is helpful to reduce the design area so that it corresponds to the effective area achieved after the appropriate interconnections. For this device a four-element ladder matching network can be used as shown in Fig. 26. The interconnecting bond wires are combined into an external series inductor of about 5 nH in series with the device bond impedance. The impedance of this structure is plotted in the Smith chart of Fig. 26 as curve A. The first stage of the matching network is an additional 9-nH series inductor and a 12-nH shunt inductor the effect of which is shown in curve B. The matched impedance (curve C) is then obtained with an additional 5-nH series inductance and a 13-pF shunt capacitor at the RF connector. The device was constructed with a 7.0-pmthick LiNb03 transducer and has an effective area 0.15 mm2. The top electrode is a 0.6-km-thick Au layer and the bond is a 0.4-pm In layer between two 0.05-pm Au layers. The unmatched device had an untuned conversion loss of about 1.5 to 3.5 dB over the passband (Fig. 27). After matching, the conversion loss is reduced to less than 0.5 dB. Figure 28 shows the corresponding unmatched and matched VSWRs. It can be seen that the worst-case-matched VSWR is below 1.8 over the full passband. Figure 29 shows the actual TeO, device. Air-wound inductors were adjusted (while the performance was measured via a network analyzer) by changing the spacing between windings. At these operating frequencies (i.e., below 500 MHz) adjustable capacitors may also be used, 4.3 Multichannel Power Delivery Often implementation constraints can dominate the selection of a power delivery network. This is especially true for the networks used in conjunction with multichannel A 0 devices. Figure 30 shows a 64-e1ectrode7 200-pm, center-to-center-spacing, power delivery network used for a 64channel shear GaP A 0 deflector. The .network provides spatial separation for theinco.ming signal lines. The transmission lines serve several purposes:

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Figure 26 (Bottom) Four-element ladder matching network for the phased array transducer of the longitudinal 250-450 MHz TeO, device. (Top) Curve A of the Smith chart shows the impedance of the unmatched device, curve B shows the effect of the 9-nH series inductor and the 12-nH shunt inductor, and curve C shows the effect of the full matching network.

(1) they provide a matching element; (2) they separate the 64 channels spatially; and (3) they maintain the element-to-element electrical isolation. The implementation of the matching network (a section of which is shown in Fig. 31) is constrained to a length of 1.3 in. This allows sufficient length to separate the connectors for the incoming signals while limiting the pack-

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Figure 27 Untuned and tuned conversion loss for the four-element ladder matching network example of Figure 26.

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29 Photograph of the phasedarray TeOzdevice showing the four-element matching network. (Courtesy of Hams Corporation.)

age to a reasonable size. The shunt inductor at the device load (shown in the two previous matching-network examples) isomitted here dueto electrical crosstalk considerations. The bond wires are kept as short and as close to the ground planes as possible. Curve A in the Smith chart of Fig. 31 shows the impedance of a single channel including a very small bond inductance of about 0.2 nH. The66-R transmission line rotates the impedance (curve B), allowing a nominal shunt capacitance of 3 pF tobring the response to the real axis (curve C). The untuned conversion loss shown in Fig. 32is obtained from design values of a 0.2-pm-thick Au electrode layer of 0.17 mm2area ona 1.44-pm-thick shear LiNb03 transducer. The bond is a 0.3-km-thick Ag layer sandwiched between two 0.2-pm-thick Au layers. Note, unlike the previous examples, the measured values are further from the design values. This is because as the operating frequencies increase, the simple transducer model described earlier does notcompletely characterize the device impedance. Parasitic field couplings become in-

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30 Power delivery network for a 64-channel shear GaP (Courtesy of Harris Corporation.)

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creasingly significantat higher operating frequencies, requiring special fabrication care especially above 1 GHz. The power delivery network lowers the matched VSWR to about 2.1 (Fig. 33). Figure shows the complete package of the "channel deflector. While preserving a compact package size, the device is able achieve better than 30-dB signal isolation; an important criterion unique to multichannel device operation.

GOUTZOULIS AND BEAUDET

31 (Bottom) Section of the &channel power delivery network. (Top) Curve A of the Smith chart shows the impedance of a single channel including a bond inductance of about 0.2 nH. Curve B shows the effect of a transmission line which rotates the impedance thereby allowing a shunt capacitor of 3 pF to bring the response to the real axis (curve C).

4.4 High-FrequencyDeviceConsiderations There are some general guidelines in selecting an approach to electrically match A 0 devices. At frequencies below 1 GHz lumped-element designs provide good results with minimal investment in components and good

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34 Photograph of the complete 64-channel shear GaP device package. (Courtesy of Hams Corporation.)

flexibility in implementation.As operating frequencies extend above 1 GHz matching withdistributed components yields more acceptable results. This requires fabrication of transmission line substrates. Design iterations can be reduced by careful attention to parasitic coupling as a modification to the starting point impedance. At frequencies above 2.5 GHz wave mode propagation becomesa concern. The RF power delivery accesses the device electrode surface in a coplanar manner throughbond wires for signal path

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and return. Transmission line networkscouple better when the device interface includes a coplanar wave launch. This level of RF design requires a field-competent design package. Although many devices have been assembled using less sophisticated approaches to matching, one should not expect reliable implementation using lumped elements o r even impedancemodeled transmission lines at frequencies above 2.5 GHz. When accurate models are not available, careful measurement of the device impedance in the final field conditions (i.e., with appropriate mounts andcovers) may produce arealistic estimate of parasitic elements toallow a successfulmatch implementation. An estimate of the match stability may be judgedby applying a literal “ruleof thumb.” If the VSWR changes with yourthumb on the device cover, stray coupling is likely to be a problem in operation.

ACKNOWLEDGMENTS Akis Goutzoulis thanks Bob Weinertof Westinghouse STC for many fruitful philosophical discussions and technical recommendations concerning the optimization of acoustic impedance-matching procedures. He also thanks Betty Blankenship, Harry Buhay, andMilt Gottlieb, also of Westinghouse STC, for their expert technical advice concerning the use of various metals as bonding layers.

REFERENCES 1. Mason, W. P,, Electromechanical Transducers and Wave Filters, 2nd ed. Van Nostrand, New York, 1948, pp. 201-209, 399-404. 2. Berlincourt, D. A., Curran, D. R., and Jaffe, H., Physical Acoustics, Vol. 1A (W. P. Mason, ed.), Academic Press, New York, 1964, pp. 233-242. 3. Sitting, E. K., Transmission parameters of thickness-drivenpiezoelectric transducers arranged in multilayer configurations,IEEE Trans. Sonics Ultrasonics, SU-14, 167-174 (1967). 4. Sitting, E. K., Effects of bonding and electrode layers on the transmission parameters of piezoelectric transducers used in ultrasonic digital delay lines, IEEE Trans. Sonics Ultrasonics, SU-16,2-9 (1969). 5. Sitting, E.K., Warner, A. W., and Cook,H. D., “Bonded Piezoelectric Transducers for Frequencies Beyond 100 MHz,” Ultrasonics, 108-112, April 1969. 6. Kossoff, G . , The effects of backing and matching on the performance of piezoelectric ceramic transducers, IEEE Trans. Sonics Ultrasonics, SU-I3, 20-30 (1966). 7. McSkimin, H. J., Transducer design for ultrasonics delay lines, J. Acousr. Soc. A m . , 27, 302-309 (1955). 8. Reeder, T. M., and Winslow, D. W., Characteristics of microwave acoustic transducers for volumewave excitation, IEEE Trans.MicrowaveTheory Techniques, MTT-17, 927-941 (1969).

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9. Hopp, T., Computer-aided design of bulk microwave acoustic delay lines, Report number NTIS (1974). 10. Hueter, T. F., and Bolt, R. H., Sonics: Techniques for the Use Sound and Ultrasound in Engineering and Sciences, Wiley, New York, 1965, p. 39. A thin film mosaic transducer for bulk 11. Weinert, R. W., and deKlerk, waves, IEEE Trans. Sonics Ultrasonics, SU-19, 354-357 (1972). 12. Onoe, M,,Relationships between input admittance and transmission characteristics ofan ultrasonic delay line, IRE Trans. Ultrason. Eng., UE-9,42-46 (1962). 13. Meitzler, A. H., and Sitting, E. K., Characterization of piezoelectric transducers used in ultrasonic devices operating above 0.1 GHz, J . Appl. Phys., 40(11) (1969). 14. Inamura, T.,The effect of bonding materialson the characteristics of ultrasonic delay lines with piezoelectric transducers, Japan. J. Appl. Phys., 9, 255-259 (1970). 15. Collin, R. E., Theory and design of wide-band multisection quarter-wave transformers, Proc. IRE, 43, 179-185 (1955). 16. Riblet, H., General synthesis of quarter-wave impedance transformers, IRE Trans., MTT-5, 36-43 (1957). 17. Young,L., Tables for cascaded homogeneous quarter-wave transformers, IRE Trans., MTT-7,233-237 (1959). 18. Kittinger, E.,and Rehwald, W., Improvement of echo shape in low impedance materials, Ultrasonics, 211-215 (1977). 19. Goll, J., and Auld, B., Multilayer impedance matching schemes for broadbanding of water loaded piezoelectric transducers and high Q electric resonators, IEE Trans. Sonics Ultrasonics, SU-22, 52-53 (1975). 20. Desilets, C., Fraser, J., and Kino, G., The design of efficient broad-band piezoelectric transducers,IEEE Trans. Sonics Ultrasonics, SU-25,115-125 (1978). 21. Bagshaw, J. M., and Willats, T. F., Anisotropic Bragg cells, GEC J . Res., 2, 96-103 (1984). 22. Huang, H., Knox, J. D.,Turski, Z., Wargo, R., and Hanak, J. J.,Fabrication of submicron LiNbO, transducers for microwave acoustic (bulk) delay lines, Appl. Phys. Lett., 24, 109-111 (1974). 23. Kirchner, E. K., Deposited transducer technology for use with acousto-optic bulk wave devices,SPZE, 214 (acousto-optic bulk wave devices), 102-109 (1979). 24. Warner, A., Onoe, M,, and Coquin, G. A., Determination of elastic and piezoelectric constantsfor crystals . . . ,J. Acous. A m . , 42,1223-1231 (1967). 25. Foster, N.F., and Meitzler, A.H., Insertion loss and coupling factors in thinfilm transducers, J . Appl. Phys., 39, 4460-4461 (1968). 26. Meitzler,A. H., in Ultrasonic Transducer Materials (0.E, Mattiat, ed.), Plenum, New York, 1971. 27. Jaffe, H., and Berlincourt, D. A., Piezoelectric transducer materials, Proc. IEEE, 53, 1372-1386 (1965). 28. Spenser, E. G., Lenzo, P. V., and Ballman, A. A., Dielectric materials for electro-optic, elastooptic, and ultrasonic device applications, Proc. IEEE, 55, 2074-2108 (1967).

TRANSDUCER DESIGN Temperature dependence of the elastic, 29. Smith, R. T., andWelsh, F. piezoelectric, and dielectric constants of lithium tantalate and lithiumniobate, J . Appl. PhyS., 42,2219-2230 (1971). 30. Gottlieb, M., Buhay, H., andBlankenship, B., WestinghouseScience & Technology Center, Pittsburgh, Pennsylvania,January 17,1992, private communication. 31. Slobodnik, A. J., Jr., Delmonico, R. T., and Conway, E. D., Microwave Acoustics Handbook,Vol. 3, Bulk Wave Velocities, TR-80-188,National Technical Information Services, Springfield VA, 1980. 32. American Institute of Physics Handbook, McGraw-Hill, NewYork, 1963, pp. 3-88. 33. Katzka, P., and Dwelle, R., Large spectral bandwidth acousto-optic tunable filters, Poster paper,IEEE I986 Ultrasonics Symposium, Williamsburg, VA. 34. Chang, I. C., Selection of materials for acousto-optical devices, Opt. Eng., 24, 132-137 (1985). 35. Goutzoulis, A. P., andGottlieb, M., Characteristics and designof mercurous halide Bragg cells for optical signal processing, Opt. Eng.,27,157-163 (1988). 36. Elston, G., Amano, M., and Lucero,J., Material tradeoff for widebandB r a g cells, Proc. SPIE (Advances in Materialsfor Active Optics),567,150-158 (1985). IEEE 1988 Ultrasonics 37. Chang, I. C., High performance wideband Bragg cells, Symposium, 1988, pp. 435-438. 38. Onoe, M., Tiersten, H. F., and Meitzler, A. H., Shiftin the location of resonant frequencies causedby large electromechanical coupling in thicknessmode resonators, J . Acoust. Soc. A m . , 36-42 (1963). 39. Weinert, R.W., Very high-frequency piezoelectrictransducers, IEEE Trans. Sonics Ultrasonics, SU-24, 48-54 (1977). 40. Gottlieb, M., Goutzoulis, A. P., and Singh, B., N. Mercurous chloride (HgzClz) acousto-optic devices,Proceedings of the IEEE Ultrasonics Symposium, 1986, pp. 423-427. 41. Gottlieb, M., Goutzoulis, A. P., and Singh, N. B., Fabrication and characterization of mercurous chloride acousto-optic devices, Appl. Opt.,26,46814687 (1987). 42. Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J . Quantum Electron., QE-3, 85-93 (1967). 43. Bademian, L., Parallel-channel acousto-optic modulation, Opt. Eng., 25,303308 (1986). 44. Mattaei, G. L., Young,L., and Jones, E. M. T., Microwave Filters, Impedance Matching Networks and Coupling Structures, McGraw-Hill, New York, 1964. 45. Rosenbaum, J. F., Bulk Acoustic Wave Theory and Devices, Artech House, Norwood, MA, 1988.

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6 Acousto-Optic Device Manufacturing Vjacheslav G. Nefedov St. Petersburg State Academy

Aerospace Instrumentation St. Petersburg, Russia

Dennis R. Pape Photonic Systems Incorporated Melbourne, Florida

1 INTRODUCTION Acousto-optic (AO) devices combine physical features found in both ultrasonic delay lines and optical windows. Like an ultrasonic delay line, the A 0 device has a piezoelectric transducer mechanically bonded to an acoustic substrate, as shown in Fig. 1. Also like an ultrasonic delay line, an impedance-matching network is used to efficiently couple RF energy into the transducer. Like an optical window, the acoustic medium is a transparent optical block polished to a high degree of parallelism, flatness, and surface quality. It is not surprising, then, to find that the manufacture of A 0 devices combines technologies and processes found in both the manufacture of ultrasonic delay lines and optical windows. Indeed the proliferation of A 0 device manufacturing capability throughout the world is a result of the mature development of ultrasonic delay line and optical window manufacturing processes and the relative ease with which they can be combined to produce an device. A flowchart containing the primary steps in the manufacture of an A 0 device is shown in Fig. 2. The manufacturing process starts with the growth of the A 0 device material, and, if a platelet transducer is used, the transducer material as well. The A 0 device material, usually in boule form, is oriented and rectangular optical blocks, with dimensions and orientation determined by the device design, are cut. The optical'faces as well as the

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340 Piezoeleclrictransducer structure

\

RF driver connection

Impedance matching network

\

Optical cell block

Acousto-optic device showing piezoelectric transducer structure with impedance-matching network and transparent optical cell block.

transducer bonding surface of the A 0 device optical block are then polished. An antireflection coating is then applied to the optical faces. If a platelet transducer materialis used, this material is also,oriented and cut, again with dimensions and orientation determined by device design. The transducer platelet material is also polished. This completes that portion of the manufacturing process that utilizes optical window processing techniques. The A 0 device optical blocks are now ready for the application of the transducer. Here manufacturing techniques used in the production of ultrasonic delay lines are employed. Two types of transducers can be used: thin film and platelet. If a thin-film transducer is used, the device optical block is placed in a vacuum chamber where the thin film transducer is deposited. If a platelet transducer is used, the platelet transducer is prepared and bonded to thedevice optical block. The platelet is then reduced in thickness to achieve the appropriate device center frequency. A metallic electrode is then deposited on top of the piezoelectric material. An impedance matching circuit is designed to match the impedance of the A 0 device to the electronic driver. The A 0 device and theimpedancematching circuit are then mounted in the device housing. An RF connector on the housing is electrically connected to theinput side of the impedance-matching circuit while wires from the output side are bonded to the topelectrode of the A 0 device. This completes that portion of the manufacturing process that utilizes ultrasonic delay line processing techniques. Finally, an acoustic absorber is attached to the end of the device to frustrate acoustic reflections in the device. This completesthe fabrication of the A 0 device.

ACOUSTO-OPTIC DEVICE MAh'UFAClURlNG

I

Materialgrowlh

341 Manufacturlng steps

I

I

Malerial orientation

I Optical windowblock sawing

I Optical window Mock surfacepolishing

I Antirefledion coating Thin

Platelet

I

t

Bottom electrodelbond layer deposition

Bottom electrodedeposition

a I Platelet bonding

Plezdeclric lhin-Wm deposition

Platelet

1

I

Top eledrode deposition

I Impedance matching circuit

I Wue bonding

I

pcoustic absorber

2 Flowchart

acousto-optic device manufacturing steps.

2 ACOUSTO-OPTICDEVICEOPTICAL WINDOW MANUFACTURING The starting point in the manufacture an device is the preparation the device optical window block. The choice the device block material is usually determined by the type of device being produced and the specific device performance required, as discussed in Chapters 2, and 4. Table 1 shows the parameters of the most often used materials.

X W

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Material Growth In general, the starting material for the A 0 device optical window block as well as the platelet transducer is a boule of single-crystal A 0 material. A 0 materials are grown usingstandard crystal growth techniques including directional sublimation, the Bridgman technique, and the Czochralski technique (someA 0 devices are also made from amorphous andpolycrystalline materials) [l].In the Czochralski growth technique, as shown in Fig. 3, powder of the crystal to be grown is placed in a platinum (or other nonreacting material) crucible. A heating element surrounding thecrucible is used to melt the powder. The temperature of the melt is also precisely controlled with the heating element during growth. A seed crystal, attached to a rotating rod (typically 60 rpm), is lowered into the melt. the rod is slowly withdrawn, material from the melt solidifies on the seed. Continued slow withdrawalof the rod,typically at ratesof 1to 10 mmh, results in the formation of a crystal boule.

t

-

3 Czochralskicrystalgrowthtechnique

[l].

344

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2.2 Material Orientation After the boule is grown, the direction of the principal crystal axes are determined. These axes can be found knowing the growth direction and the symmetry of the crystal as well as by observing the decayed crystal faces on the surface of the boule. The directionof the axes can be determined, for a piezoelectric material, by knowing the sign of the piezoelectric modulus and measuring the response of the crystal to a clamping deformation [2]. piezoelectric tester used to measure the polarity of the piezoelectric response is shown in Fig. The procedure used for determiningthe direction of the crystalline axis in a piezoelectric material is illustrated in Fig. 5 for L i m o 3 grown along the z axis. The crystalline facet along the boule can be used to find the position of the crystal plane of symmetry which is the yz plane. Thus, the position of the y axis is determined. In order to find its direction, the polarity of the piezoelectric response to clamping deformation applied along y axis at the point a is measured. If the piezoelectric response and the sign of the piezoelectric modulus are positive, the axis y at the point

Piezoelectric tester used to determine crystal axes direction. (Photo .courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

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5 LiNbOJ crystalline

345

orientation procedure.

is in the positive direction. Similarly, the positive direction of the t axis can be found. The direction andsign of the x axis follows from geometric considerations.

2.3 Optical Window Block Sawing Once the boule has been oriented the A 0 device optical window blocks are cut. The boule is cut with a sawing machine with reciprocally moving metallic saws and abrasive pulp (water with abrasive powder). A sawing machine is shown in Fig: The oriented crystal boule is fastened on the saw table with easilymeltable compounds or plaster.A section sawed from a GaPboule is shown inthe upper portionof Fig. 7. The lower left portion shows a device optical block cut from the boule section. After sawing, the device blocks must be tested for opticalhomogeneity. The opticalwindow surfaces of the device block are polished to allow optical inspectionof the material (thesawed pieces in Fig. 7 have been polished). Thedevice blocks are inspection polished on a standard opticalpolishing machine, shown in Fig. 8. The material is tested for defects (bubbles, cracks, fissures, etc.) by illuminating the device block with a polarized collimated light beam -A homogeneous transmitted optical beam indicates no defects are present. Optical window blocks passing the optical quality test then undergo final orientation. The required accuracy of the device optical window block final orientation depends upon the type of A 0 interaction. For example, for an

PAPE

346

6 Optical window block sawingmachine. Corporation.)

NEFEDOV AND

(Photo courtesy of Harris

isotropic interaction, the orientation accuracy must be greater than30 arc minutes. For an anisotropic interaction, the orientation accuracy varies from parts of arc minutes to several arc minutes. For example, for anisotropic diffraction using the slow shear mode in Te02, the [l101 acoustic face must be oriented with accuracy greater than 40 arc minutes and the [OOl] optical face greater than arc minutes. The final Orientation is made with an x-ray goniometer This instrument, shown in Fig. 9, measures the intensity of x rays Bragg diffracted by the crystal as a function orientation angle. With a priori knowledge of the crystalline structure of the material, the orientation of the material can be determined from the angular x-ray intensity profile.

Optical

Block Surface

After sawing, the A 0 device optical window blocks are finish-polished. Four surfaces of the device blocks are polished: the two optical window

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347

7 Acousto-optic device optical window block manufcturing:(upper) section of GaP boule;(lower left) optical block; (lower right) optical block with bonded platelet transducer. (Photo courteryof Hams Corporation.)

surfaces, the transducer bonding surface, and the surface opposite the transducer bonding surface. Finish polishing is performed in the same optical polishing machine used to perform the inspection polish, shown in Fig. 8. Both coarse and finepolishing abrasives are used to obtain a highquality optical window. The optical window surfaces are typically polished parallel to 30 arc seconds with flatness and a 10-5 scratch dig surface quality. The acoustic transducer bonding surface and the opposite device block surface are also optically polished to the same specifications. Figure 10 shows TeOz optical window blocks mounted foracoustic bonding surface polishing.

2.5 Optical Window Block Antireflection Coating It is desirable to reduce optical losses at the device block windows by using antireflection coatings. Both single and multilayer AR coatings can

NEFEDOV AND PAPE

8 Optical polishing machine. (Photo courtesy

Harris Corporation.)

be used. A single-layer AR coating is designed such that the reflections from the AR coating surface cancel in phase and amplitude the reflections from the optical device block window surface. The thickness of the layer must therefore be an odd number of 1/4wavelengths. The intensity I , of a reflected beam from a single surface is [4]

[:I:1’

I=I, -

where Io is the intensity the incident beam and p is the ratio of the indices of the two materials at the interface. Table 2 shows the calculated ratio of the intensity of the reflected beam to the incident beam as well as the transmitted beam ( I t = 1 - I,) to the incident beam the four most commonly used A 0 materials (optical wavelength A = 0.63 nm) when no AR coating is used.

ACOUSTO-OPTIC MANUFACTURING DEVICE

349

I

9 X-ray crystal orientation goniometer. (Photo courtesyof St. Petersburg State Academy of Aerospace Instrumentation.)

In order that the two reflected beams from an AR coated surface cancel completely, they must be equal intensity. It is thus necessary that p be the same at both the interfaces: -=nair ~ A w Ra t

coat substrate

Since nair = 1.0, the index

refraction of the AR coating ltAR

must

be As shown in Table most A 0 materials have high refractive indices, usually between 2.0 and Thus the index a singlelayer AR coating will vary between about and Most single-layer AR coatings use chloride or fluoride compounds Magnesium fluoride, with an index of at nm, and cerium fluoride, with an index of are commonly usedcoatings. Silicon dioxide ( n = and aluminum oxide (n = films, easily produced by reacting sputtering in a dc magnetron sputtering system; are also used.

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10 TeO, opticalwindowblocksmountedforacousticbondingsurface polishing. (Photo courtesy of Hams Corporation.)

Table 2 Transmission and Reflection Coefficients for Acousto-OpticSubstrates Without Measured Calculated AR coating Material GaP LiNbO, PbMoO, TeO,

R,(%)

RR, ,((%%))

With AR (Si02) coating

R,(%)

R,(%)

R,(%)

ACOUSTO-OPTIC DEVICE

MANUFACTURING

3.51,

For normal incidence, the single-pass reflectance from an AR coated surface is 2

R = [

sub sub

-

nAR coat

n%.R coat

3’

Table 2 shows the theoretically calculated and experimentally measured reflection and transmission ( l - R ) coefficients of SiO, films deposited on LiNb03, Te02, Gap,and PbMoO,. Multilayer AR coatings can also beusedwhenlower reflectivity or broadband optical illumination is desired. After the antireflection coating is applied the device block optical window surfaces are covered with a protective paint to prevent scratches and mechanical damage during subsequent device processing.

3 PIEZOELECTRICTRANSDUCER MANUFACTURING The piezoelectric transducer is a multilayer structure mechanically bonded to theA 0 substrate. The transducer structure, asshown in Fig. 11, consists of a piezoelectric material sandwiched between top and bottom metallic layers. This structure is mechanically attached to theA 0 substrate through the bottom metallic bonding layer. nonmetallic bonding layer can also be used in which case a separate metallic bottom electrode layer is required.) The piezoelectric material converts electrical energy into acoustic energy. The bottom electrodebondinglayer is designed not only to attach the transducer structure to the substrate but also to efficiently couple the acoustic energy into the substrate. The topmetallic layer serves as the top electrode andits geometry defines the initial length and width of the sound column. Two types of transducer structures are used in A 0 devices, thin film and platelet [6]. Thin-filmtransducers areformed directly on thetransducer surface of the device optical window block by thin-film deposition techniques. The piezoelectric layer is typically polycrystalline. Platelet transducers are single-crystal platelets of piezoelectric materials whichare bonded to the transducer surface. One of the key performance parameters in transducer technology is the efficiency with which the appliedelectrical energy can be converted into acoustic energy. The conversion efficiency is determined by the piezoelectric coupling coefficient of the transducer material as well as its dielectricconstant, frequency constant, acoustic impedance, electrical resistivity, and breakdownvoltage. Table 3 shows the values of the main properties of the most widely used piezoelectric materials for piezoelectric transducer manufacturing.

NEFEDOV AND PAPE

/

Piezoelectrictransducerstructure. The piezoelectric coupling coefficientisdirectly proportional to the electrical to acoustic conversion efficiency and is thus the main parameter determining transducer efficiency. The dielectric constant determines the electrical capacity of the piezoelectric transducer and affectselectrical impedance matching. The impedance of the transducer determines the degree to which acoustic energy is coupled into the bonding layers and A 0 substrate. The optimal thickness of the piezoelectric material is established by the resonance condition that the thickness d of the transducer be nominally one-half of the acousticwavelength:

where is the acoustic velocity of the piezoelectric material and fo is the resonance frequency. The frequency constant, fo X d , determinesthe thickness the piezoelectric material at the desired operating frequency, and thus, the fabrication technology of the piezoelectric layer (thick trans-

ACOUSTO-OPTIC DEVICE MANUFACTURING

354

NEFEDOV A N D PAPE

ducers, i.e. ,those operating below 100 MHz usually require a platelet since it is difficult to deposit a high-performance thick piezoelectric thin film). All of the parameter values shown in Table 3 are for bulk single-crystal materials. Since thin-film piezoelectric layers are typically polycrystalline , these parameters can vary and therefore must be controlled during the manufacturing process. The piezoelectric transducer is under the influence of internal mechanical stresses. These internal stresses (actually the ratio between the internal stress and the bonding cohesion) affect the operation of the A 0 device and can cause partial or full destruction of the piezoelectric transducer. Moreover, they can even destroy the A 0 substrate. Internal stresses can be divided into two classes: (1) those stresses caused by differences in the properties of the bonding materials and (2) those stresses caused by structural imperfections in the materials within the piezoelectric transducer which occur during the manufacturing process. Thermal stresses caused by the difference in the thermal properties of the transducer materials belong to the first group. Stresses within the layers of transducer structure belong to the second group. In this group, stresses within the thin-film piezoelectric layer are most important, as they can, even without the destruction of the piezoelectric transducer, considerably decrease piezoelectric properties. Minimization of these stresses are considered in the discussion on thin-film piezoelectric transducers. Thermal stresses are caused by temperature variations during the manufacturing process. The main source of thermal stress in the transducer structure is the difference in the thermal coefficients of linear expansion of the piezoelectric material and the A 0 substrate. In order to minimize thermal stresses the thermal coefficients of linear expansion of the transducer material should be closely matched to the A 0 substrate and transducer manufacturing processes should be employed which use minimal heating. Usually, materials for the piezoelectric transducer and A 0 substrate as well as their orientation are chosen in such a way to maximize the efficiency of acoustic wave generation and A 0 interaction. Given these materials, an estimate of the difference in thermal coefficients of linear expansion and the allowable level of thermal stresses should be determined in order to choose the appropriate transducer manufacturing process. Because most piezoelectric and A 0 materials are monocrystals or patterned films, the thermal coefficient of linear expansion depends both on the orientation of the materials. Figures 12-18 show the distributions and difference in the thermal coefficient of linear expansion for the most common orientations of the piezoelectric material and the A 0 substrate. In these figures TeO, and LiNb0, are chosen as A 0 substrates (curve l),and LiNbO, and ZnO

ACOUSTO-OPTIC DEVICE MANUFACTURING

355

Y TC LE X 106/"K)

of Figure 12 Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1)A 0 crystal [LiNbO, (loo)], (2) piezoelectric transducer [LiNbO, ( y + 36")], (3) difference [2-11.

Figure 13 Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1) A 0 crystal [TeO, (OOl)], (2) piezoelectric transducer [LiNbO, ( y 36")], (3) difference [2-11.

+

356

Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1)A 0 crystal [TeO, (110)], (2) piezoelectric transducer [LiNbO, (loo)], (3) difference [2-11.

Aco~sto-opticcrystal substrate and transducer thermal coefficient of linear expansion: (1) A 0 crystal [TeO, (110)], (2) piezoelectric transducer [LiNbO, ( y + 163")], (3) difference [2-11.

ACOUSTO-OPTIC DEVICE MANUFACTURING

357

Acousto-optic crystal substrate and transducer thermalcoefficient of linear expansion:(1) A 0 crystal [LiNbO, (loo)],(2) piezoelectric transducer [ZnO (OOl)], difference [2-l].

Acousto-optic crystal substrate and transducer thermalcoefficient linear expansion: (1) crystal [TeO, (OOl)], (2) piezoelectric transducer [ZnO (OOl)], difference [2-l].

358

NEFEDOV AND PAPE

Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1) A 0 crystal [TeO, (llo)], (2) piezoelectric transducer [ZnO (loo)], difference (2-11.

as the piezoelectric material (curve 2). Curve is the difference in the thermal coefficients of linear expansion (TCLE). These plots are in units of 106/K. From thesecurves we cansee that forseveral combinations of materials there is a considerable difference in the thermal coefficients of linear expansion. a rule of thumb, the difference in the thermal coefficients of linear expansion should not exceed 0.1 to 1.0 106/K in order topreserve the integrity of bonded materials if a high-temperature manufacturing process is used. The actual stresses in a particular layer is determined by the strength of materials, adhesion forces, and manufacturing temperature levels. 3.1 . Thin-Film Transducer Fabrication Thin-film piezoelectric transducers are formed directly on the substrate using vacuum deposition technology. The thin-film transducer has a number of advantages over a platelet transducer: (1) no transducer bonding layer is required which mayintroduce extrainsertion losses, (2) the platelet reduction process is eliminated, electrical impedance matching is simpler due to thelower capacitance of the thin-film piezoelectric transducer, and (4) thin-film transducers can be deposited on large areas and curved

ACOUSTO-OPTIC DEVICE MANUFACTURING

359

surfaces. The primary disadvantage of the thin-film piezoelectric transducer is its much lower piezoelectric coupling coefficient than the platelet transducer. The simplicity, reproducibility, and relatively low production costs of thin-film transducer fabrication, involving only film deposition processes, over the more involved processes required to fabricate platelet transducers (particularly at higher frequencies) led to thepreference of this transducer technology by some A 0 device manufacturers. Although most of the commercially available A 0 devices have platelet transducers, thin-film transducers remain the preferred approach among some manufacturers. Ultrasonic transducers have been fabricated using thin films of AIN, CdS, LiNb03 and ZnO [7]. ZnO has the highest piezoelectric coupling coefficient (see Table of these piezoelectric thin-film materials and is the usual choice for thin-film transducer fabrication in A 0 device manufacturing. ZnO Deposition Technology ZnO can be deposited using thermal evaporation techniques but the film quality is poor [7]. The highest-quality ZnO films are formed by the ion sputtering process. In this process the ZnO deposition material forms the cathode of an anode-cathode assembly inside a vacuum chamber. An inert rare gas, typically Ar, introduced into thevacuum chamber at low pressure becomes ionized when a high voltage (either dc or RF) is applied across the anode-cathode assembly. Accelerated by the electric field between the anode and the cathode, theAr+ ions bombard the cathode and cause ZnO atoms to be ejected. The ZnO atoms diffuse to the A 0 substrate where they are deposited into a thin film and form the piezoelectric transducer. Various ion sputtering anode-cathode configurations have been employed to deposit ZnO including the diode triode and magnetron [ll].The diode configuration, where the anodeserves as theA 0 substrate holder, typically yieldspoor quality films due to substrateheating and film damage caused by secondary electron bombardment. Also, the diode configuration requires a relatively high Ar gas pressure which results in film contamination from Ar atoms trapped in the ZnO film. The triode configuration uses an auxiliary thermionic cathode to inject electrons into the Ar gas to create ionization. Unlike the diode configuration, electron emission is independent of gas pressure and thus the triode configuration can be operated at lower gas pressures. Nevertheless, this configuration too suffers from substrate heating, film contamination from the thermionic cathode material, and thermionic cathode decay if reactive gasses are used in conjunction with Ar (in order tomodify the properties of the deposited film).

360

NEFEDOV A M ) PAPE

The magnetron sputteringconfiguration overcomes the secondary electron induced substrate heating problem which is the major disadvantage of both the diode and triode sputteringconfigurations for the production of highquality ZnOthin-film transducers. Several different types of magnetron sputtering designs (cylindrical, planar, and magnetron gun) have been developed for thin-film deposition. The planar magnetron sputtering configuration is the most widely used[12]. The main elements of the planar magnetron sputtering source, shown in Fig. 19 for both circular and rectangular geometries, are a planar circular cathode target parallel to an anode surface, usually grounded, that serves as the substrate holder. permanent magnet underneath the cathode creates a circular closed path where the magnetic field lines are perpendicular to the cathode surface. The magnetic field confines the plasma to the circular closed-path region. The electrons are captured by the magnetic fieldand, because of the crossed electric and magnetic fields, move in long helical paths through the argon gas. The trajectory of the secondary electrons emitted by the cathode due to ion bombardment, however, is bent away from the substrate. These unwanted secondary electrons are captured by a ground shield, thus eliminating substrate heating. In addition, the probability an electron colliding with an argon atom is greatly increased in this system because of its helical path. This results in higher film growth speeds than that available with either the diode or triode systems. Film growth speeds of 15 p d h r havebeenachievedwithmagnetron sputtering systems. The increased

l/ Figure 19 Circular and rectangular planar magnetron sputtering sources. Curved lins> rcprsscnt magnetic field lines

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361

collision probability also allows the system to be operated at even lower gas pressures than the diode system, thus reducing film contamination. Figure 20 shows a photograph of a circular planar magnetron cathode assembly whichis used for thin-film piezoelectric transducer manufacturing at the St. Petersburg State Academy of Aerospace Instrumentation. The operation of a magnetron deposition unit is as follows. A 0 substrates areplaced on theanode holder and loaded into thesystem chamber. Pa, After pumping the chamber down to a pressure of about 1.3 X gases are backstreamed into the chamber to a pressure of about 0.1 Pa. A voltage of approximately 300 to 400 V is applied between the anode and cathode,which creates an abnormalglow discharge concentrated near the target. Plasma ions then begin to bombard the target and sputtering is initiated. The sputtered atoms, condensing on the substrate, form the thin-film transducer. ZnO Film Characteristics ZnO is a hexagonal (wurtzite) crystal of class 6mm. ZnO films produced by standard vacuum deposition techniques on metal substrates (as in A 0

20 Circular planar magnetron cathode assembly. (Photo courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

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NEFEDOV AAlD PAPE

transducer fabrication) are not epitaxial but instead are polycrystalline structures with varying degrees of misorientation between individual crystallites [7]. A uniformly oriented polycrystallinefilm will, however,exhibit a piezoelectric coupling constant close to that of the bulk single-crystal material. A group of crystallites in a polycrystalline film with the same crystallographic orientation forms a "texture." A polycrystallinefilm can be characterized by threeparameters: (1) thetextureratio & l , the ratio of crystallites with c-axis orientation perpendicular to the(hk.l) plane to the total number of crystallites in the film, (2) the misorientation angle the angular spread of the crystallites orientation about the c-axis direction, and (3) the c-axis direction angle 8, the angle between the c axis and the normal to the film plane. The magnitude of the ZnO thin-film piezoelectric coupling constant as a function of 8 for various values (with &k.[ = 100%) is shown in Fig. [7,13]. The 21 (where the electric field is along the direction 8 = longitudinal mode coupling is maximum when the c axis is parallel to the electric field while shear mode coupling is maximum when the c axis is inclined at anangle of about 30". a increases, the piezoelectric coupling constant decreases (with no coupling when the film crystallites are randomly ordered). In addition,nonuniform orientation results in the simultaneous generation both longitudinal and shear waves. From the figure we see thata c-axis orientation parallel to theelectric field is optimum for longitudinal mode transducers (where the longitudinal mode coupling is maximum and no shear mode coupling occurs) and a c axis orientation inclined to theelectric field by about 40" is optimum for shear modetransducers (where no longitudinal mode coupling occurs). Thin films of ZnO, like other wurtzite class crystals, grow primarily with the (00.1) plane parallel to thesubstrate surface, i.e., the c axis is oriented perpendicular to the substrate [7]. With the piezoelectric film sandwiched between electrodes parallel to the A 0 substrate (i.e., the electric field is parallel to the c axis), this orientation yields a longitudinal mode transducer. Pure shear mode transducers (where the c axis is inclined to the normal by about 40", as shown in Fig. 21) can be formed by obliquely depositing the film [14]. (The crystalline structure of the metallic electrode upon which the piezoelectric material is deposited does not appreciably impact the ZnOfilm orientation. It is important, however, that themetallic surface be clean and smooth [7].) ZnO Film Quality and Deposition Parameters A number of factors, both equipment and process related, influence the type and quality of a sputtered thin-film piezoelectric transducer. Equip-

363

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0.2

30

60

90

9 (degrees)

KS

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ment factors include (1) the type of pumpdown system, (2) the maximum available vacuum, the type and construction of the magnetron sputtering system, and (4) the method for gas composition mixing and backstreaming to the vacuum chamber. Process factors include (1) glow discharge parameters, (2) gas composition and pressure, thermaland temporal parameters of the sputtering process, and (4) geometry of the substratekarget arrangement. Pumpdown systems employing oilmust contain adequatecryogenic trapping for high-quality thin-film piezoelectric transducer deposition.Oil vapor affects the structure of the deposited film and contamination of the transducer substrate surface reduces film adhesion. Also, organic compounds in the vacuum chamber affect the crystallographicstructure of ZnO films [8]. Pumpdown systemswithout oil or oil vapor are ideally preferred. The maximum available vacuum must be highin order to provide a sufficiently clean deposition environment. The type and construction of the magnetron sputtering system determines the configuration of the substrate holder and the maximum area over which film uniformity can be maintained. The type of supplied voltage (ac or dc) determines the target material. If dc sputtering is used, the targetmust be electrically conductive to remove electrical charges generated on its surface. Usually, metallic targets are used. If ac sputtering is used, the target can alsobe made of semiconducting and dielectric materials. The target also determines the gas composition. The method for mixing the working gas and backstreaming it into the vacuum chamber influence chemical reactions, gas mixture uniformity, and stability of glow discharge parameters within the vacuum chamber [15,16]. Stability is particularly important because if the discharge extinguishes during sputtering, crystalline disorientation occurs and the film’s piezoelectric coupling constant is reduced. Film growth speed decisively determines the film’s texture characteristics. When the film growth speed decreases, the atoms depositedon the substrate have sufficient time to become incorporated within the existing crystal lattice before another layer is deposited. more uniform film generally results from aslow film growthspeed. (Onemust, however, take into account the bombardment by high-energy particles which can considerably change the dependence between growth speed and film quality [17,181.) Rhk.Jon film growth The dependenceof the film structure (texture ratio speed is shown in Fig. [19]. Below the boundary growth speed V , the crystallites form with the (00.1) plane orientation (c-axis orientation perpendicular to the film surface). Above this speed, the number of (00.1)

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oriented crystallites decreases and crystallites with both (10.0) and the (li.O) orientation axis in plane of film) begin to form resulting in a mixture of both perpendicular and horizontal c-axis orientations. The boundaryfilmgrowth speed increases with increasing substrate temperature. An elevated substrate temperatureincreases atom mobility, providing close to equilibrium conditions where (00.1) planes form parallel to the film substrate. Unfortunately, it is not possible to increase v b substantially through substrate heating because the atoms will begin to reevaporate from the substrate surface. The limitation in growth speed severely limits the practicality of obtaining films withthicknesses greater than10 pm (i.e., of ZnO transducers with center frequencies below about MHz). For example, when v b = 0.25 ndsec, it takes 9 hr to obtain a 10-pm-thick film. Such an extended deposition period requires a sputtering system with a very high degree of temporal stability. The growth process can be made considerably shorter by using a twostage sputtering process [20]. It has been found that the deposition speed influences the film's texture pattern even at the earliest stages film deposition (up to thicknesses of 0.1 to 0.3 pm). At this early stage the

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orienting sublayer is formed. Once the orienting sublayer is formed, the film growth speed can be accelerated without a decrease in film quality. This two-stage growth process can yield films with thicknesses up toseveral tens of micrometers. During the first stage, sputtering is carried out at a speed lower than the boundary speed (typically0.05 to 0.1 ndsec). During the second stage, the speed can be increased to 1to 2 ndsec. Thick films have been obtainedwith texture patternaxis angular spreads corresponding to thatassociated with the first-stage growth speed. This two-stage process can reduce the time needed to deposit a 10-pm film from 9 to 3 hr. The film growthspeed, the uniformity of film thickness, and thequality of the crystal structure also depend on thedistance between the target and the substrate. To reduce film defects the particle mean free path length must be longer than the distance between the target and the substrate. Table 4 showsthe required particle mean free pathlength for different gas pressures. Given that the working pressure in the magnetron sputtering system is usually about 0.1 Pa, the distance between the target and the substrate must be less than about 5 cm. The sputtering target size and the distance between the substrate and the target also influence the thickness uniformity. The geometry forthesubstrate(A)/target (B) assemblyis shown in Fig. 23. For a film with radius R, equal to the radius of the sputtering zone R , a thickness nonuniformity of less than 2.5% can be achieved if the distance between the target and the substrate, H , as well as the target radius, R , is appropriately chosen, as shown in the graph in Fig. 24. For a flat target = 0), the ratio HIR must be between 0.8 and 1.0 cm. This means that if the distance between the target and the substrate (determined by gas pressure) is chosen to be cm, the sputtering zone diameter must bemore than8 to 10 cm in order toobtain the given thickness nonuniformity. The sputtering zone diameterin turn determinesthe target size and thus the mechanical design of the magnetron. Table 4 MeanFreePath between Particle Collisions free

MeanPressure (Pa>

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23 Geometryforsputteringsubstratekargetassembly.

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It is possible to deposit films withanisotropic properties in the substrate plane by introducing asymmetry in the growth conditions, e.g., by changing the incident angle of the sputtered material. By choosing the right angle, the c axis of the film crystallites can be forced to form either horizontally or vertically in the film plane. These biaxial growth patterns can be used to produce efficient shear wave piezoelectric transducers. As shown inFig. 21, the piezoelectric coefficient for the shear mode has two maximums: 4 = 30" (Ks= and 4 = 90" (Ks= 0.31). Films for efficient shear wave piezoelectric transducers either must have the tilted pattern axis, or this axis must be in the film plane. Experiments show that if the substrate is tilted up to the pattern with the tilted c axis is formed, whereas if the tilt angle is more than the c axis lies in the substrate plane. Different incident angles of the material particles sputtered from the target surface result in crystal surface nonuniformity over the substrate surface. The smallest tilt angle is in the central part of the film. The tilt angle 0 increases from the centerto the border, where crystallites with the (11.0) and (10.0) orientations appear. ZnO Piezoelectric Thin-Film Transducer Performance ZnO films have been deposited for longitudinal acoustic wave excitation with frequencies from 1 to 10 GHz [15,21-231. One way to characterize the quality of a deposited thin film is to measure the angular spread of Bragg diffracted x rays from the film surface in the goniometer setup shown in Fig. 9. The resulting "rocking curve" [2] is a measure of the spread in the misorientation angle a. Figure 25 shows rocking curves for various thicknesses of ZnO films deposited in a planar magnetron sputtering system by a Zn target sputtering in an Ar-0, gas mixture: (a) 2 pm, (b) pm, (c) 8 pm, and (d) 12 pm. The sputtering parameters for this film were target diameter, 120 mm; distance between the target and the substrate, 50 mm; voltage, between 350 and V; current, between 0.2 and 1.0 A; Ar-0, ratio,l:3; gas mixture pressure, 0.13 Pa; growth speed, 0.25 ndsec; substrate temperature, 250°C. The substrate materials are SiO,,LiNbO,, and A1203previously metallized with Al. The ZnO films deposited under these conditions have the following crystal pattern parameters: Rm,l = 99-loo%, a = &5", and 8 = 3". These parameters make it possible to achieve a piezoelectric coupling constant coefficient of K L = 0.25 (i.e., 90% of that found in monocrystal ZnO). Current research activities in ZnO thin-film transducer deposition have concentrated on (1) increasing film thicknesses up to 35 to 50 pm without texture decay, (2) depositing films on a number of A 0 materials (e.g., TeO,, PbMoO,, NaBiMoO), and (3) depositing films with a tilted c-axis orientation.

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The primary limitation in increasing film thickness is the accompanying increase in internal stresses caused by both film texture pattern imperfection and differences in the thermalcoefficients of linear expansion between the film and the substrate. we noted earlier, these stresses may not exceed the strength of the ZnO film and the substrate and adhesion forces. For LiNbO,, SiO,, Gap, and A1203 crystals, films with thickness up to about 50 p m can be deposited with the required pattern. Rocking curves from a 50-pm-thick film with R , , , = = = and K L = 0.24 are shown in Fig. 26. Both the sample and the x-ray detector were rotated in Fig. 26(a), while only the sample was rotated in Fig. 26(b). A bottom A1 electrode with a'thickness between 0.5 and 1 pm provides both good ZnO adhesion to the A 0 substrate and internal stress decoupling.

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As the thermalcoefficient of linear expansion for A1 is higher than that of ZnO or the A 0 substrate, an A1 film can reduce the internal stresses in the transducer film and the A 0 substrate. The high level of internal stresses in ZnO films and the low strength of TeOz and PbMoO, crystals make it impossible to deposit thin-film piezoelectric transducers directly on these materials [24]. For these materials other methods for stress decoupling between the piezoelectric transducer and theA 0 substrate have to be used including deposition of a buffer layer and reducing substrate temperature. As the buffer layer, an A1 electrode of half-wave thickness can be used for frequencies from MHz to 1 GHz, W2 ranges from 32 to 3.2 pm. Low substrate temperature, unfortunately, resultsin low film quality. Thehighest-quality film results from a trade-off between the characteristics of themultilayer structure, theA 0 substrate, theadhesion sublayer, the ground layer, the orienting sublayer, thepiezoelectric film, and the top electrode. Figure 27 shows rocking curves for a 3-pm (7.27(a)) and 8-pm (7.27(b)) ZnO film deposited as a multilayer structure on an (001) TeO, crystal. The texture parameters for this ZnO film are thefollowing: for athickness of 3 pm (Fig. 7.27(a)) Rnk.,= 99%, = +6", 8 = +7"; for a thickness Of 8 pm (Fig. 7.27(b)) Rnk,l = 97%, (T = 8', 8 = For shear acoustic wave generation in the GHz region, e.g., for anisotropic diffraction in LiNb03 crystals [25,26], the films must have either tilted = 30') or horizontal = 90') c-axis orientations. Furthermore, it is necessary that in the film plane, the axis should be oriented in the direction that will yield the most efficient A 0 interaction in the A 0 substrate. Figure 28 shows rocking curves for a ZnO film with a tilted axis (with sample and detector rotated in 7.28(a) and sample only rotated in 7.28(b)), while Figs. 29 and 30 show films witha horizontal axis (in each case showing both the sample and detector rotatod profile in (a) and the sample-only rotated profile in (b)). In thetilted c-axis profile, the axis tilt angle is between 25 and 40', while in the horizontal axis either the(11.0) and (10.0) planes (Fig. 7.29) or only the (10.0) plane (Fig. 7.30) are parallel to the film plane. The disorientation angle of the axis in the film plane can be experimentally measured with a piezoelectric tester using a piezoelectric response diagram with the tilted acoustic probe pulse generation. For the film with the (10.0) plane orientation, this angle is = 10".

3.2 Platelet TransducerFabrication Platelet transducers are fabricatedby first mechanically bonding a singlecrystal piezoelectric plate to the A 0 substrate and thenreducing the plate thickness to achieve the required transducer resonance frequency. While

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the manufacturing process for platelet transducers is more complicated than that for theproduction of thin-film transducers, a platelet transducer can provide distinct performance advantages. The generally superior performance of the platelet transducer makes it the most commonly used transducer by the majority of commercial and custom device manufacturers. The material of choice for the piezoelectric platelet is lithium niobate (LiNbO,). The piezoelectric coupling coefficient of LiNbO, is large (approximately a factor of 2 larger than that of ZnO, both for longitudinal

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28 Rocking curves for a ZnO film with atilted c axis: (a) both the sample and the x-ray detector rotated and (b) sample only rotated.

and shear modes) (Table 3). LiNb03 also has the requisite physical properties (good mechanical strength, hardness, and stability) necessary to withstand the bonding and reduction process. The material is produced in large scale throughout the world and thus is relatively inexpensive and easy to obtain. The manufacturing process for a platelet transducer consists of the following steps: (1) manufacturing the piezoelectric platelet, (2) depositing

74

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the bottom electrode, (3) bonding the platelet to the A 0 substrate, (4) reducing the platelet to the required thickness, and (b) depositing the top electrode on the platelet surface. Manufacturing the piezoelectric platelet involves the same steps asthat for the A 0 substrate (as discussed in Section 1). A boule of LiNbO, is grown and oriented. Platelets of the material are then removed from the boule by sawing. The platelets are individually oriented with an accuracy greater than 30 arc minutes. Finally, the bonding surface of the platelet is polished. Two LiNbO, orientations exhibit large piezoelectric coupling, the yz plane orientation and the plane orientation. Figure 31(a) shows the piezoelectric coupling-of LiNbO, in the yz plane and Fig. 31(b) shows the coupling in the plane For longitudinal excitation, the 36" Y-cut orientation in the yz plane is preferred because no shear mode.coupling is present. In this direction the longitudinal mode piezoelectric coupling constant is 0.49. For shear mode excitation, either the 163" Y-cut orien-

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tation in the yz plane or an X-cut orientation inthe xy plane is preferred. The X-cut orientation is usually usedto excite shear waves in A 0 deflector devices because (1) it has a higher shear mode coupling constant (0.48 versus (2) it excites a pure mode and there is n o coupling to the quasilongitudinal mode. There is, however, coupling to the orthogonal shear mode. In those cases where orthogonal shear mode coupling must be suppressed, the Y-cut orientation in the yz plane is used. The thickness of the platelet is usually minimized to limit the amount of material that must be removed during the reduction process. The platelet must be thick enough, however, to withstand the bonding process. Usually,

NEFmOV AND PAPE

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LiNb03 platelet transducer is

Transducer Platelet Bonding Bonding the piezoelectric platelet to the substrate is a critical part of the platelet transducer manufacturing process. The quality of the bond determines in large part theefficiency, frequency, and passband performance of the device. bonding layer with lowacoustic loss and an acoustic impedance closely matched to thatof the adjoining substrate is desired. If the loss is high or the acoustic impedance is poorly matched, the efficiency of the device will be poor and the bandwidth will be severely restricted unless the layer is made extremely thin. Propertiesof material used for bonding the bonding layer, as well as the electrode, are shown in Table 5.

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The commonly used methods for bonding the piezoelectric platelet to the substrate are[28,29] (1) adhesive bonding, (2) thermocompression bonding, cold vacuum compression bonding, and (4) optical contact bonding. Adhesive Bonding Adhesive bonding with organic compounds (e.g., epoxy, varnish, stopcock grease, silicon oil, phenyl compounds, etc.) is a relatively easy way to attach a transducer to an substrate. TeOz Bragg cell devices fabricated with transducers bonded with a thin epoxy layer (less than 1 pm thick) have demonstrated good performance at frequencies up to 160 MHz [29]. Epoxy-bonded transducers have also been reported to work as high as 250 to MHz The utility of this technique above this frequency is limited, however, due to the large acoustic impedance mismatch between the organic compound and the adjacent piezoelectric material and the A 0 substrate. The acoustic impedance of organic compounds is typically an order of magnitude smaller than both the bottom metallic electrode layer and the A 0 substrate (see Table 5). The bond thickness must be made “acoustically

378

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32 LINbO,platelettransducers:(right)sawed, (left) photoresistprotected for bonding. (Photo courtesy of Hams Corporation).

thin” in order that such a large mismatch will not substantially reduce the bandwidth of the transducer. Indeed, above 100 MHz the layer thickness cannot exceed several tenths of micrometers, or severe bandwidth reduction occurs Not only are such thin bonds difficult to fabricate (although 0.1-pm-thick epoxy bonds have been reported but thin bonds increase the requirements for substrate surface flatness and polishing quality. In addition, if high-frequency operation is required, this thin layer cannot provide the mechanical strength necessary for themechanical reduction of the LiNbO, platelet. Thermocompression Bonding Metal layers, with acoustic impedances more closelymatched to the adjoining materials than those of organic compounds, can be used to join the piezoelectric transducer to theA 0 substrate with thermocompression bonding Using the thermocompression bonding technique, metal surfaces can be bonded without the application of the destructively high temperatures necessary to melt the metals.

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In the thermocompression bonding process both the transducer bottom electrode and theA 0 substrate are coated with a metal layer. Gold, silver, aluminum, indium, and tin have been used (see Chapter 5). The metal surfaces are then brought together under the mutual application of heat and pressure. Typical bonding temperatures arebetween 250°C and 350"C, and pressures are lo8 Pa applied over a period of one-half hour or more. The resulting plastic deformation and diffusion occurring at the interface results in a rugged, uniform bond. Thermocompression bonding consists of twosteps:(1) metallic film deposition on the surfaces to be bonded and (2) application of pressure and temperature to achieve bonding. These two steps can be performed either in one vacuum chamber (without breaking vacuum) or in different vacuum chambers. When performed without breaking vacuum, the metallic surfaces are protectedagainst dust and oxidation, and the processing time is shortened. Itis difficult,however, to control thequality of the deposited films, and the device for mechanical positioning and applying pressure to the bonded materials must be very precise.In thesecond case, the surfaces to be bonded are easily aligned. The bonding surfaces, once exposed to air, however, quickly develop an oxidation layer, which mustbe eliminated through longer bonding time. Figure 33 shows a photograph of the equipment used for the thermal deposition of the bonding layers on thepiezoelectric platelet and the A 0 substrate prior tothermocompression bonding. Figure shows the inside of the thermocompression bonding apparatus. The thermocompression bonding technique uses high temperatures and, for thebest bond, should be performed without breaking vacuum after the bonding layer deposition. Because of the high temperatures, only those materials with almost identical thermalcoefficients linear expansion can be reliably bonded. For the material combinations shown in Figs. 12-18, only a LiNbO, platelet bonded to a LiNbOj(Fig. 12) or a TeO, (Fig. 15) substrate satisfies this condition. Thermocompression ultrasonic bonding [33]is a modification to the thermocompression bonding technique. In addition to heat and pressure, ultrasonic energy is also applied. This results in lower temperature and pressure requirements. Italso allows the bonding process to be performed in the ambient. Figure 35 shows a thermocompression ultrasonic bonding apparatus [33]. Longitudinal acoustic waves (typically 18 kHz with a power of 0.4 W) are excited by a transducerand transmitted via a horn waveguide to thebonding surface. ball joint provides the ability to align the waveguide directly to the bond surface. A glass pressure platethermally isolates thepiezoelectric layer from the waveguide. The substrateis clamped in a holder.A heating

ACOUSTO-OPTIC MANUFACTURING DEVICE

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33 Vacuum equipment for metal evaporation. (Photo courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

coil around the holder provides heat for the bonding process. Instead of requiring 400°C and lo8 Pa (as is the case for thermocompression bonding) bonds using gold, indium, and silver have been made at lower temperatures and an order of magnitude lower pressures Pa). Another advantage of this method is that the application the ultrasonic energy breaks down the oxidization layer on thebonding surface. Thus a high-quality bond can be achieved by using different machines for the bond layer deposition and the bonding. A LiNbO, platelet thermocompression ultrasonic bonded to a quartz crystal using a Ni-Cr/Au bonding layer 0.15 p,m thick was reduced to a thickness of 2.5 p,m corresponding to a device center frequency of 1.5 GHz Despite the reduction in temperature, materials with dissimilar coefficients linear expansion still may fracture as the transducer is cooled back to room temperature. ColdVacuumCompressionBonding Cold vacuum compression bonding at room temperature eliminates the stresses induced in either of the pre-

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34 Thermocompressionbondingapparatus. (Photo courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

viously described thermocompression bonding techniques [35]. It is the bonding technique of choice for many A 0 device manufacturers. In this process, both the platelet transducer andthe A 0 substrate are coated with the metallic bonding layer and immediately brought into contact under a high veryhighvacuum (at least to 10” Pa). Theshorttimeand vacuum prevent the formation of an oxidation layer which will cause unreliable bonding. A pressure of lo9 Pa isapplied to thetransducer assembly to achieve the bond. A photograph of a cold vacuum compression bonding apparatus is shown in Fig. 36. Indium [36], silver, tin, and gold have been used as bond layers in cold vacuum compression bonding. A LiNbO, platelet cold vacuum compression bonded to a spinel crystal using a gold bonding layer 0.3 pm thick was reduced to a thickness of 0.24 pm corresponding to a device center frequency of 10 GHz [37]. The device in theright-hand side of Fig. 7 shows a GaP cell with a cold-vacuum compression-bonded LiNbO,platelet transducer.

ACOUSTO-OPTIC DEVICE MANUFACTURING

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35 Thermocompression ultrasonic bonding apparatus schematic

Optical Contact Bonding Optical contact bonding eliminates the necessity for the bonding material Optical contact bonding occurs between two highly polished surfaces when the gap between them is less than tens of Angstroms. Cohesive forces appearing between the surfaces result in a bond which can be as strong as that of the substrate material itself. The strength of the cohesive force between the flat surfaces of two materials is a function of the dielectric constant of the materials and the distance between the two surfaces The A 0 device transducer structure must contain a metallic electrode layer between the optically polished piezoelectric transducer platelet and the substrate. In orderto make.an adequateoptical contact bond, the electrode metallic layer between the piezoelectric transducer and the A 0 substrate must satisfy two requirements: (1) the layer thickness must be limited, and (2) the electrical resistivity and acoustic attenuation of the electrode layer must be low. One of the conventional materials for this

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layer is Au. A Cu electrode layer with a Cr adhesive sublayer can also be used. A disadvantage of an electrode made of Cu, however, is its low corrosion stability. It is possible to increase this stability if Cr is used not only as the adhesion sublayer, but as a protective layer deposited over the Cu layer. The thickness of the adhesive Cr sublayer is 10 to 15 nm, and the thickness of electrical conductive Cu layer is 25 to 30 nm. Electrical resistivities for the sublayer and the layer are 0.7 X ohm-cm and 0.7 x ohm-cm, respectively. The thickness of the protective layer is approximately equal to 15 nm. The process for optically contact bonding-the piezoelectric transducer platelet to the surface of the A 0 substrate has the following steps: (1) deposition of the metallic electrode layer on the A 0 substrate, (2) contacting the platelet to the substrate using water, and (3) removing the water from the bond region.

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The piezoelectric transducer is first placed on the water-moistened surface of the A 0 substrate. When the piezoelectric transducer platelet is positioned at the right place on the A 0 substrate surface, the platelet is lightly clamped to the substrate. An optical probe should show that the interference fringes in the contact layer have disappeared. If the surfaces are well cleaned, the contact process is easy and fast. Next a pressure of approximately lo6 Pa is applied to the assembled piezoelectric transducer in order to remove water from the contact region. Optical contact technology considerably simplifies the manufacturing process for A 0 devices and has two advantages over the metallic compression bonding techniques: (1) piezoelectric bonding is made without vacuum, and it becomes possible to position the plate on the A 0 substrate more accurately, (2) no loss or passband distortion occurs due to the bonding layer. Optical contact technology can be realized on widely used A 0 substrates such as fused and crystal quartz, Ge, TeO,, PbMoO, [41]. Transducer Platelet Reduction The thickness of the transducer platelet is reduced to the thickness that will produce the desired device center frequency. This thickness is nominally the thickness of the resonance frequency, but its exact dimension is modified by the surrounding materials (see Chapter 6). Figure 37 shows roughly the thickness of a LiNbO, platelet transducer for a given device operating frequency for both longitudinal and shear acoustic modes. Two techniques are commonly used for platelet reduction: mechanical lapping and ion milling [7]. Mechanical lapping involves the removal of the platelet material using abrasive compounds. The procedure is usually performed by hand, one device at a time. Platelet transducers as thin as 0.4 pm are routinely produced using this method. Ion milling involves the removal of material by sputtering. This procedure is performed in lieu of mechanical lapping when transducer thicknesses below 1 pm are required. Ion-milled transducers 0.25 pm thick have been achieved. Prior to reduction the bond region of the transducer is protected with optical paint to prevent it from being damaged. Mechanical Reduction The thickness of the piezoelectric platelet can be gradually reduced through a process of mechanical lapping with coarse abrasive grit and then finish polishing with fine polishing grit. The mechanical lapping jig is essentially the same apparatus as that used for optical window polishing (Fig. 8). The A 0 substrate is blocked on all sides with pieces of the same material as that of the platelet transducer. The entire assembly is lapped by hand using a slurry of water and carborundum or diamond grit. A schedule of a typical reduction of LiNbO, is

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Unloaded Transducer Resonant Frequency (MHz)

Figure 37 LiNbO, thickness vs. nominal resonance frequency.

Table 6 LiNbO, Mechanical Reduction Schedule Grit sue (pm)

Coarse 25 9 5 1 0.5 0.2

Reduction time

Reduction (pm)

30 min 30 min 30 min 30 min 1 hr 1 hr 4 hr

2 mm-600 600-300 300-100 100-10 10-4 4- 1 1-0.5

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shown in Table 6 [42]. Starting with a coarse grit, a 2-mm-thick Lm03 platelet can be reduced to about 10 pm using successively smaller grit sizes in,about 2 hr. The platelet can be reduced to a final thickness of 0.4 pm with careful polishing over another 6-hr period. Chemical polishing can be used after mechanical lapping to remove the abrasion groves in the platelet surface. High-frequency devices finished with a chemical polish are reported to have lower insertion loss than those without the chemical polish [42]. A GaP deflector with a LiNbO, transducer mechanically reduced to 1 pm thickness is shown in Fig. 38. Ion Milling While high-frequency platelet transducers can be finish-lapped by mechanical polishing techniques for operation at frequenciesover 1GHz, this approach is difficult to reproduce in a reliable manner and it requires skilled opticians. Ion milling is an excellent microthinning technique for frequen-

Figure 38 GaP cell with LiNbO, platelet transducer reduced to 1 Fm. (Photo courtesy of Harris Corporation.)

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cies above 1 GHz. Ion milling was originally used for thinning transducers for bulk acoustic delay lines. Delay lines with frequency operation as high as 11.5 GHz have been achieved [36]. Rosenbaum et al. have reported A 0 deflectors with LiNbO, ion-milled transducers that operate at 1 GHz [43]. Shear LiNbO, A 0 deflectors using ion-milled LiNbO, transducers with thicknesses of 0.3 pm operating at 3.5 GHz have been demonstrated at Westinghouse STC [44]. In the ion-milling process, atoms are removed from the target surface by bombardment with energetic ions. Atoms are ejected, or sputtered, from the substrate as a result of momentum transferred to them by the impact of the beam ions on the substrate. This is significantly different from plasma etching where chemical reactions dominate rather than physical ion bombardment process. The average number of atoms ejected per incident ion is referred to as the sputtering yield. For incident ions in the 400 to 1000 eV energy range, sputtering yields are on the order of 0.1 to 10 atoms per incident ion. In general, the yield is affected by the target material through the binding energy between atoms, which is of the order of 1 to 10 eV, depending on the material. The typical ion-milling beam energy is a few thousand electrovolts range because at higher energies the yield is reduced (the ions penetrate deeper into the substrate giving less energy to the surface atoms). The impact angle is important since for ions incident at more oblique angles to the substrate, more energy is transferred to the atoms near the surface, and this permits more atoms to escape from the surface. The ion-milling process has some important inherent features which include (1) no significant lower limit on the feature size that can be etched, (2) good control of the slope of the etched features, (3) any material can be ion-milled, and (4) excellent repeatability form run to run and uniformity within a run. Ion milling can reduce the platelet thickness at a rate of tens to hundreds of Angstroms per minute, so that total minute times are in the range of a few hours, depending on the starting thickness and the beam power used. Depending on the beam power, significant heating of the substrate may occur since it absorbs energy from the ion beam; thus intermittent operation may be required for system cooldown to avoid thermal damage to the substrates. This cooling causes no serious deterioration even at submicrometer thicknesses [43,44]. In general, ion milling is nonreactive, and it is carried out in argon atmosphere around 1.3 x Pa. It is important to carefully monitor the etch depth as the finish thickness is approached. Optical techniques, as well as control methods peculiar to the ion-milling process, can be used for precise thickness control. Figure 39 shows a typical ion-milling system made by Veeco Instruments Inc. which can operate on substrates as wide as 3 in. Prior to ion milling,

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39 Photograph of a3-inion-millingsystemmadeby Veeco Instruments Inc. The vacuum system is shown at the left whereas the control electronics for the ion milling are shown at right. (Courtesy of Westinghouse Electric Corporation.)

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the transducer is mechanically thinned to a few micrometers. The transducer/AO crystal structure is then mounted in a target fixture assembly (Fig. left). Before inserting the target fixture into ion-milling the system, a glass plate with an appropriate aperture is set on top of the transducer (Fig. center). The plate shields the remaining transducer structure from unwanted ion milling, whereas the aperture allows thinning only at a specific location on the transducer surface (the shape and area of the thinned part of the surface is determined by the shape and area of the aperture). Figure shows an example of a finished,ion-milled well with dimensions x 2.0 mmz in a LiNbO, transducer (the area and shape the well are similar to that of the shielding plate shown in the center of Fig. A deposited Au top electrode within the well is also visible. The waves around the well are characteristic the ion-milling process and are due to edge milling occumng fromoff-axis ions. The uniformity of the milling process is demonstrated in Fig. which shows the interference fringes obtained with an ion-milled LiNbO, transducer 0.3 Fm thick. The small number of wide fringes showsthat excellent uniformity has beenachieved;

Photograph of the fixturing for holding the A 0 device (left), etching mask (center) and actual A 0 device (right). (Courtesy Westinghouse Electric Corporation.)

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41 Photograph of mounted device in the fixture of Fig. 2, showing the finished ion-milled well in the transducer, with deposited top electrode. The dimensions of the ion-milled well are 1.5 X 2.0 mm2. (Courtesy of Westinghouse Electric Corporation.)

over an area of 100 X 100 pm2 the uniformity waswithin 10% of the transducer thickness or f15 nm. It has been reported that devices with transducers ion-milled to pm exhibited similar performance to those mechanically lapped to these dimensions The primary advantage of this approach (asidefrom not requiring askilled optician) is the ability to remove and test thedevice periodically during reduction-a procedure not possible with the parallel alignment tolerance requirement in the mechanical reduction process.

3.3 Top Electrode Definition The piezoelectric transducer substratemanufacturing process ends with the deposition anddefinition of a metallic electrode on topof the piezoelectric substrate surface. The top electrode not only provides the means to drive the transducer,but it alsodefines the height and width of the sound column, an integral part of an optimum A 0 design.

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42 Photograph of an ion-milled LiNbO, transducer with a thickness of 0.3 Fm. The small number of wide fringes shows the excellent uniformity of the pmz) was within 10% of the transthinned transducer which (over an area of

ducer thickness. (Courtesyof Westinghouse Electric Corporation.) The top electrode material is chosen to be both thick enough to provide a stable substrate for the attachment of the bond wire yet thin enough that excessive transducer loading and passband distortion are avoided. The specific material and thickness are optimized through a transducer impedance-matching analysis as discussed in Chapter 5 . Common top electrode materials include copper, aluminum, and gold. Typically the top electrode is fabricated using a single material a few tenths of a micrometer thick. Usually, a “lift-off’ photolithographic technique is used to define the electrode. photolithographic resist is applied to thepiezoelectric substrate surface and exposed witha mask the desired electrode shape. The exposed resist is then removedfrom the surface leaving an opening in the resist. The top electrode metal materialis then deposited on the resist. Removing the resist leaves the top electrode metallization in the desired shape. This process avoids the use of chemical

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metal etches which can damage the bonding layer. A GaP deflector with a top electrode is shown in Fig. If the thin-film transducer process is used, the top electrode can be deposited in the same vacuum cycle as the piezoelectric layer. Figure 44 shows a sputtering system with two magnetrons which can deposit both the metal electrode andthe piezoelectric layer. A high-quality A1 electrode can be formedfrom a target made of an Al-Cu-Si alloy. The copperreduces the surface roughness and the silicon improves the aluminum adhesion. Optimum deposition occurs when the substrate has a temperature of 160 to 200°C. The A1 forms in the [loo] orientation with the texture axis perpendicular to the substrate. The mean crystallite size is 0.5 pm. A typical electrode is 0.3 to 0.5 pm thick. Typical growth rates are 2 ndsec.

43 GaP deflector with top electrode defined. (Photo courtesy of Harris Corporation.)

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l

44 Dual magnetronsputteringapparatus. (Photo courtesy tersburg State Academy Aerospace Instrumentation.)

St. Pe-

4 FINAL DEVICE ASSEMBLY Once the fabrication of the transducer on the optica€block is completed, the device is ready for final assembly. An impedance-matching circuit is designed to match the impedance of the A 0 device to the electronic driver. The A 0 device and the impedance-matching circuit are then mounted in the A 0 device housing. An RF connector on the housing is electrically connected to the input side of the impedance-matching circuit while wires from the output side are bonded to the top electrode of the A 0 device. Finally, anacoustic absorber is attached tothe endof the device to frustrate acoustic reflections in the device. 4.1 Impedance-MatchingCircuit Once the fabrication of the transducer is complete,the RF impedance of the device ismeasured with a network analyzer.An impedance-matching network is then designed to match the impedance of the device to that of the external sourcedriver(typically 50 Cl). Thisnetworktypicallyconsists of discrete capacitors and inductors arranged in a pi-shaped circuit on a circuit board.

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Microstrip transmission lineelements also be used to simulate capacitors and inductors [&l. microstrip transmission line impedance-matching network is shown in Fig. The network consist of a series a high-impedance line shunted to groundandaserieslow-impedanceline. The networkis approximately equivalent to a series inductor, a shunt inductor, and a shunt capacitor. The input to the circuit is attached to an F W connector (typically SMA) on the device housing, while the output to the circuit is attached to the device transducer.

The device is attached to the impedance-matching circuit via wire bonding. The choice of the bond wire material andthe bonding mechanism is usually governed by the composition of the transducer top electrode

LOW IMPEDANCE LINE.

JPD 1

-"-

I

,

SHUNT LINE

/ /GROUND

HIGH IMPEDANCE LINE

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material. It is desirable to bond like materials together. Thus, if gold is used as the top electrode material, gold wire is used for the wire bond, and similarly for aluminum top electrode and aluminum wire. (When dissimilar metals are bonded,e.g., aluminum and gold, an intermetalliccompound can which can cause the wire bond to degrade and fail Gold wire is typically thermocompression bonded to the top electrode while aluminum wire is ultrasonically bonded at room temperature. Figure shows a photograph of a wire-bonding machine.

An acoustic absorber is usually attached to the back surface of the device to frustrate internal acoustic reflections. A metal or epoxy material with an impedance matched to the A 0 substrate is used. further reduce unwanted A 0 interaction, abevel can also be cut in the back surface prior to the attachment of the impedance-matching circuit.

46 Wire-bonding machine. (Photo courtesy

Harris Corporation.)

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Assembled acousto-optic cavity dumper device. (Photo courtesy of Hams Corporation.)

The A 0 device, with the impedance-matching network and acoustic absorbed, is mountedin a rectangular housing. The housing has openings on the side for optical illumination and mounting holes on the bottom for attaching opticalmounting hardware. Thehousing mayalso have additional features, such as cooling, for specific device requirements. finished cavity dumper device with cooling tubes in the housing is shown in Fig. A finished multichannel A 0 deflector is shown in Fig. 48.

The authors would like to thank V. Kulakov for the English translation of the work of Professor N. G. Nefedov, which was written originally in Russian. The authors also thank P. Fadeev of the St. Petersburg State Academy of Aerospace Instrumentation for his contribution to the dis-

398

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48 Assembled multichannel device. (Photo courtesy of St. Petersburg State Academy Aerospace Instrumentation.) cussion on platelet transducers and A. Goutzoulis and M. Gottlieb of Westinghouse Science and Technology Center forcontributing the section on transducer thinning via ion-milling techniques. D. R. Pape wishes to acknowledge stimulating conversations with B. Beaudet and E. Bryant of the Harris Corporation and M. Shah of MVM Electronics concerning the fabrication of A 0 devices. The photographs from the St. Petersburg State Academy of Aerospace Instrumentation were taken by N. M. Jakovleva, and the photographs from the Harris Corporation were taken by Ron Carman and furnished by John Watkins and Ed Bryant.

1. Castelli, L., Lithium niobate applications in optics and acousto-optics, Laser FocuslElectro-Optics, December 1985, pp. 120-123. 2. Bond, W. L., Crystal Technology, Wiley, New York, 1976. 3. Efremov, A . A . , and Salnikov, Ju.V., Manufacturing and Testing of Optical Workpieces, Vyshaja Shkola, Moscow, USSR, 1983. (Russian) Hecht, E., Optics, Addison-Wesley, Reading, MA, 1987, Chap.

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5. Krylova, T. N., Interference Coatings: Optical Properties and Study Methods, Mashinostroenie, Leningrad, USSR, 1973. (Russian) 6. Reeder, T. M., and Winslow, D. K., Characteristics of microwave acoustic transducers for volume wave excitation, ZEEE Trans. Microwave Theory Tech., MTT-17, 927-941 (1969). 7. Foster, N. F., Piezoelectric and piezoresistive properties of films, in Handbook of Thin Film Technology (L. Maisse and R. Glang, eds.), McGrawHill, New York, 1970, Chap. 15. 8. Chji, R., Yamozaki, O . , Wasa, K., et al., New sputtering system for manufacturing ZnO thin film SAW devices, J. Vac. Sci. Tech., 15, 1601-1604 (1978). 9. Foster, N. F., Crystallographic orientation of zinc oxide films deposited by triode sputtering, J . Vac. Sci. Tech., 6 , 111-114 (1969). 10. Mochalov, B. F., Streltsova, N. N., and Shermergor, T. D., Deposition of ZnO piezoelectric films by ion-plasma sputtering methods, Electron. Tekh., Ser. 6, No. IZ (Z36), 126-128 (1979). (Russian) 11. Danilin, B. S., Mochalov, B. F., Streltsova, N. N., et al., Zinc oxide piezoelectric film deposition in a magnetron ion sputtering system, Elektron. Tekh., Ser. 3, No. 3(87), 62-65 (1980). (Russian) 12. Waits, R.K., Planar magnetron sputtering, in Thin Film Processes, Academic Press, New York, 1978, Chap. 11-4. 13. Kenigsberg, N. L., Piezoelectric coefficients of patterned zinc oxide films, Acustich. Zh., 35, 368-370 (1989). (Russian) 14. Foster, N. F., The deposition and measurementof zinc imideshear mode and other thin film transducers, J . Vac. Sci. Tech., 6 , 111 (1969). 15. Shermergor, T. D.,and Streltsova, N. N., Film Piezoelectrics, Radio i Sviaz, Moscow, USSR, 1986. (Russian) 16. Foster, N. F., The deposition and piezoelectric characteristics of sputtered lithium niobate films, Appl. Phys. Lett., 40,420-421 (1969). 17. Tominaga, K., Iwamura, S., Fujita, I., et al., Influence of bombardment by energetic atoms on c-axis orientation of ZnO films, Jap. J. Appl. Phys., 21, 999-1002 (1982). 18. Kotelianskiy, I. B., and Luzanov, V. A., Crystallization of patterned zinc oxide filmsunder the conditions of bombardment by high-power oxygenparticles, Fiz. Khim. Obrabotka Mater., No. 4, 14-19 (1989). (Russian) 19. Grankin, I. M., Kalnaja, G.I., and Prishepa, N. N., High oriented zinc oxide films, Zzv. AN SSSR, Neorgan. Mater. 132,820-823 (1982). (Russian) 20. Bukharev, V. I., Mochalov, B. F., Streltsova, N. N., et al., Experimental study of pattern properties of zinc oxide films deposited with a magnetron method, Elektron. Tekh., Ser. 10, No. 5(29), 35-38 (1982). (Russian) 21. Nefedov, V. G., Gusev, 0.B., Mikhailov, V. N., et al., Technological process of piezoelectric transducer manufacturing based on zinc oxide films,Inform. Add., No. 90-91, Leningrad, TsOONTZ-ONZ NZZVSh, (1990). (Russian) B., Nefedov, V. G., Mikhailov, V. N., et al., Investivation on 22. Gusev, possibility to manufacture acousto-optic modulators with zinc oxide piezo-

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23.

24. 25. 26.

27. 28. 29. 30. 31.

32.

33. 34.

35.

36.

37.

electric transducers for the metric and decimetric ranges, Abstracts of Reports of All-Union Conference on Optical Information Processing, LIAP , Leningrad, USSR, 1988. (Russian) Nefedov, V. G., Gusev, 0. B . , Mikhailov, V. N., Gabaraiev, 0. G., et al., Zinc oxide films for acousto-optic and acoustoelectronic devices, Abstracts of Reports of XV All-Union Conference Acoustoelectronics and Physical Acoustics, LIAP, Leningrad, Part 3, USSR, 1991. (Russian) Kirgtn, E. K., and Yaeger, D. R., Today’s capabilities of microwave (0.218 GHz) acousto-optic devices, Proc. SPZE, 90 (1976). Soos, J. I., Rosemeier, R. Q. ,McFerrin, T. P. , and Sheerer, R. L. , 2.5 GHz bandwidth shear Bragg cells, Proc. SPZE, 936 (1988). Demidov, A. Ja., Zadorin, A. S . , and Pugovkin, A. V., Wideband abnormal light diffraction by hypersound in a LiNbO, crystal, in Acousto-optic Methods and Information Processing Technology, LETI, Leningrad, Vol. 142, USSR, 1980. (Russian) Rosenbaum, J. F. , Bulk Acoustic Wave Theory and Devices, Artech House, Boston, 1988, Chap. 4. Morozov, A. I., Proklov, V. V., and Stankovsky, B. F., Piezoelectric Transducers for Radioelectronic Devices, Radio i Sviaz, Moscow, USSR, 1981. (Russian) Uchida, N., and Niizeki, N., Acoustooptic deflection materials and techniques, Proc. ZEEE, 61, 1073-1092 (1973). Chang, I. C., Acoustoptic devices and applications, ZEEE Trans. Sonics U1trasonics, SU-23, 2-21 (1976). Sittig, E. , Effects of bonding and electrode layers on the transmission parameters of piezoelectric transducers used in ultrasonic digital delay lines, IEEE Trans. Sonics Ultrasonics, SU-16, 2-10 (1969). Konig, W. F., Lambert, L. B. , and Schilling, D. L., The bandwidth, insertion loss, and reflection coefficient of ultrasonic delay lines for backing materials and finite thickness bonds, IRE Znt. Conv. Rec., Pt 6, 9 , 285-295 (1961). Larson, J. D. , and Winslow , D. K. , Ultrasonically welded piezoelectric transducer, ZEEE Trans. Sonics Ultrasonics, SU-18, 142-152 (1971). Uchida, N., Fukunish, S., and Saito, S., Performance of single-crystal LiNbO, transducers operating above 1 GHz, ZEEE Trans. Sonics Ultrasonics, SU-20, 285-287 (1973). Sittig, E. K . , and Cook, H. D. ,A method for preparing and bonding ultrasonic transducers used in high frequency digital delay lines, Proc. ZEEE, 56, 13751376 (1968). Warner, A. W . , and Meitzler, A. H., Performance of bonded, single-crystal LiNbO, and LiGaO, as ultrasonic transducers operating above 100 MHz, Proc. ZEEE, 56, 1376-1377 (1968). Huang, H. G., Knox, J. D., Turski, Z., Wargo, R., and Hanak, J. J., Fabrication of submicron LiNbO, transducers for microwave acoustic (bulk) delay lines, Appl. Phys. Lett., 24, 109-111 (1974).

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38. Eschler, H. , Oberbacher, R. , Weidinger, F. , and Zeitler, K.-H. , Sirnens Forsch und Entwickl., 4 , 180 (1975). 39. Torgashin, A. N., and Gabaraiev, 0. G., Optical contact technology and its use in acousto-optics, Acousto-Optic Devices and Their Applications, RIO SOGU, Ordzhonikidze, USSR, 1989, pp. 56-62. (Russian) 40. Lifshitz, M. E., Theory of molecular adhesion forces between condensed matters, D A N USSR, 97, 643-646 (1957). (Russian) 41. Tavaciev, A. F., Talalaev, M. A., Torgashin, A. N., et al., Use of optical contact in acousto-optic device manufacturing technology, Abstracts of Reports of XI11 All-Union Conference on Acoustoelectronics and Quantum Acoustics, Kiev, Part 11, USSR, 1986, pp. 338-339. (Russian) 42. Private conversation with Ed Bryant, Harris Corporation, Melbourne, FL, December 1992. 43. Rosenbaum, J. ,Price, M. ,Bonney, R. ,and Zehl, 0.,Fabrication of wideband Bragg cells using thermocompression bonding and ion beam milling, IEEE Trans. Sonics Ultrasonics, SU-32 , 49-55 (1985). 44. Private communication with M. Gottlieb and A. Goutzoulis, Westinghouse STC, Pittsburgh, PA, September 1992. 45. Bagshaw, J. M., and Willats, T. F., Anisotropic Bragg cells, GEC J . Res., 2, 96-103 (1984). 46. Young, E. H., and Yao, S-K., Design considerations for acousto-optic devices, Proc. IEEE, 69, 54-64 (1981). 47. Glaser, A. , and Subak-Sharpe, G. E. , Integrated Circuit Engineering, AddisonWesley, Reading, MA, 1979, Chap. 16.

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Testing of Acousto-Optic Devices Akis P. Goutzoulis and Milton S. Gottlieb Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

Dennis R. Pape Photonic Systems Incorporated Melbourne, Florida

1 INTRODUCTION The testing of acousto-optic (AO) devices is the step that follows the device fabrication and its main purpose is to determine the degree to which the design goals have been achieved. The detailed testing of experimental A 0 devices, which are based on new designs or fabrication techniques, is often of crucial importance because it may reveal performance issues and/or effects not previously estimated or even known. Similarly, testing is important for characterizing new A 0 materials and estimating their performance when used in conjunction with specific device designs and applications. In this chapter we describe in detail a variety of different tests that can be performed on the four basic A 0 devices: single-channel deflectors (Section 2) , multichannel deflectors (Section 3) , modulators (Section 4) , and tunable filters (AOTF) (Section 5 ) . Since all A 0 devices involve electric, acoustic, and optical parameters, the tests must cover all three domains to the degree necessary for each device type and the application. In general, the tests and test procedures depend mainly on the A 0 device type, although several tests are common among all devices. These common tests involve (1) the acoustic pulse echo which shows the transducer bond quality, (2) the Schlieren imaging which shows the quality and characteristics of the propagating acoustic field, (3) the electric impedance, reflection 403

loss, and voltage standing-wave ratio (VSWR), which determine the electrical performance of the device, (4) the optical scattering which determines the quality of the crystal used, and (5) the acoustic attenuation of the crystal. Tests specific to deflector devices include (1) the overall frequency response or bandwidth which is determined by the acoustic, electric, and A 0 interaction responses, (2) the diffraction efficiency which determines the amount of light diffracted on a specific order, (3) the third-order intermodulation products which determine the level of spurious, unwanted intermodulation signals, (4) the single- or two-tone dynamic range, and (5) the time bandwidth product which relates to the number of resolvable elements and is of crucial importance for high-resolution spectrum analyzers and correlators. Multichannel deflectors require, in addition to the above tests, several tests that are concernedwith the (1) performance uniformity from channel-to-channel, (2) channel-to channel isolation which includes electric and acoustic crosstalk and affects the device dynamic range, and channel-to-channel phase and time uniformity of the input signal. The tests peculiar to themodulars include the (1) determination of the rise time, which is vital for digital applications, (2) modulation bandwidth, which is important for analog modulation applications, (3) modulation transfer function, which is critical for applications with stringent linearity requirements, and (4) modulation contrast ratio. AOTFs also require their own characteristic tests, which include the (1) determination of the tuning relation, (2) optical bandwidth, (3) spectral resolution, which is a key parameter for spectroscopic applications, (4) out-of-band transmission, which can seriously degrade the overall resolution, (5) RF power dependence of transmission, polarization rejection ratio, which is very important for overlapping diffracted and undiffracted orders, (7) spectral dependence of the spatial separation of the various orders, (8) angular aperture or field of view, and (9) spatial resolution of spectral images, which is important for spectral imaging applications. In the following sections we describe all the above tests with enough detail to allow the reader to successfully test any device. However, we emphasizethat each custom device design may require refinements of these test procedures.

2

DEFLECTOR TESTING

The full and precise characterization of an deflector requires several tests, which include acoustic echo measurements, Schlieren imaging, electric impedance, frequency response, scattering measurements, third-order intermodulation products, dynamic range, time-bandwidth product, and

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acoustic attenuation. The purpose, setup, and procedure for performing these tests are discussed in this section.

AcousticEcho Measurements One of the most critical steps in fabricating an A 0 device is the bonding of the transducer to the A 0 crystal. Following bonding, there are many steps in the fabrication procedure before the transducer structure is completed. Therefore, it is critical to assure before proceeding with these later steps that thebond is good, to thedegree that it can be tested atthis point. Since the transducer is, in general, not polished to its final thickness on bonding, the test cannot ensure that the mechanical bond, as determined by the bond layer thicknesses and composition, is correct according to the design. The test can, however, at least indicate that a continuous mechanical bond, with good contact .between the transducer and the crystal has been made. This is a quick, routine type of test, which issuitable forquality control when producing large numbers of similar devices. The basis of the procedure is to examine the acoustic pulse echo pattern produced by a small, movable electrode. A schematic of the measurement setupis shown in Fig. 1. The metallic bond layer forms the ground electrode, while the top surface of the transducer will normally have no conducting layer on it.*A movable top probe electrode can be easily made from a polished metal disc, about 5 mm or smaller in diameter, which is held gently in

1 Schematic of test setup forexaminingtransducerbondqualitywith movable electrode.

WVlZOULIS, W I I Z I E B , AND PAPE

(a>

2 Oscilloscope display of test patternsfrom (a)good bond, showing undistorted input pulse and return echo pulses, (b) poor bond, showing distortion of input pulse due to reflection of acoustic energy within transducer, and (c) undistorted input pulse for b. contact on the selected area of the transducer. pulse width small in comparison to thetravel time across the crystal is set, usually on the order of a few microseconds. With the probe held in contact with the transducer, the frequency is tuned until return echos are observed on theoscilloscope. If the transducer has not yet been thinned, this will be at some low frequency, around 5 MHz for typical bonding thicknesses. The pattern seen from a good bond is shown in the oscilloscopetrace in Fig. 2(a); the input pulse is undistorted and the echo pulses are reasonably clean replicas of the input pulse. The test involves probing the entire transducer area to ensure that the bond is uniform. An example of the test results obtained from a poor bond is shown in the oscilloscope trace in Fig. 2(b), whereas for comparison purposes we show in Fig. 2(c) the input pulse obtained when the probe is not in contact with the transducer. It can be seen that the pulse of Fig. 2(b) is distorted due to high reflection of acoustic energy within the transducer plate. In the region of a poor mechanical bond, the acoustic energy cannot be transmitted to the crystal. This diagnostic test easily shows suchpoor transmission, and the probeserves to pick up even a small such region if the transducer area is well sampled.

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2.2 Schlieren Imaging High-performance A 0 processors require A 0 deflectors with uniform, well-collimated acoustic beams (in the plane perpendicular to the plane of the A 0 interaction) without acoustic reflections from the sides of the A 0 crystal and without beam walkoff. These requirements are even more important in multichannel devices where the lack of highly collimated acoustic beams may result in severe crosstalk which limits the dynamic range and thus the usefulness of the device. In general, a uniform and well-collimated acoustic beam is achieved byusing a carefully oriented A 0 crystal in conjunction with (1) apodized transducer electrodes [l],or (2) acoustic collimating modes in materials such as GaP or (3) cylindrical transducers that focus the acoustic beam Regardless of the collimating technique(s) used, however, it is always necessary to examine the quality of the resulting acoustic pattern. This can be achieved via the use of the knife-edge method used by Toepler to examine Variations in the index of refraction of a medium, and which is known as schlieren imaging The schlieren imaging allows the observation of the phase variations generated in the A 0 crystal along the sound path, and it can be explained with the aid of Fig. 3. Collimated light from a laser illuminates the crystal which isdriven by a single RF tone. The acoustic grating(s) induced by the propagating acoustic beam(s) results in variations in the index of refraction, which causes variations in optical path through the deflector. These optical path variations result in emergent optical wavefronts that aredistorted. Lens L, focuses the undistorted (zero order) and distorted (diffracted orders) wave forms. At the focal plane a slit is used to pass only the first diffracted order, which is subsequently imaged onto a photographic film. Any shadow formed on the film reveals an angular displacement the optical beam, and thus it indicates the rate

DEFLECTOR

ORDER

3 Schematic of schlieren imaging system for observing the 2-D acoustic protile of

deflectors.

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and location of the change of refractive index across the input optical plane of the deflector; i.e., itprovides a mapping of the propagating 2-D sound beam. Figure 4 shows the photograph of an experimental schlieren imaging system as well as the schlieren image itselfat the far right of the photograph. The device under test is a S[110] TeO, deflector which uses a diamondshaped apodized top electrodedesigned to produce awell-collimatedacoustic beam. Figure 5a shows the schlieren image obtained from a similar device which uses nonapodized, rectangular-shaped top electrodes. Itcan be seen that the resulting sound profile is nonuniform, and it contains at least six acoustic sidelobes on each side of the main lobe, as well asacoustic reflections from both sides of the crystal. In Fig. 5b weshow the schlieren image from an L[lOO] A 0 deflector in which the selfcollimating acoustic mode results in a highly collimated, uniform acoustic profile free.from side lobes or acoustic reflections. Schlieren imaging is also useful for testing the orientation in materials with high elastic anisotropy such as TeO,, Hg,Cl,, and Hg,Br,. In these

Figure 4 Photograph of an experimental schlieren imaging system used with a S[ TeO, deflector with apodized, diamond-shaped top electrodes. (Courtesy of Westinghouse Electric Corp.)

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5 (a) Example of a nonuniform, noncollimated 2-D sound profile from a TeOz deflector with nonapodized, squared top electrodes. (b) Example of a uniform, well-collimated 2-D sound profile from a L[lOO] TI,AsS, deflector in which the specificacoustic propagation direction used resultsin self-collimation of the acoustic beam.

TESTING OF ACOUSTO-OPTIC DEVICES

41 l

(b)

6 (a) Example of the electrical impedance of a GHz L[lOO] LiNbO, deflector matched to 50 R. (b) Example of the return for the deflector of Fig. 5(b), covering the GHz range. (c) Example of the VSWR the deflector of Fig. 5(b).

materials the elastic anisotropy leads to a significant difference in direction between the group and phase velocities. This may result in significant acoustic walkoff, which limits the maximum usable aperture of the deflector. For example, for shear waves propagatingin the [l101plane of Hg2Br2 a misorientation is multiplied by a factor of 20, so for propagation in long-

412

1

WUIZOVLIS, WTi'LIEB, ANDPAPE

m /

GHr M2

Figure

Continued.

delay devices the transducer face must be oriented to 0.1" or better.Since typically a good x-ray from an etched surface can provide an orientation to an accuracy of O S " , a potential for beamwalkoff as much as 10" exists if only x-ray orientation is used. Schlieren imaging can be used to overcome this orientation problem in conjunction with a temporary, low-frequency transducer mounted on a ground test face of the crystal. From the measured schlieren imaging walkoff angle, a correction is calculated for the surface and the face is reground. second schlieren test follows the regrinding to verify the calculation and the followed correction.

2.3 ElectricalImpedanceTesting The electrical impedance and the return loss of an deflector can be easily measured via the use of a standard network analyzer. The test is usually automated and the results are plotted as a function of frequency. The impedance is plotted on a typical Smith chart, whereas thereflection loss is plotted in dB versus frequency. From the reflection loss data we can easily calculate the transmitted power as a function of frequency thereby determining the electrical bandwidth of the deflector. In a similar way we can also measure the VSWR of the deflector. Figures 6(a, b) show examples of the impedance and return loss of a matched L[100] LiNb03 deflector centered at1GHz with a 3-dB bandwidth of 500 MHz. Figure 6(a) shows that the electric impedance covering the 0.75-1.25 GHz band is very close to 50 CR with the worse

TESTING OF ACOUSTO-OPTIC DEVICES

413

case real impedance being about 43 at a frequency of840 MHz. Figure 6(b) shows that the worse case return loss, over the band of interest, is 14 dB at 1.25 GHz. This means that the worst-case power transfer to the transducer is 96% and that only 4% of the power is reflected. Figure 6(b) also shows that this particular deflector has a wide 3-dB electrical bandwidth which exceeds 950 MHz. In practice, however, the acceptable electrical bandwidth corresponds to a VSWR of 5 2 or a return loss of better than 9.5 dB. In this case the electrical bandwidth of the deflector is over 850 MHz and covers the 0.65-1.5 GHz range. Finally, in Fig. 6(c) we show the VSWR of the deflectorover the 0.75-1.25 GHz range which satisfies 1.1 SVSWR

The frequency response or bandwidth (BW) of an deflector is determined by the product of the electric, acoustic, and interaction responses [5]. Each of these responses is determined by various factors which depend on the deflector design, the material, and the fabrication technique used. TheBW of a deflector can be measured via the use of an power spectrum analyzer [6] (Fig.7). In this systema collimated optical beam of uniform intensity is incident on the deflector which is driven by a leveled RF sweep of center frequency!, and bandwidth 2Af. The sound field propagates at an angle, €li, with respect to the optical beam which propagates along the axis. The angle €li is set such that theBragg condition issatisfied for f,. Fourier transform lens collects and separates the diffracted and undiffracted orders and focuses the first diffracted order onto a linear detector array, the output of which is an exact replica of the deflector BW. Using spatial Fourier transformanalysis [6,7] we canrelate

fc f INPUT RF SWEEP

+FL +

7 Schematic an acousto-opticpower spectrum analyzer used to evaluate the bandwidth an deflector.

WUl'ZOULIS, W Z Z I E B , AND PAPE

41

distance, x , at the focal plane and RF frequency, f, in the A 0 deflector bY x = (+)f

where h is the optical wavelength, FL is the focal length the Fourier transform lens, and V is the velocity of sound in the material. Figure 8(a) shows an example of BW testing using the system Fig. 7, for the case a L[lOO] LiNb03 deflector driven by a 1-GHz BW sweepcentered at 1 GHz. For this example the deflector has an actual 3-dB BW covering the - 1350 MHz range. By varying the angle €li we obtain different A 0 responses, the envelope of which is independent of the interaction response, and representsa replica of the combined electric and acoustic responses. Since it is possible that the electroacoustic response is broader than the interaction re-

(a) Exampleof A 0 frequency response for anL[lOO] LimoBdeflector. centered at 1GHz. The horizontal represents frequency(100MHz per major division) from 500 to 1500 MHz.The vertical axis represents diffraction efficiency (1%W per major division).(b) Example of electroacoustic frequency response for the example of Fig. 8(a). Five different A 0 responses have been recorded and optimized at different Bragg angles. (c) Schematic of a single-detector acoustooptic system used to evaluate the bandwidthof an A 0 deflector.

415

TESTING OF ACOUSTO-OPTIC DEVICES

CTOR

OUTPUT TRIGGER TRIGGER

SWEEP GENERATOR

INPUT

OSCILLOSCOPE

sponse, an input RF sweep BW larger than that expected for the A 0 BW should be used in orderto measure the true electroacoustic BW. Figure 8(b) shows an example the electroacoustic response obtained for the previous deflector example. Five different A 0 responses have been recorded for which8, was optimized formaximum response at 750,875,1000,

41

WUlZOUJ5IS. W T I Z I E B , AND PAPE

1125, and 1250 MHz, respectively. It can be seen that the electroacoustic response in the 750-950 MHz range is about 2.5 dB higher than that in the 1200-1400 MHz range. This information is not apparent from Fig. 8(a), where the interaction was optimized at -1150 MHz in order to obtain the widest possible smooth response centeredat 1GHz. Note that for a fixed tIi the output of the detector array represents the averageBW response of the deflector over an A 0 time aperture determined by the width (D,along the axis) and the position of the input opticalbeam in the plane. By using a small D and probing different parts of the deflector in the plane, we can measure theA 0 response as a functionof position relative to the transducer. Thisallows a coarse examination of the effects of acoustic attenuation and the acoustic beam spreading, and helps identify the optimum operating area of the deflector. An alternativesystem for measuring the BW of an A 0 deflector is shown in Fig. 8(c). This system is similar to the spectrum analyzer shown in Fig. 7, with the exception of a single-element detector which has replaced the detector array at thelocation of the first diffracted order. Inthis system, the focal length of the Fourier transform lensis adjusted so that all of the first-order diffracted lightover the deflection BW is captured by the singleelement detector. The output of the detector is input to an oscilloscope triggered by the swept FW input to the deflector. The temporal trace on the oscilloscope is then a display of the power in the first-order diffracted optical beam versus FW frequency. Thedisplay can easily be converted to diffraction efficiency versus RF frequency by manually scaling the output to the productof the opticalpower in the zero-order opticalbeam and the RF power input to the deflector.

2.5 Scattering Measurements deflectors aretransmissive optical components, andthey include scattering sources such as [8] (1)surface imperfections and contamination, (2) permanent index fluctuations due to imperfections in the A 0 crystal lattice structure, and bulk particulates including smallbubbles, inclusions, and contamination. Theangular dependence and strengthof the scatteredlight depends on several factors, the most important of which are the size of the scatterers relative to the optical wavelength, their periodicity and relative population, and the propagationand polarization of the opticalbeam. The types and origins of scattering can be measured and characterizedby various techniques and instruments,including low-angle transmissive scatterometers formeasuring the bidirectionaltransmission distribution function birefringent interferometry formeasuring the optical homogeneity of the bulk [lo], various surface roughness profiling techniques, etc. The

TESTING OF ACOUSTO-OPTIC DEVICES

41 7

results of the scattering measurementscan be used not only in comparing A 0 deflectors but also in the modeling of A 0 systems with the goal predicting their ultimate performance [ll]. The light scattered by the A 0 crystal acts as noise that limits the performance of the A 0 deflector. Thisis most important when the deflector is used in an RF spectrum analyzer or channelized receiver, where the scattered light is very frequently the limiting factor of the system dynamic range (DR). For these applications, the important scattering parameters are (1) the level of the zero-order scattering that extends overpassband the of the device and (2) the sidelobe level of the first-order diffracted beam. The zero-order scattering level determines the DR floor or equivalently the minimum (or threshold) level of the input RF signal that produces a detectable output. The sidelobe level of the first-order diffracted beam determines theminimum detectable level of a weak RF signal in the presence of a strong RF signal, when the frequency separation of the two signals equals the frequency separation of the peak and the sidelobe. Furthermore, the increase of the output sidelobes and the widening of the diffracted beam result in decreased system resolution and increased crosstalk among parallel output channels. Once theA 0 deflector has been fabricated, an accurate characterization of the zero-order scatteringand the diffracted beam sidelobe structurecan be made by using the deflector in an power spectrum analyzer configuration and accurately recording the profiles of the zero and first diffracted orders [12, 131. This is also useful prior to deflector fabricationin (1) selecting anA 0 crystal adequate quality, and (2) gaining some idea about the diffracted beam sidelobe structure by observing the sidelobe structure the zero order, because in general the former resembles an attenuated version of the latter. This is more valid for isotropic A 0 interaction and less for anisotropic where polarization filtering [14, 151 between the two orders is used to reduce the overall scattering level and improve the diffracted beam profile. The schematic of such a scattering system is shown in Fig. 9. A laser beam is expanded through a two-lens system ( L , and L,) to give a collimated beam of diameter D.This beam is used the as probe for the scattering measurements from the test crystal or device. After passing through the A 0 crystal the emerging beam is focused onto the slit of a beam scanner. This scanner consists of a very narrow (10-25 km) slit with anoptical fiber probe attached immediately behind the slit. The slit/fiber assembly is in turn joined to amotorized linear drive. The fiber transmitslight the passing through the slit onto a photomultiplier (PM), the output of which is fed to alogarithmic amplifier (LOG AMP). Since typical PMssaturate atvery low optical power levels (-1 kW) an optical attenuator is used prior to

AND PAPE

WuIzOUL,IS, Wlli!,IEB,

418 GAUSSIAN-PROFILE COLLIMATOR

l

A 0 DEVICE

MOTOR-DRIVEN SCANNING SLIT

F3

FIBER-OPTIC COLLECTOR

9 Schematic of a scanning, slit-based scattering measurement system.

the PM in order tomatch the DR of the slit-fiber-PM subsystem with that of the spectrum analyzer optical system. The output of the amplifier is displayed on an X-Y recorder, the X-input being driven with a signal proportional to the linear displacement of the slit. Thus, the output from the X-Y recorder provides a spatial intensity profile of the focused beam incident on the slit. By comparing the profiles with and without the test crystal or device in the optical path, a quantitative measure of the scattering of the beam by the crystal is obtained. The diameter D of the probing beam isdetermined by the magnification of the lens system L,-L,: D =

where is the diameter of the collimated laser beam and Fl and F, are the focal lengths of lenses L 1 and L2 respectively. Use of a relatively large probing beam effectively averages any localized imperfections in the crystal and provides a realistic measure of the scattering limitations of a particular device or crystal boule. The same system can be used prior to deflector fabrication with a narrow probing beam in order to identify the least scattering region(s) in the material and thusaccurately determine the transducer and top electrodelocations for optimized performance. To identify the region of zero-order scattering that extends over the deflector’s passband or thefrequency separation the peak andsidelobes,

TESTING OF ACOUSTO-OPTIC DEVICES

41 9

we must translate the linear displacement Ax of the scanning slit to an RF frequency scale Af. This can be done from the relation =

VAX hF3

where F, is the focal length of the focusing lens L,. For a given A 0 material and RF resolution, Eq. (3) determines the minimum practical F, (in conjunction with the slit width in order to perform a meaningful sampling of the scattering profile. This is because as F, decreases does the width of the focused beam and thus for large d, the sidelobe structure may be smoothed or even lost because of the spatial integration over the width of the slit. Much finer sidelobe structure information can be obtained if we take into account the continuous spatial integration performed by the slit and deconvolve the results. For many A 0 applications, however, this type of-informationmay be unnecessary because a similar spatial integration is performed by the output detector arrays, which in most cases have widths compatible with those of the scanning slits [16]. A photograph of a laboratory scattering measuring system is shown in Fig. 10. The optical part consists of a 3-mW He-Ne laser beam (not shown in Fig. 10) which isfocused by a 10 X objective lens onto a 25-pm-diameter spatial filter. The resulting filtered beam is collimated by a spherical lens ( F L = 70 mm), passed through a sample two-channel A 0 deflector, and is then focused by a 175-mm focal length lens onto the scanning slit assembly. The latter consists of a 25-pm (W) X 2500 pm ( H ) scanning slit mounted on a scanning motor drive which has a travel distance of 10 mm and is readable to20 pm. A precision micrometer screw drives the slit and the associated fiberoptic collector probe across the focal plane. Automatic scan with controller direction and speed is accomplished with use of a scan control unit. An output from 0-100 mV is available whichisused for correlating the position of the slit with respect to the X axis of the X-Y recorder. The fiberoptic collector is 0.9 m long and consists of a fiberoptic bundle housed in a flexible stainless steel sheath. Thecollector terminates in a special adaptor which includes a filter cavity to allow neutral density filters to beinserted between the fiber probe and the PM. The PM assembly contains a thermoelectric water-cooled PM with temperature control, power supply, water pump, water reservoir container, and an S1 photosurface with spectral response from 300 nm to 1.1pm. The output of the PM drives a LOG AMP, which in turn drives the X-Y recorder. The scanning slit, motor drive, control unit, adaptor, and PM assemblyare Gamma Scientific Models 700-10-65A, 700-10-70, SG-1, 2020-6, and DC-45A, whereas the LOG AMP is a HP 7563A. The LOG AMP has a 55-dB optical DR, whereas the PM has a 45 dB DR and saturates for input optical power

WUlZOVLJS, Wli'LIEB, AND PAPE

Figure 10 Photograph an experimentalscatteringmeasurementsystem. (Courtesy of Westinghouse Electric Corp.)

levels of 2 pW. Use of He-Ne lasers (or infrared laser diodes) with power levels of several milliwatts in conjunction with neutral density filters extends the system DR to over 70 dB. An example of a first-order diffracted beam scattering profile taken by the system of Fig. 10 is shown in Fig. 11. The A 0 deflector used in this example and was is a L[100] T13AsS4with a 200-MHz BW and a TBW of considered for use ina channelized receiver. Figure 11shows thatthe focused probe beam has no sidelobes to at least dB, and thus in principle it allows the detection a weak single-tone signal(at about -40 dB)separated from a strong single tone by 10 MHz. However, the scattering the T13AsS4 ,crystal enlarges the widthof the diffracted beam and introduces sidelobes that significantly deteriorate this detection capability. Specifically,the power the weak signal must now increase by at least 8 dB (to dB)in order to allow discrimination from the sidelobe structure. Some demanding A 0 applications require deflectors with sidelobes suppressed to better than dB at A = nm. The testing of these deflectors demand that the probebeam has an adequateGaussian profile so that when focused it shows no sidelobes to at least- dB. In practice

TESTING OF ACOUSTO-OPTIC DEVICES

421

0-

-5 -

-m

-10

-

-15

-

'CI

2-20c

c

-25

-

-30

-

/Scattering /Input

Profile Beam Profile

fc

+ 20MHz

f,.+ 10 MHz

Frequency

C '

Example of a scattering profile from an experimental deflector.

this is possible with a good optical design in conjunction with carefully selected single-mode laser diodesand precision spatial filters. Such designs typically usea lens to collimate the laser diode light followedby a Keplerian expander with a spatial filter to eliminate the noisy components of the laser beam profile that generateunwanted sidelobes. Note that thespatial filter truncates the Gaussian profile and this results in distorted, sinc-type sidelobes weighted by the Gaussian profile. Hecht has studied this effect and has shown that for a dB sidelobelevel a perfect Gaussian profile must be maintained to at least the -29-dB points. For a given source size this determines the beam angular divergence that must 'be maintained through the system and it sets the f-numbers of the lenses as well as the width of the spatial filter.

422

WUlZOUL.IS, W77LIEl3, AAD PAPE

Figure 12 shows a miniaturized laser diode collimator which was designed using the above principles, and which is used for scattering measurements of a line-illuminated GaP deflector. The collimator uses commercially available, multiple-element lenses designed for operation with laser diodes, and an in-house-built precision spatial filter assembly. Figure 13(a) shows the profile of the resulting Gaussian probe beam, which has a clean, Gaussian-like shape with minimal distortion to at least the -29 dB points. When this beam is focused (Fig. 14(a)), the resulting sidelobes are about -41 dB, which is marginally acceptable for our purposes. A significant improvement of several dB is possible if the collimator’s output is passed through a single-mode fiber, which acts as a filter that virtually eliminates already suppressed modesand remaining noisycomponents [17]. Figure 13(b) shows the Gaussian profile resulting from propagating the beam of Fig. 13(a) through a 12-cm-long74/85-~mfiber segment. It can be seen that the beam has a broader, nearly Gaussian profile with no sidelobes to atleast the -36.5-dB level. When this profile is focused (Fig.

12 Photograph a miniaturized laser diode collimator with spatial filtering used scattering measurements a line-illuminated GaP deflector. (Courtesy Westinghouse Electric Corp.)

TESTING OF ACOUSTO-OPTIC DEVZCES

-1

\

-1

-25

-35

2.0 Distance (mm)

13 Gaussian profiles from(a) the miniaturized collimator Fig. 12, and (b) when the miniaturized collimator is used in conjunction witha 4/85-~msinglemode fiber.

14(b)), asmall sidelobe appearsat the - 44-dB level, whereas most of the noisy sidelobe structure appears at the -48-dB level. Note that an additional 1-2 dB reductionin sidelobe level is possible if the fiberis subjected to mode striping.

2.6 DiffractionEfficiency Measurements The diffraction efficiency, q, of an A 0 deflector is defined as the ratioI,/ I , of the first-order diffracted beam power to the zero-order transmitted

0

-5 0

5

m^

S

.-m C

(U

-20 -25

-30

c

-

-35

-4 5 -50

-1.6

-0.8 0 Distance

0.8

1.6

14 FocusedGaussianprofilesfrom (a)the miniaturizedcollimator of Fig. 12, and (b) when the miniaturized collimatoris used in conjunctionwith a 12cm 4/85-pm single-modefiber.

beam power, and for the frequency for which exact momentum matching occurs is given by [l81

where

In Eq. ( 9 , X is the optical wavelength, M2 is an material figure of merit, L is the interaction length, H is the transducer height, and P, is the acoustic power. The diffraction efficiency can be easily measured with a calibrated detector which measures Io at the input face of the deflector and Zl at the first diffracted order. The variation of the applied P, with frequency can be eliminated by normalizing the measured ZJZ0 by the applied P, and expressing the results in percent per watt (%/W). This procedure

TESTING OF ACOUSTO-OPTIC DEVICES

425

can be repeated for different RF frequencies that q can be plotted as a function of the input RF frequency. Since q depends on H , care must be taken so that the height of the optical beam is less than H.

2.7 Third-Order lntermodulation Product Testing The presence of multiple acoustic waves in an A 0 deflector results in multiple diffracted beams which contain spurious intermodulation products. The mechanisms responsible for these spurious signals are not only multiple optical diffraction due to the presence multiple tones simultaneously in the deflector [l91 but also material dependent acoustic nonlinearities [20, 211. When two tones of frequenciesfi and fz are present in the deflector, the strongest in-band spurious signals are the two-tone (or third-order) intermodulation products (IMP) 2fl-f2 and 2f2-fl,which are of major concern in A 0 spectrum analyzer systems since they limit the two-tone DR. Hecht [l91 has shown that the intensityof the third-order IMPS due to multiple optical diffraction is given by ZZ,l

=

q3 -

where q is the diffraction efficiency of the main diffracted modes at fi or dB) deflectors,q must be less than 0.02. This low efficiency in conjunction with typical detector arrays of dB dynamic range makes the detection of Zz,l via power spectrum analysis-type techniques very difficult and inaccurate. A more effective technique involves an interferometric Mach-Zender-type scheme in conjunction with an RF spectrum analyzer [21]. Figure 15 shows the schematic of this approach in which the deflector under test is fed with two equal-amplitude RF tones of frequencies fl and fz at a level that a predetermined q is produced. The two-tone diffracted beam is made to interfere with the diffracted beam from a reference deflector drivenby a single tone at frequency f3. The output is detected by a high-gain, lownoise detector/amplifier system and is then analyzed by an RF spectrum analyzer, which allows the simultaneousdisplay of the intensities of all the spectral componentsof interest. Note that for accurate measurements the two-tone RF input to the deflectormust be IMP free to better than10 dB below the minimum IMP level expected from the deflector. The system of Fig. 15 can operate without the reference deflector[22]; however, in this case the detector/amplifiersystem is required to have an RF bandwidth equal to2fz-f1. For multi-GHz deflectors this is nottrivial a task, especially whenwe consider the low-noise requirement. The detection

fz. Equation (6) shows that forwide-DR (e.g.,

426

WK'ZOULJS, WK'LIEB, AND PAPE Input Laser

Amplifier

Schematic of an interferometric system for IMP characterization of

deflectors. bandwidth can be significantly reduced with the addition of the reference deflector. This is because the latter acts as a mixer and downconverts the IMP bandwidth, BW-, given by BW- = (2f2-fJ - (2f1-f2) = 3(f2-f1) (7) to a much lower center frequency, equal to 0.5(f1 + f2) - f3, for which the low-noise requirement can be easily accomplished. Figure 16 shows the measured IMP level [23] using the system of Fig. 15 in conjunction withtwo T13AsS, deflectors at frequencies fi = 830 MHz, f2 = 838 MHz, and f3 = MHz, and for q = 0.05. For this example IMP levels as low as -31 dB (relative to the main diffracted tones) were measured, the limiting factor being the scattering of the A 0 crystal. Note thatby focusing the input optical beam onto thetest deflector, we can probe different areas of the sound field. This allows the measurement of the IMP level as a function of the distance from the transducer, which isvery important for large TBWP deflectors when they areused in channelized receiver applications. It also provides the ability to distinguish between the IMP level produced by multiple optical diffraction and by acoustic nonlinearities [22].

2.8 Determination of Dynamic Range Once the diffraction efficiency, third-order IMP, and the scattering level over the passband of the deflector are measured, we can determine the

TESTING OF ACOUSTO-OPTIC DEVICES

427

16 Photograph of themaindiffracted tones and thethird-order IMPs for a Tl,AsS, deflector with f, = MHz, f2 = 838 MHz, = 0.05, at A = 633 nm. For this example the reference deflector was drivenby an 800-MHz tone.

deflector DR. The useful DR largely depends on the specific application, most frequently however, it is the spurious-free dynamic range (DR,). DR, is defined as the input level variation range over which spurious signals are not developed above the minimum detectable signal level. For A 0 deflectors the level of the spurious signals isequal to thelevel of the thirdorder IMPs, whereas the minimum detectable signal is equal to the zeroorder scattering extending over the deflector passband. To obtain DR2 we plot the relative diffracted optical powers (in dB) the main diffracted tones at fi and f, versus the input RF power level (in dBm). The DR, is then determined bymeasuring the range from the interception the IMP curve and thecrystal scattering to theinterception of the main diffracted tone curve and the crystal scattering. In addition to the measured IMP curve, it is often useful to plot the IMPcurve determined by the multiple optical diffraction becauseit sets the limit of maximum theoretical spurious-free dynamic range(DR2T)in any deflector. Comparison of DR, and DRzTallows'us to determine how much improvement is possible in a specific deflector if acoustic nonlinearities were to be reduced. An example of an actual DR plot determined by the above procedure is shown in Fig. 17 for the case of a deflector operating over the

GOUlZOULIS, GOTTLIEB, AND PAPE

428

550-1050 MHz range [23]. For this example DR, = 30.7 dB and DR2, = 38.9 dB, which implies that an improvement of 8.2 dB would be possible if the acoustic nonlinearities that limit DR, were eliminated. The plot of Fig. 17 also shows the single-tone dynamic range (DR,) which is defined as the power range from the maximum acceptable safe input power level (P,,,) to the crystal scattering level. For the example of Fig. 17 Pmax= 26 dBm and thus DR, = 53.7 dB. Regarding DR, we note that when safety is not an issue P,,, is determined by the maximum acceptable deviation from a linear response. Typically the acceptable deviation is 1 dB, and the input power level to which this occurs is called the 1-dB compression point.

2.9 Time-Bandwidth Product The most important parameter of an A 0 deflector is its time-bandwidth product (TBWP) defined as the product of the time aperture ( T A ) and BW. The TBWP is equivalent [25]to the number of resolvable elements, defined as the ratio of maximum deflection angle over the angular spread

10

ti -10

:

n ; -20

.-0

c,

Q

U

-30

Q)

4-

0

-40 .n Q)

.L -50

-

c,

Q

Q,

-60

Figure 17 Example of a DR plot for the case of a Tl,AsS, deflector operating over the 550- 1050 MHz range where acoustic nonlinearities limit the spurious-free DR.

TESTING OF ACOUSTO-OPTIC DEVICES

429

of the diffraction-limited optical beam. Depending on the application, TBWP determines different system performance parameters. For example, for spectrum analyzers it determines the frequency resolution, for space-integrating correlators it determines the processing gain, and for time-integrating correlators it determines the number of parallel correlations (or, equivalently, the delay resolution of the correlation). It is well known that the BW of the deflector is determined [5] by the product of electric, acoustic, and A 0 interaction BWs. The useful TA is determined [26] by the (1) optical aperture, (2) acoustic attenuation, (3) geometric spreading of the acoustic beam due to diffraction from a finitewidth transducer, and (4) in some cases, by the spreading of the acoustic beam due to elastic anisotropy in the A 0 crystal [3]. Given the number of factors affecting the TBWP, it is often necessary to perform a test in order to verify the predicted TBWP performance. This is most often accomplished by using the deflector in an A 0 power spectrum analyzer in conjunction with a detector array (Fig. 18). The deflector is driven by two sine waves of equal amplitude which are separated in frequency by Af. By gradually reducing Af and observing, at the output of the detector array, the depth of the dip relative to the height of the two peaks we can determine the actual resolution of the deflector. The minimum acceptable depth is determined by the Rayleigh criterion [27, 281, which states that two spots are barely resolved by a diffraction limited system when the central dip between them is 19% of the maximum intensity of each spot. Once the Rayleigh resolution has been reached, Af must be measured in the R F domain via an R F spectrum analyzer. From the measured Af resolution and BW we can determine the actual TBWP.

WAVEFORM

Figure 18 Schematic of an A 0 power spectrum analyzer driven by two tones used to determine the frequency resolution of an A 0 deflector.

W K T O U L I S . Wl’i’LIEB, AND PAPE

430

In designingfrequency resolution experiments, much considerationmust be given to the pixel width of the detector array (along the direction of sound propagation) relative to the width of the focused spot. Using Eq. (1) we find that the distance, W, between the lowest and highest frequencies at the frequency planeof the spectrum analyzer of Fig. 18, is equal to W = XFL(BW) V Sampling theory requires that the detector arraysamples W at least twice per resolvable spot, which means that the pixel width, Dp, must satisfy

Dp

Wl2TBWP

(9)

If Eq. 9 is not satisfied, the detector array undersamples the output and this results in resolution loss. In practice, thefocal length of L3 is selected that the resulting W satisfies Eq. 9 for a given array with pixel size Dp. For example, for L[lOO] a LiNbO, deflector with BW=500 MHz, TA=2.0 psec, and a detector arraywith Dp= 10 pm, we find fromEq. 9 that W 2 20 mm. Subsequently, use of Eq. 8 with W 1 20 mm, shows that FL must be at least 415 mm at X = 633 nm. An experimental frequency resolution testing system is shown in Fig. 19. It is used for the testingof a L[100] LiNb03 deflector which operates over the 0.75-1.25 GHz range with a theoretical TBWP of1100 spots. Figure 20 shows the best resolution achieved with a detector array of Dp= 19 pm, when used with FL = 175 mm. This particular example demonstrates undersampling with W= 8.44 mm and a theoretical system TBWP of only 222, i.e., a theoreticalAf of 2.25 MHz. This is indeed the case as the RF spectrum analyzer measurement of the inputtwo tones shows (Fig. 21). Figure 22 shows the best resolution achieved with a detector arrayof Dp= 11 km, when used with FL=580 mm. For this setup W=27.9 mm, and thus a theoretical system TBWP of 1268 spots can be resolved. The data of Fig. 22 correspond to an experimentalAf of 494 kHz (Fig. 23) or an experimental TBWP of1012,which isin good agreement with the theoretical TBWP of 1100. In addition to detector undersampling, lens (L3)aberrations can also result in resolution loss because they increase the width of the focused spot, thereby increasing Af and thus reducing TBWP (note that by definition the maximum TBWP assumes diffraction-limited spots). Resolution loss alsooccurs when a nonuniform optical beamis used, because it always has a higher-frequency content than a uniform beam, and thus a wider spot when focused. Hecht[6] has studied thewidening the focused spot when a Gaussian beam profile is used, and has shown that little widening

TESTING OF ACOUSTO-OPTIC DEVICES

431

I Figure Laboratory power spectrum analyzer used for frequency resolution testing of an L[lOO] LiNbO, deflector. (Courtesy of Westinghouse Electric Corp.)

Figure 20 Example of frequency resolution measurements demonstratingundersampling usingthe system of Fig. 19.The test deflector is a 500-MHz L[lOO] LiNbO, with a theoretical TBWP of 1100. For this exampleFL is 175 mm and D, is 19 Wm.

432

WUl'ZOU5IS, WlTLIEB,

A M ) PAPE

21 RF spectrumanalyzer photograph showinga2.25-MHz separation for the two tones used in the example of Fig. 20.

22 Example of frequency resolution measurements demonstrating sufficient sampling usingthe system of Fig. 19. The test deflector is a 500-MHz L[100] LiNbO, with atheoretical TBWP of 1100. For this example withFL is 580 mm and D, is 11 p,m.

TESTING OF ACOUSTO-OPTIC DEVICES

23 RF spectrum analyzer photograph showing a 494-kHz separation for the two tones used in the example of Fig. 22.

occurs (55% of uniform case) when the truncation ratio is 0.75; i.e., the intensity of the Gaussian beam at the edges of the deflector is down by exp( - 1.125). In this case the resolution loss is about 5% and the TBWP is reduced to 95%.

2.10 AcousticAttenuationMeasurement The acoustic attenuation of most A 0 crystals used for A 0 devices are well known and documented in the literature [29]. Quite frequently, however, it is necessary to make an attenuation measurement on a device crystal because (1) there may be significant variation from one crystal batch to another, (2) a different orientation is used for which a good measurement has not yet been performed, and the crystal has been prepared by a new process [30-321. There are classical techniques for measuring the acoustic attenuation in solids, which are well described in the literatureon acoustics. These techniques require specialized apparatus, while an adequate measurement can often be done by an A 0 probe method, forwhich the necessary apparatus is typically foundin laboratories where A 0 device work is done. A convenient setup for measuring acoustic attenuation by the optical probe method is illustrated in Fig. 24. Since it is usually most

WUlZOULJS, Wi'TL,IEB, AND PAPE ROTATION TABLE

OSCILLOSCOPE

OSCILLATOR

24 Schematic a system employing the optical probe method uring the acoustic attenuation in device crystal.

meas-

useful to determine the frequency dependence of the attenuation in order to verify the expected p dependence for high-purity crystals it is helpful to bond a fairly low frequency (-20-30 MHz) transducer to the crystal, and perform the measurements on thehigher harmonics as well as on the fundamental frequency. Depending on thebond impedance match, it is often possible to obtain data beyond the ninth harmonic. The measurement accuracy can be optimized by working with a small laser beam diameter, e.g., 1 mm, in order to maintain good spatial resolution. For each frequency, the Bragg angle is optimizedfor peaksignal level. pulsed input RF signal is used, with pulse width, T,, that is small in comparison to the device time aperture The intensity of the diffracted signal, is measured for several positions of the incident laser beam at distance, d , from the transducer. If the input RF power level is set so that the diffracted signal intensity nearest to the transducer, I,, is well within the linear range of the device, then as the laser beam is translated to

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some distance d, the corresponding diffracted beam intensity will decrease according to In this equation a is a frequency-dependent attenuation constant which is approximately equal to where a, is the attenuation constant per unit length at 1 GHz, f is the frequency inG&, and m = 2 for most crystals of interest In general, it is difficult to obtain an accurate estimate of the attenuation coefficient by this method, even when the attenuation coefficient is high. However, the overall accuracy can be greatly improved by making as many measurement as there are laser beam diameters along the crystal length, and obtain a(f)for a given frequency, from the slope of a plot of loglo(Z/Zo) against d. This procedure is carried out at as many frequencies as can be accessed withhigher harmonics. By usingthe various a(f)values, the value of the coefficient a, can beobtained from a best fitto a quadraticdependence.

3 A 0 MULTICHANNEL DEFLECTOR TESTING multichannel deflector is constructed in the same way as a common single-channel device with the replication of single channels on a common A 0 substrate. Therefore most of the procedures employed in testing an individual channel of a multichannel deflector are the same as thoseused to test a single-channel device. These common procedures include acoustic echo, schlieren imaging, electrical impedance and VSWR, BW, scattering, diffraction efficiency, and third-order IMP. The additional tests required for a multichannel deflector include the channel-to-channel performance uniformity, channel-to-channel isolation, and thesignal-phase error. These additional test procedures are described in this section. 3.1 Channel-to-ChannelPerformance Uniformity The measurement of channel-to-channel performance uniformity entails comparing the results of the performance measurements of the individual channels of the multichannel device. Each channel of the multichannel deflector is individually tested with all other channels OFF. For electrical testing the same experimental setup and procedures used to test a singlechannel device are employed. For optical testing almost the same experimental setup and procedures as that used to test a single-channel device can also be employed. The experimental setup is modified so that the

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multichannel device is mounted ona vertical translation stage. Each channel is tested by translating the cell that the channel is illuminated in the same way as that used for single-channel Bragg cell testing. Typically the performance of any one channel shouldnot vary bymore than & 20% from the average performance of all of the channels.

3.2 Channel-to-ChannelIsolation The measurement of channel-to-channel isolation entails the measurement of crosstalk (an undesired signal appearing in one channel as a result of coupling from other channels). A crosstalk measurement typically determines the intensity of a signal in a nominally OFF channel due to the presence of a signal in a neighboring ON channel. The crosstalk level is usually defined as the ratio of the intensity of the signal in the OFFchannel to the intensity of the signal in the neighboring ON channel. Crosstalk in a multichannel Bragg cell results from both electrical and acoustic coupling between channels, as shown in Fig. 25. Electrical crosstalk arises primarily from coupling between the individual electrode matching networks and/or thetransmission lines connected to each of the multiple transducers. Acoustic crosstalk arises from the diffraction spreading of the acoustic beam fromone channel intoneighboring channels. Acoustic crosstalk increases as a function of distance from the transducer plane.

3.3 ElectricalCrosstalk Measurement Electrical crosstalk can be conveniently and unambiguously measured with an RF network analyzer Two adjacent channels of the multichannel device are connected to the transmission and reflection ports of the analyzer. The frequency source of the analyzer is swept through the bandwidth

RF Crosstalk

Acoustic Crosstalk

25 Multichanneldeflectorcrosstalk.

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of the device. The electrical transmission (crosstalk) through the two channels is then displayed directly on the analyzer as a function of frequency. Electrical crosstalk can also be measured using one of the “acoustic” crosstalk measurement techniques described below. Near the transducer, acoustic crosstalk is negligible since the acoustic beam divergence is negligible. An acoustic crosstalk measurement made near the transducer plane thus measures electrical crosstalk [36]. High-performance multichannel devices exhibit electrical crosstalk levels less than - 40 dB [37].

3.4 AcousticCrosstalkMeasurement Acoustic crosstalk, as discussed above, increases as a function of distance from the transducer plane. Acoustic crosstalk measurements involve measuring the intensity of the undesired diffracted optical beam from a nominally OFF channel due to thepresence a signal in an ON channel. The acoustic crosstalk measurement techniques described here actually measure the total crosstalk (both electrical and acoustic) between channels. One optical setup formeasuring acoustic crosstalk is shown [36]in Fig. 26. An optical beam is focused within a channel of the multichannel device.

PHOTOMULTIPLIER TUBE DETECTOR

LASER

SPECTRUM ANALYZER

12 M H z MODULATION

SIGNAL GENERATOR

26 Multichanneldeflectorcrosstalkmeasurementsetup.

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'

The device is mounted on a translation stage that measurements can be made at different positions along the length of the channel. The diffracted optical beam is collected by a photomultiplier tube detector whose output is fed to a spectrum analyzer. The output of the spectrum analyzer is connected to a strip chart recorder driven at the same rate as the multichannel cell translation stage. modulated carrier is fed to the channel and the intensity of the detected modulated output, Io, is recorded. modulated carrier is then fed to an adjacent channel (where now the illuminated channel is OFF). The intensity of this detected modulated output, I,, is also recorded. The crosstalk is defined as the ratio (in dB) of I , to Io. plot of the adjacent channel crosstalk in a 64-channel TeO, longitudinal mode multichannel cell (center frequency 400 MHz, bandwidth 200 MHz, transducer height pm, transducer center-to-center spacing 250 km) isshown[36]inFig. 27. The graph clearlyshows the spatial dependence the crosstalk. In most applications crosstalk levels less than -30 dB are desired. By measuring the spatial dependence of the acoustic crosstalk the useful TA of the device can be determined. Another crosstalk measurement setup is shown [38] in Fig. 28. The entire aperture of the multichannel Bragg cell is illuminated with a single colli-

t -100.0 0.0 0

.o 50

2.0 100

3.0 150

'

4.0 200

5.0 250

27 Multichanneldeflectorcrosstalkmeasurement.

6.0 DISTANCE (mm) 300 TIME-BANOWITH PROOUCT

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28 Intensity profile multichannel deflector crosstalk measurement setup

mated optical beam. A pair of lenses is used to form an image the acoustic waves withineach channel using the schlieren imaging technique. Here thezero-order light is blocked by a schlieren stop in the Fourier plane the optical system and the image isformed using the first-order diffracted light. An optical power meter is mounted on a two-dimensional translation stage in the image plane and is scanned orthogonal to the acoustic propagation direction across the images of the individual channels. pinhole in front the photodetector is used to provide good spatial resolution. The opticalpower meter output, as a functionof the scan distance, yields an intensity profile the acoustic waves ineach channel. Intensityprofiles at different locationsin the multichannel cell can be obtainedby translating the optical power meter in the direction of acoustic propagation. Acoustic crosstalk ismeasured by activating a channel andscanning the photodetector across the image of the ON channel as well as the adjacent OFF channels. The crosstalk level is defined as the ratio of the signal intensity measured in an OFF channel to the signal intensity measured in the neighboring ON channel. An example of a measurement taken using the above procedure is shown [39] in Fig. 29. Here a scan is made across the schlieren image of a multichannel device where two adjacent channels are simultaneously activated. Thesignal in the neighboring channel to the right the ON pair of channels is about 32 dB below the signal in the ON channels, indicating the crosstalk level at this scan location is about - dB. The accuracy of this approach may be less than desired as some

Intensity profile multichannel deflector crosstalk measurement

of the intensity of the signal measured in the OFF channel may be the result of spurious light scatter. (This background light scatter could be measured in a scan prior to activating the ON channel and then subtracted from the crosstalk level measured from the ON channel scan.) The previously described measuring technique overcomes this difficulty.

The measurement of channel-to-channel phase or time nonuniformity entails measuring the difference in the signal time-of-arrival between channels. Signal time of arrival is defined as thetime a signal is optically detected relative to thetime the signal is applied to themultichannel device. Channel-to-channel phase or time nonuniformity is the result of electrical phase differences between the matching networks and/or the transmission lines connected to each of the multiple transducers and acoustic and optical path differences between channels. An experimental setup for measuring channel-to-channel phase nonuniformity is shown [40] in Fig. 30. The optical setup is the same as that used in the first acoustic crosstalk measurement technique. A modulated RF carrier is fed into one channelof the multichannel device as well as to the reference input of a network analyzer. The output from the photomultiplier tube is connected to thetest input of the network analyzer. The network analyzer compares the phase of the modulated input to thephase

441

TESTING OF ACOUSTO-OPTIC DEVICES Multichannel Bragg Cell Swept Frequency Source

Mixer Photomultiplier Tube Detector

Network Analyzer

30 Electrical multichannel deflector phase nonuniformity measurement

setup

of the modulated output detected by a photomultiplier tube detector. detect the modulated output, the output from thephotomultiplier tube is mixed with the carrier. The phase difference between the input and output is displayed directly on the network analyzer as a function of frequency. A linear phase variation across the band is the result of a time delay between the input and output andcan be removed by adjusting a time delay in the reference channel. This measurement serves as a reference. The same measurement is then made of adjacent channels. A typical multichannel deflector has & 10" of channel-to-channel phase nonuniformity. An alternative optical approach to measuring channel-to-channel phase nonuniformity is shown in Fig. 31. The entire aperture of the multichannel Bragg cell is illuminated with a collimated optical beam. A lens is used to form the 2-D Fourier transform of the signals in the device in the back focal plane of the lens. The optical intensity distribution in this plane gives the power spectrum in the acoustic propagation dimension and phase difference between channels in the orthogonal dimension. Phase differences between adjacent channels result in an optical fringe pattern which is shifted vertically away from the transform center in proportion to the phase difference. Since the origin of the transform pattern is not known exactly, a series of phase difference measurements can be made between sequential pairs of channels for a relative phase difference measurement.

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31 Opticalmultichanneldeflectorphasenonuniformity setup [NI.

I measurement

This measurement technique might be attractive when the application is direction of arrival signal processing, but it is not as accurateas the electrical technique described above.

MODULATOR TESTING

4

Most of the modulator tests(acoustic echo, schlieren imaging, electric, acoustic, and interaction BW, scattering, diffraction efficiency, thirdorder IMP, and VSWR) are similar to those of the deflectors. In addition, the modulator must be tested for its risetime (t,), modulation bandwidth (BW,), modulation transfer function (MTF), and modulation contrast ratio (MCR). These additional tests are unique for modulators, and fortunately they can be performedwith the same test setup, a schematic of which is shown in Fig. 32.

4.1 RisetimeTesting The risetime, t,, of an modulator determinesthe maximum digital data rate usable, and thusit is of primary importance forapplications involving digital modulation. The 10-90% t, depends on the transit time of the acoustic wave across the input optical beam, and is defined [41] as t, =

1.33 W, V

where W, is the l/$ radius of the laser beam incident on theacoustic field of the modulator, and V is the acoustic velocity. Equation (12) shows that

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t 32 Schematic of a system used for testing the risetime an

modulator.

for a given material and configuration, t, is proportional to W,. This means that for small t, values (e.g., 110 nsec) focused optical beams should be used. This is because typical narrow collimated optical beams have a diameter of 20.5 mm which, for most materials, results in t, of several tens of nanoseconds. Figure 32 shows the schematic of a risetime test system which employs focused optical beams. In this system light from a laser source is collimated via lens L1 and is subsequently focused onto the sound field by lens L2. The diffracted optical beam is collected and focused onto a single-element high-speed detector by lens L,, which has a focal length of F3. The distances between modulator, L, and detector is 2F,. The output of the detector is displayed on an oscilloscope along withthe envelope of the modulated RF input signal. The latter is generated by mixing the output of a pulse generator with a sine wave whose frequency equals the center frequency, f,, of the modulator. For these tests the outputof the pulse generator is usually a square pulse train with risetime significantly smaller than that expected from the modulator. By observing the 10-90% t,of the detected pulses, we can determine the t, of the modulator for the specific W, used. Figure 33 shows an example of t, testing for the case of a Te02 modulator with f, = 60 MHz. For this example 2w, 80 pm and the resulting 1090% t, is 90 nsec, which isin good agreement with the t, = 86.6-nsec value predicted from Eq. (12). Figure 33 also shows the envelope of the modulating RF input signal, which has a t, < nsec. By using different combinations of lenses L, and L2 we can generate various focused beam sizes which result in different t, values. This information can be used to generate a plot of f, versus the input spotsize, which can be used to verify the design of the modulator and determine the ex-

-

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Example of modulator risetime measurement using the system of Fig. 32, for S[llO] TeO, modulator withf, = 60 MHz and 2w0 = 80 pm.

pected data rate as a function of the size of the input optical beam. An example of such a plot is shown in Fig. for a L[100]Tl,AsS, modulator of fc = MHz, which was tested with four different spotsizes. In performing the f, test careful attention should be given to various factors which can seriously degrade the accuracy of the measurements. Since focused optical beams are used, we must ensure that the zero and first diffractedorder beams are well separated. This means that angular the spread ( s e d ) of the diffracted beam satisfies 20B. In principle, can be somewhat different from the angular spread of the input optical beam However, in practice is the limiting factor, and therefore care must be taken in selecting the f-numbers of the L,-L, lenses. Note that in addition to the proper f-numbers, lenses L1-L2must also be of adequate quality in order to avoid aberrations which increase W, thereby increasing fr.

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1

34 Example of a risetime

optical beam diameter plot for a L[lOO] modulator of 480-MHz center frequency.

When the modulator is used for analog rather than digital applications, the modulation bandwidth (BW,,,) rather than t, is of importance. The SW, associated with a 3-dB falloff in output intensity is defined [26] as 0.5 SW,,, = tr

and thus one can use the measured t, value to evaluate SW,,,. The alternative is to use the system of Fig. 32 in conjunction with different sine wave modulating signals (instead of a pulse train) to directly determine SW,,, for a given By varying the frequency of the modulating sine wave and observing the voltage at the detector’s output, we can identify the frequency f,,, = SW,,, for which the output intensity drops by 50%. An example of this test is shown in Figs.35(a),(b), which show twooscilloscope photographs of the S[110] TeO, modulator’s output for a 100-kHz and a 5.5-MHz modulating sine wave, respectively. For this example the 5.5MHz frequency has about 50% of the low-frequency tone (i.e., 100 kHz)

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35 Example of modulation bandwidth testing for a TeO, modulator with fc = 60 MHz and 2w, = 80 pm. (a) 100-kHz tone, and (b) f, = 5.5MHz tone with half the amplitude of the 100-kHz case (in both cases the lower line corresponds to 0 V).

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amplitude, and thus it corresponds to f, = SW, = 5.5 MHz. For higheraccuracy measurements, the oscilloscope shouldbe replaced by an RF spectrum analyzer, which will allow the precise characterization of both the amplitude and frequency of the detected signal. Note, however, that in this case the f, will correspond to the frequency that is lower by 6 dB since the 3-dB SW, is defined with respect to theintensity rather than the RF power of the detected signal.

4.3

Modulation TransferFunctionTesting

For analog applications with stringent linearity requirements, the modulation transfer function rather thanSW, is important. MTF is defined [26] as

where = 2wJVis the acoustic transit time. By combining Eqs. (14), (12), and (13) we can show that the MTF can be expressed as a function of the flf, ratio:

m

=

exp

[ -0.69g)2]

where f, = SW,. The MTF can be evaluated by measuring the voltage at the output of the detector as a function of the modulating frequency using the setup of Fig. 32. These data are then normalized by the voltage measured at a very low modulating frequency (i.e., near DC). The experimentally determined MTFis then obtainedby plotting the normalized data as a function of the ratio flf,. Figure 36 shows an example of the calculated and measured MTF for the S[110] TeO, modulator with 2 4 , = pm and f, = BW, = 5.5 MHz. It can be seen that there is excellent agreement between the calculated and measured data. 4.4 ContrastRatioTesting The modulation contrast ratio determines the visibility or contrast of the modulation maxima and minima, and is given by

where I,,,,, and Imin are themaximum and minimum values of the intensity for a given modulation. The MCR is a maximum and equal to unity if the minima are zero, and zero if there is no longer visible modulation. For a

WUl'ZOULJS. Wli'UEB, AND PAPE

1.2 1.4 1.6 1.8 2.0

36 Measured and calculated modulation transfer function for a TeO, modulator withf, = 60 MHz, 2w, = 80 pm, and c, = nsec.

given modulation MCR is measured using the system of Fig. 32 simply by observing the maximum and minimum values of the detected voltage on the oscilloscope. For example, the MCR for Figs. 35(a), and (b) is 0.86 and 0.46 respectively. In a similar manner we can evaluate the static contrast ratio (SCR) defined as

In evaluating SCR caremust be taken in eliminating the RF leakage which may significantly deteriorate the SCR of the modulator which is usually caused by scattering from the crystal. 5

TESTING

The majority of tests required for characterizing the are quite different from those required for deflectors or modulators. This is because of the substantially different nature of an as compared with that of a deflector or a modulator, as well as because of the diversity and types of applicationswhich are different than those of deflectors or mod-

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ulators. The common tests are acoustic echo, schlieren imaging, electrical impedance and VSWR, scattering and acoustic attenuation. The additional AOTF tests include (1) tuning relation, (2) optical BW, (3) spectral resolution, out-of-band transmission, (5) RF power dependence of transmission, (6) polarization rejection ratio, (7) spatial separation of orders, (8) angular aperture, and (9) spatial resolution of spectral images. These tests are described in this section.

The most important AOTF test is the verification of the AOTF tuning relation defined as

where V is the acoustic velocity, An is the birefringence,and Fis a function only of the design angle of incidence Oi. Note that F(Oi) is unity for the collinear AOTF and is a numerically evaluated function for the noncollinear AOTF. Thepurpose in verifying the tuning relation is to ensure that the crystal configuration conforms to thatof the design to the desired degree of accuracy. The tuning agreement willbe affected by the accuracy to which the design angle Oi conforms. Since to each value of Oi there is a corresponding acoustic propagation angle, O,, and since generally V = V(O,), an error in crystal orientation will change the tuning relation. Itmay be important to takeinto consideration the temperature coefficients of the acoustic velocity, as well as the refractive indices, as these, too, may have a significant impact on the measurement. A typical setup used in order to perform this test is shown schematically in Fig. 37. A laser source is used to provide a well-calibrated wavelength standard. Thebasic instrument of the test setup is a sweep frequency RF signal generator, whose sweep rate can be adjusted to a low rate, typically less than 1 MHdmin. The output from the sweep generator is chopped by an RF switch which is controlled by a square-wave generator at a rate of about 1 kHz. The square-wave generator is also usedas the reference forlock-in a amplifier which receives the AOTF signal from the detector. An X-Yrecorder is used to provide a plot of the AOTFsignal as a functi?q~of the sweep frequency. By using a second wavelength in the AOTFspectral range, agood fit the tuning curve over the entirerange can be obtained. Anexample of a typical tuning curve is shown in Fig. 38, for thecase a Tl,AsSe, (TAS) AOTF covering the 8-12 pm range. In general, very high precision can be achieved with this technique with commonly available laboratory signal generators.

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DETECTOR C

AOTF

Y-CHANNEL

RECORDER I I

1 SWITCH

SQUARE WAVE GENERATOR

X-CHANNEL REFERENCE

A

SWEEP FREQUENCY SIGNAL GENERATOR

37 Schematic of a test system for measuring the tuning relation of the AOTF.

5.2 Optical

Test

The 3-dB optical BW of the AOTF, is defined as the spectral range over which the transmission efficiency for a fixed RF drive power remains above and is a very important characteristic for broadband AOTF applications [ M ] .The test setup used to measure theoptical BW is verysimilar to thatshown in Fig. 37, withthe difference that thelaser source is replaced with a broadband light source, preferably one which closely approximates a blackbody emitter. Although an incandescent filament source may be used for the near-UV and visible, a heated Sic rod or a globar is typically used to cover the entire range from the visible through the far-IR. Its operating temperaturecan be adjustedto optimize it for any spectral range and choice of detector, andits lack of protective envelope avoids associated

TESTING OF ACOUSTO-OPTIC DEVICES

8

9

10 Wavelength (

451

urn)

38 Example of a tuning curve for a

11

12

AOTF for the 8-12 pm

range.

absorption limitations. Note that theAOTF optical BW is determined by the transduceracoustic and electric BW and by the h-* dependence of the A 0 diffraction efficiency (see Eq. (5)). The measurement consists of scanning the RF over the full range of interest at a constantdrive power level whilerecording the AOTFfiltered light signal. The magnitude of the signal must be normalized to take into account the spectral intensityof the source,as well asthe spectralsensitivity of the detector, both of which can vary greatly over any sizable spectral range. Note that frequently it is necessary to use two different detector types to adequatelycover the spectralrange of interest. Anexample of an optical BW scan is shown in Fig.39 for the case of a TAS AOTF with an incident angle Ol = 35" and an interaction length of 1cm. For accurateresults the nonlinearitiesfrom all sources must be avoided. For example, theAOTF drive power should be kept below that value for which the diffraction efficiency exceeds 50% for any wavelength within the range of interest. Another sourceof nonlinearity is the detectoritself, especially IR detectors such as InSb or MC". Therefore, itis goodpractice either to calibrate the detector nonlinearity and provide a compensation for it or toreduce the highest signal level belowthe onset of unacceptable nonlinearity. This can be done either by reduction of the RF drive power

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$

2.5

5.0

Wavelength

39 Example of an optical bandwidth curve for a typical

AOTF.

or by reduction of the incident source intensitywith neutral-densityfilters. Note that well-calibrated neutral-density filters can be used to determine the detector linearity.

5.3 Spectral Resolution Test The spectral resolutionis a key characteristic of any spectroscopic device, and thus it is routinely measured for AOTFs In general,two different methods are used in order to ensure that the device has been well characterized. Thefirst method is similar to the oneused for testing thetuning relation. Using this method in conjunction with a laser source, a scan is taken as a function of the input frequency. The scan provides the frequency for peak transmission as well as the frequency width (Af) that corresponds to the full-width half-maximum (FWHM) intensity points. Using fo and Af, we can then calculate the spectral resolutionwhich is given by R = fJAf = XJAX. An example of such a scan is shown in Fig. for the case of a TAS AOTF. For this example R = 32.5. Depending on the resolution criterion chosen, the frequency separation between the peak and first zero the transmitted signal can also be designated. For highresolution AOTFs, it is important that the scan rate is slow enough as not to degrade the measurement. It has been observed frequently with AOTFs that the spectral resolution as determined with the above method may not correspond well with that observed when the AOTF is used to analyze broader light sources. In principle, the impulse response the device should be the same in the

v,)

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Frequency

40 Example of a spectral resolution test for the case of a TAS AOTF.

frequency space as in the wavelength space, and a scan of either frequency or wavelength should produce the same result. In practice, this is often not the case. The reason for this is due to the imperfections in the acoustic field distribution, which may arise from irregularities in the transducer structure.If there arecomponents of the acoustic field which depart from that of the designed distribution, then these componentsmay phase match withoptical wavelengths that lie beyondthe design resolution width. If the resolution test is performed with the laser, then there will be no wavelength components to phase match with these stray acoustic compo-

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nents, and the response appears to conform to the design response. For this reason, it is more reliable to measure the spectral resolution with a fixed RF applied to the AOTF,and record the light signal while scanning the wavelength of the source. A schematic for this type of measurement is shown in Fig. A simple mechanically scanned grating monochrometer is used, such as a Jarrell-Ashmodel 82 with motorized drive, which provides an output voltage related to the wavelength for the X-channel of the recorder. Of course, it is necessary to provide appropriate slits on themonochrometer to assure that the instantaneous spectral width of the source beam is substantially less than the AOTF spectral width. Otherwise, it would be necessary to deconvolve the monochrometer bandpass from the signal to obtain the AOTF resolution.

5.4 Out-of-BandTransmission The transmission curve in the immediate region of the main peak should reflect the shape of a sinc2 function. Any significant departures from this shape, in the form of additional transmission, is likely due to acoustic field

A

x-Y

41 Schematic a test system for measuring the spectral resolution of an AOTF with a broadband input light source.

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irregularities. Closely associated with this type of resolution degradation is the appearance of transmitted light at wavelengths more remote from the main peak, i.e., far out-of-band transmission. This type of irregularity may be associated with the presence of acoustic field components propagating in directions far off from the design direction. Such components typically arise from the unintentional reflections of the acoustic beam by the boundaries of the A 0 crystal. Such reflections are not unexpected, since it is very difficult to completely absorb the acoustic energy at the crystal end opposite the transducer. It is common practice to wedge this crystal end that the direction of the reflected energy does not phasematch with the incident light within the intended spectral range of the AOTF. If this condition is not satisfied, phase matching at some wavelength may be satisfied for frequencies far from the design frequency for that wavelength. Out-of-band transmission can be tested using the setup in Fig. by choosing a number of RF frequencies within the range of the device, the number depending upon the overall RF range. For each frequency the AOTF output signal is recorded as the wavelength is scanned over the entire spectral band of interest. For this test, the sensitivity the postdetector amplifier should be increased that this background transmission can be measured. For a well-designed and fabricated device, the background level should be 30 to 40 dB below the main peak value. For several applications it is necessary to evaluate the integrated out-of-band light intensity relative to the integrated intensity under the main transmission peak. In general, it is common practice to use bandpass optical filters to restrict the incident light beam range in order tominimize the out-of-band energy. Such a bandpass filter may also be used in conjunction with this test in order to measure the most meaningful quantity for the intended AOTF application. When evaluating the test results it is important to keep in mindthat thesinc2function side lobes integrated from the firstside lobe to infinity will contribute about 5% to the transmission outside the main peak.

5.5 RF Power Dependence of Transmission It is important to experimentally establish the regime of linearity for an AOTF in order to ensure that thedevice operates properly. The setup for this test is shown in Fig. 42, and utilizes an RF power meter between the input amplifier and the AOTF, and either a broadband source or different wavelength lasers. The AOTFmust be driven CW, and therefore the modulation the optical beam is obtained with a mechanical beam chopper. The chopped optical signal ismeasured on an oscilloscope. Note

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4

OSCILLOSCOPE

SIGNAL

42 Schematic of test system for measuring the linearity of the AOTF transmission vs.the RF drive power.

that if the impedance of the AOTF is not constant, the measurementmust be done for several optical wavelengths. This is because the electromechanical conversion efficiency varies with frequency, and the diffraction efficiency primarily reflects the acoustic rather than the electrical power density. Before proceeding with the measurement, the detection system should be calibrated forlinearity and if necessary the light intensity should be reduced sufficiently that it lies in the linear detection region. The measurements areeasily done manually, and consist RF power level vs diffracted signal level.Plotting andanalyzing the results in the usual manner will indicate thepower level which should not be exceeded for any desired degree of linearity. Closely associated with the above power transmission characteristicsat the wavelength peak, is the power dependence of the sidelobetransmission. It may be useful to verify by test that the power dependence of the intensity ratio of the peak to sidelobe agreewith the theoretical predictions.For a nonapodized transducer, the first and second sidelobe peaks should be down by 13 dB and 17 dB respectively, for diffraction efficiencies below 50%. the inputRF level increases, the peak-to-sidelobe ratio decreases because the nonlinear AOTF response. This is undesirable because it

TESTING OF ACOUSTO-OPTIC DEVICES

457

results in high levels of out-of-band transmission. Thus, measurement of this ratio will help optimize the AOTF operation that the out-of-band light is restricted to that caused by acoustic field irregularities or possible misalignment of the AOTFin its mount. Note thatsuch misalignment can cause unsymmetrical sidebands with higher than expected transmission.

5.6 Polarization RejectionRatio The operation of the AOTF is based upon the birefringent properties of the A 0 crystal, which may depart in some respects from ideal behavior, thereby degrading device performance. In particular, it is assumed that the filtered radiation will be 100% polarized, the positive- and negativeorder polarization being orthogonal to each other. This is of crucial importance if the inputangular field exceeds the angular separation between the zero and first diffracted orders. In this case the polarization of the filtered light must be used in order to separate it from the undiffracted light. For example, if the AOTFcrystal isstrained, theremay be sufficient strain birefringence in the optical path to cause some rotation of the unfiltered light, part of which will then appear in the diffracted beam. Furthermore, for the case of optically active AOTF crystals, low-incidentangle designs could allow unacceptably high levels of unfiltered radiation into the output beam. For these reasons, it is desirable to test the AOTF for its polarization rejection ratiosince it may limit the DR of the device. The experimental setupis similar to that of Fig. with the addition of a polarizer andan analyzer at the inputand the outputof the AOTF.Note that the input polarizer should be of high quality because the test result can be no better than that permitted by its rejection ratio.If an unpolarized laser is used, the output optical beam will consist of three components: the zero orderwith intensity Io,and the + 1 and - 1diffracted orders with intensities and respectively. The polarizer is then used to select the input polarization, whereas the analyzer is usedto select the appropriate component at the AOTF output.For this test theRF drive power should be set for 50% diffractionefficiency, that 1+1= = 0.510.By measuring the intensities of each of the three output componentswe can calculate thetwo rejection ratios: Z0/Z+*and Zo/Z-l. The measurementcan be performed with an expanded optical beam that fills the AOTF aperture or with an unexpanded beam which is used to probe individual portions of the aperture in case of nonuniform strains. If the rejection ratio is an important parameter, it may be useful to perform the test at more than one wavelength since strain birefringence is dependent not only on the geometry but also on the wavelength.

458

5.7

WUlZOUL.IS, W l T L I E B , AND PAPE

SpatialSeparation of Orders

The spatial structure of the optical beam exiting the AOTF is somewhat complex when examined in detail. However, for some applications, the details of this structure can be very important and therefore they must be characterized. This spatial structure is illustrated in Fig. 43. For an unpolarized input beam, there are four beams which appear in the output. In addition to the two first-order diffracted beams, the two polarizations in the zero order are also separated because of the birefringence of the crystal. Note that theactual separation of the orders will depend upon the (1) incidence angle Of, (2) direction of light propagation with respect to the optic axis, and path length in the crystal. The measurement the angular separation between the various orders is carried out using a laser source and a single-element detector mounted on a translation stage. Since the angular separation between the two zeroorder beams is quite small, the light beam must be well collimated and the detector plane sufficiently distant from the AOTF so that the beams will be spatially separated. The diffracted order beams will generally be between l"and 10" from the zero order. Note that these measurements must be performed at two wavelengths to fully account for dispersive effects.

5.8 AngularApertureTest The angular aperture or field of view (FOV) of the AOTF is defined as the angular field over which any input light ray may arrive and be transmitted at no less than 50% of the transmission at the optimum phasematched arrival angle. The determination of the angular aperture is carried

%=L-

+

Figure 43 Directions and polarization of the zero-order, positive and negative, first-order beams for an AOTF.

l"TING

OF ACOUSTO-OPTIC DEVICES

459

out at a fixed wavelengthand for afixed RF power. This test is most easily carried out by mounting the AOTF on a goniometer as illustrated in Fig. 44.The AOTFis held in a fixed position with its input opticalface located at the center of the goniometer, while the laser source and the detector are held on arms which are free to rotate about the AOTF. The measurement consists of determining the transmission ratio T(8) = Z(8)/Zp,where 8 is the angle of the laser with respect to theAOTF and I,, is the intensity of a perfectly phase-matched beam. It is important that theRF drive power be set at a level well below the nonlinear range in order to measure the true angular aperture. The AOTF of Fig. 44 is positioned in order to measure the polar aperture; for measuring the azimuthal aperture the AOTF must be rotated andmounted orthogonal to the plane of incidence. Note that the transmitted intensity distribution in the azimuthal plane is symmetrical about the center. However, this is not the case in the polar plane, especially for large values of the incidence angle, €li.For large FOV designs it is important to consider the effect of optical reflection losses, especially when AR coatings have been applied to the device. Depending

LASER

'h DETECTOR

\ -

/

GONIOMETER MOUNT

Determination of the angular aperture of an AOTFby measuring the transmission as the incident laser beam is rotated about the input face of the AOTF.

460

WVlZOULlS, W T I L I E B , AND PAPE

upon their design, the coatings themselves may contribute significantly to the angular variation of the transmission, and this effect should be separately evaluated from that due to the interaction. It was mentioned earlier that forOi the angular aperture (as represented on a polar plot)can be very complex, especially in certain singular directions. characterize this behavior, the must be mounted at measured angles between the polar and azimuthal planes. The measurement will be restricted by vignetting by the crystal near these singular values, where the angular aperture may be toolarge to allow even a small ray to exit the crystal output face.

5.9 Spatial Resolution of Spectral Images Optical systems whichincorporate for spectral imaging require an additional testwhich relates to thetransfer function of the or simply to the image quality resulting from the simplified method for characterizing the transfer function is shownin Fig. and uses an imaging camera. standard resolution chart is placed at a convenient distance, L , from the input to the The distance and the chart line spacings are chosen that a line pair of the chart will lie at theresolution limit of the The resolution limit can be specified as theangular separation, 8, between the line pairs at the limit, at the distance, L. This angle can be compared with the diffraction limited resolution angle from the aperture (=l.ZA/D).In general, the diffraction limit will be much smaller for an operating near the visible, while for at long-wave IR, the resolution may well be aperture diffraction limited. Figure shows an example of the chartimaged through a TeO, operating in the visible, and displayed on a TV monitor. From this photograph, it can be seen that theline pairs become indistinguishablebetween the small scale numbers 5 and For this example it is easy to verify, by

Fiol0 =

-6

45 Spatial resolution test an AOTF with an imaging camera by determining just resolved line pair on a standard resolution chart.

TESTING OF ACOUSTO-OPTIC DEVICES

461

41

aa

Example of a spectral image from a TeO, AOTF displayed on a TV monitor

examining the zero order image, that the image degradation is due to the interaction and not to the crystal or the TV camera.

The authorswould liketo thank Dr. D. K. Davies of Westinghouse Science and Technology Center forhis help in obtaining some of the experimental results presented in this chapter.

Bademian, L., Parallelchannel acousto-optic modulation, Opt. Eng., Hecht, D. L.,and Petrie, G . W., Acousto-optic diffraction from acoustic anisotropic shear modes in gallium phosphite, IEEE 1980 Ultrasonics Symposium Proceedings, Cohen, M.G . , Optical study of ultrasonic diffraction and focusing in anisotropic media, J. Appl. Phys., Longhurst, R. Geometrical and Physical Optics, Wiley, New York, Chang, I. C., and Hecht, D. L., Characteristics of acousto-optic devices for signal processors, Opt. Eng., 21,

WUIZOULIS, W l i ' Z I E B , AND PAPE 6. Hecht, D. L., Spectrum analysis using acousto-optic devices, Opt. Eng., 16, 461-466 (1977). 7. Goodman, J. W., Introduction to Fourier Optics, McGraw-Hill, New York, 1968. 8. Stover, J. C., Bjork, D. R., Brown, R. B.,and Lee, J. N.,Experimental measurement of. very small angle stray light optical performance of selected acousto-optic materials, Mater. Sci. Forum, 61, 57-92 (1990). 9. Stover, J. C., and Cady, F. M., Measurement of low angle scatter, Opt. Eng., 24,404-407 (1985). 10. Henningsen, T.,and Singh, N. B., Crystal characterization by use of birefringence interferometry, J . Cryst. Growth, 96, 114-118 (1989). 11. Brown, R.B., Craig, A. E., and Lee, J. N., Predictionsof stray light modeling on the ultimate performance of A 0 processors, Proc. SPZE, 936,29-37 (1988). 12.Goutzoulis, A., Gottlieb, M., Davies,K.,and Kun, Z., Thalliumarsenic sulfide acousto-optic Bragg cells,Appl. Opt., 24, 4183-4188 (1985). 13. Singh, N. B., Davies, D. K., Gottlieb, M., Goutzoulis, A., Mazelsky, R., and Glisman, M. E., On the quality of mercurous chloride crystals, Mater. Lett., 397-400 (1989). 14. Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J. Quantum Electron., QE-3, 85-93 (1967). 15. Hecht, D. L., Variable bandshapes in birefringent acousto-optic diffraction in LiNbOB,J. Opt. Soc. A m . , 66, 1094 (1976). 16. Goutzoulis, A. P., and Kumar, B.K. V., Detector size effects on peak-tosidelobe ratio in bulk acousto-optic spectrum analyzer, Opt. Eng., 24, 908912 (1985). 17. Hammer, J. M., and Neil, C. C., Adjustable modules for high-power (> 7.5 mW CW) coupling of diode lasers to single-mode fibers, ZEEE J . Lightwave Technol., L T - l , 485-494 (1983). 18.Chang, I. C., Acousto-opticdevices and applications, IEEE Trans. Sonia Ultrasonics, SU-23, 2-22 (1976). 19. Hecht, D., Multifrequency acousto-optic diffraction, ZEEE Trans. Sonia UItrasonics, SU-24, 7-18 (1977). 20. Chang, I. C., Nonlinearacousticeffects in widebandacousto-opticBragg cells, in Proceedings of the CLEOS Conference, 1983. 21. Shah, M. L., and Zerwekh, P. S., Intermodulation in wideband Bragg cells, 1983 lEEE Ultrasonics Symposium Proceedings, 1983, pp. 441-444. 22. Pape,D., Acousto-opticBraggcell intermodulation products, 1986 IEEE Ultrasonics Symposium Proceedings, 1986, pp. 387-391. 23. Goutzoulis, A., Davies, D., and Gottlieb, M., Thallium arsenic sulfide Bragg cells for acousto-optic spectrum analysis, Opt. Comm., 57, 93-96 (1986). 24. Elston, G., and Kellman, P., The effects of acoustic nonlinearitiesin acoustooptic signal processing systems, 1983IEEE Ultrasonics Symposium Proceedings, 1983, pp. 449-453.

TESTING OF ACOUSTO-OPTIC DEVICES

463

25. Korpel, A., Adler, R., Desmares, P., and Watson, W. ,A television display using acoustic deflection and modulation of coherent light, Appl. Opt., 5, 1667-1675 (1966). 26. Young, E. H., and Yao, S-K., Design considerations for acousto-optic devices, Proc. IEEE, 69, 54-64 (1981). 27. Randolph, J., and Momson, J., Rayleigh-equivalent resolution of acoustooptic deflection cells, Appl. Opt., 10, 1453-1454 (1971). 28. Chang, I. C., Cadieux, R., and Petrie, G., Wideband acousto-optic Bragg cells, 1981 ZEEE Ultrasonics Symposium, 1981, pp. 735-739. N., Acousto-optic deflection materials and techniques, 29. Uchida, N., and Niizei, Proc. ZEEE, 61, 1073-1092 (1973). 30. Roland, G., Gottlieb, M., and Feichtner, J. D., Optoacoustic properties of thallium arsenic sulfide, Appl. Phys. Lett., 21, 52-54 (1972). 31. Issacs, T. J., Gottlieb, M., and Feichtner, J. D., Optoacoustic properties of thallium phosphrous selenide,Tl,Pse,, Appl. Phys. Lett., 24,107-109 (1974). 32. Singh, N. B., Gottlieb,M., and Goutzoulis, A.P., Mercurous bromide acoustooptic devices, J. Cryst. Growth, 89, 527-530 (1988). 33. Bolef, D., in Physical Acowstics(W. P. Mason, ed.), Vol. IV,Part A, Academic Press, New York, 1966, p. 113. 34. Spenser, E.G., Lenzo, P. V., and Bellman, A. A., Dielectric materials for electro-optic, elasto-optic, and ultrasonic device applications, Proc. IEEE, 55,2074-2108 (1967). 35. Beaudet, W. R., Hams Corporation, private conversation, 1992. 36. Pape, D. R., Multichannel Bragg cellsfor optical systolic matrix processing, Topical Meeting on Optical Computing, March 18-20,1985, Incline Village, N V , Tech. Digest, Paper TuC6-1, 1985. 37. Beaudet, W. R., Popek, M., and Pape, D. R., Advances in multichannel Bragg cell technology, Proc. SPZE, 639,28-33 (1986). 38. Lin, Crosstalk characteristics of multichannel acousto-optic Bragg cells, Proc. SPZE, 936, 76-84 (1988). 39. Lin, S., and Boughton, R. Some performance characteristics of a channel Bragg cell with self-collimating acoustic waves, Optical Society of AmericaAnnualMeeting, Oct. 15-20, Orlando, FL. Tech. Digest, Paper MG1, 1989. 40. Lee, J. P. Y., Simple phase-tracking measurement technique for multichannel Bragg cells, Opt. Eng., 27, 677-683 (1988). 41. Maydan, D., Acousto-optical pulsemodulators, IEEE J . Quantum Electron. , QE-6, 15-24 (1970). 42. Singh, N. B. ,Gottlieb, M., and Goutzoulis, A. P.,Devices madefrom vaporphase-grown mercurous chloride crystals, J. Cryst. Growth, 82,274-278 (1987). 43. Singh, N. B., Denes, L. J., and Gottlieb, M., Growth and characterization of large Tl,AsSe, crystals for collinear AOTF devices, J. Cryst. Growth, 92, 13-16 (1988).

464 44.

WUlZOUL.IS, W l ' l U E B , A M ) PAPE Steinbruegge,K. B., Gottlieb, M., and Feichtner,J. D., Automated acoustooptic tunable filter infrared analyzer, Proc. SPZE, Feichtner, J. D., Gottlieb, M., and Conroy, J., Tunable acousto-opticfilters and their applications to spectroscopy, Proc. SPZE,

Computer-Aided Design Program for Acousto-Optic Deflectors. Oleg St. Petersburg State Academy

Gusev

Aerospace Instrumentation St. Petersburg, Russia

In general, the total frequency-dependentefficiency of an A 0 device is

where is the A 0 efficiency, q D is the efficiency loss associated with the diffraction acoustic energy outside the illumination aperture of the device, is the efficiency loss associated with acoustic attenuation in the deflector, and qTRAN is the loss associated with converting electric energy into acoustic energy at the transducer. The first term in Eq. (A.l) is discussed in Chapter 1 on A 0 deflectors, in Chapter 2 for A 0 modulators, and in Chapter for A 0 tunable filters. The second and third terms are primarily present only in deflectors and tunable filters and are discussed in Chapter 1 and Chapter respectively. The fourth term is discussed in Chapter 4. In Fig. A.l we provide a computer-aided design program from the St. Petersburg StateAcademy of Aerospace Instrumentation,which calculates the overallefficiency an A 0 deflector. Theprogram calculates the A 0 efficiency for an isotropic Bragg interaction using user-supplied device operating parameters,A 0 material characteristics,and transducer length. (The program can be modified to include the routine from the isotropic design program shown in Chapter 1 in Fig. which calculates a nominal value of L. The program can also be modified to include the other A 0

APPENDIX A OPEN 'PLOTDATA-1' FOR OUTPUT #l OPEN 'PLOTDATAQ' FOR OUTPUT #2 OPEN 'PLOTDATA-Y FOR OUTPUT #3 OPEN'PLOTDATAJ' FOR OUTPUT #4 OPEN 'PLOTDATAB' FOR OUTPUT #5 OPEN "PLOTDATA-6' FOR OUTPUT #6 OPEN 'PLOTDATA-7' FOR OUTPUT #7 OPEN 'PLOTDATA-C FOR OUTPUT #8 PRINT 'HARDCOPY ? YES 1, NO 0 INPUT N PRINT 'ELECTRICAL RESPONSE7 YES l,ELECTROOPTICAL RESPONSE? YES INPUT XX1 Pl=3.14159 F9=3E+08 FFO=F9 PRINT 'CENTRAL FREQUENCY FS..',FS;'GW FFF=.333 PRINT 'RELATIVE BANDWIDTH FFF=',FFF FF1 =FFO'FFF PRINT "BANDWIDTHFFl=;FFl W0=3E+O8/(F9*SQR(2.1)) P=l PRINT 'MAXIMUM BRAGG ANGLE MISMATCH P=',P PRINT 'ELECTRIC WAVELENGTHIN DIELECTRIC WO=';WO;'pTI' L1=.006 PRINT 'LENGTH OF LOAD TRANSMISSION LINE Ll=';Ll ;'pTI' LO=Ll/WO PRINT 'WAVELENGTH OF LOAD TRANSMISSION LINE LO=':LO 20 =20 2W;ZO;'Ohm' PRINT 'CHARACTERISTIC IMPEDANCE OF LOAD TRANSMISSION LINE T=.000003 PRINT TIME APERTURE T=';T E=38.6 PRINT 'DIELECTRIC CONSTANT OF PIUOELECTRICS E=';E L8=.0025 PRINT "TOP ELECTRODE LENGTH L8=';L8;'mm U7=4200 PRINT 'ACOUSTIC VELOCITY IN A 0 SUBSTRATE U7=';U7;'dsec' D9=T'U7 PRINT 'OPTICAL APERTURE D9=';D9;'m' F5=F9-.5'FFF'F9 PRINT 'LOWEST FREQUENCY F5=';F5;'Hzm PO=1 PRINT 'GROUP VELOCITY ANISOTROPY RATIO PO=';PO H=SQR(U7"2'T/F5'PO)

-

-

-

Computer-aideddesignprogramfor

-

deflectors.

467 PR~NT"TOPELECTRODE WIDTH (NEAR ZONE C O ~ D ~ T ~ o H=";H;"m" N) H=.0004 PRINT "CORRECTEDTOP ELETRODE HEIGHT H=";H;"m" N0=2.412 L9=6.328E-07 PRINT "OPTICAL WAVELENGTH L9=";L9;"mN PRINT "REFRACTIVE INDEX NO=*;NO U 1=4790 PRINT *ACOUSTIC VELOCITY IN PlEZOELECTRlCS u1=";u1 ;"dsec" R6=50 PRINT "SOURCE IMPEDANCE RW;R6;"0hmn K0=.49 PRINT "REFERENCE ELECTROMEC~ICAL COUPLING COEFFICIENT=";KO K6=KOA2/(1-K0"2) PRINT "REFERENCE ELECTRIC COUPLING COEFFICIENT OF EQUIV. NET.K6=";K6 K6=.2 ~RINT 'ELECTRIC COUPLING COEFF. OF EQUIV. NETWORK PIEZOEL. TRANSD. K6=";K6 Q9=4 PRINT "FIGURE OF MERIT OF LCR CIRCUT Q9=";Q9 C9=E*8.85E-l2*L8*H*2~F9/Ul RlNT 'STATIC CAPACIT. OF SINGLE ELEM. PIEZOEL. TRANSD. C9=";C9;"F" 01 =I PRINT "CO DECREAS. COEFF. FOR MULTIELEM. PIEZOEL. TRANSD. 01=";1 c9=c9/1 ~RINT "CO DECREASED=';C9;"FN R 9= 1/( 2 * P I * F9* C 9* K6*Q9) PRINT "RADIATION RESISTANCE OF PIEZOEL. TRANSD. R9=';R9;"0hmn c2=0 PRINT "SOURCE CAPACITANCE C2=";C2;"F" C3-0 cco=o PRINT 'CAPACITANCE PARALLEL TO LOAD TRANS.LINE INPUT CCO=";CCO;"~F' INT 'CAPACITANCE PARALLEL TO C9 C3=";C3;"Fn C8=C9+C2+C3 PRINT "TOTAL CAPACIT. C9+C2+C3=";C8;'Fn K8=C9*K6/(C9+C2+C3) PRINT "ELECTRIC COUPL.COEFF. WITH PARALLEL CAPACIT. K8=";K8 RE^ * IF NO EXTERNAL SERIAL CAPACIT. C4=0 C4=0 PRINT 'EXT~RNALCAPACIT. SERIAL TO c9+c2+C3=";C4;'Fn GOSUB 3470 R3=1/(2*PI*FO*CO*K*Q) F'RINT "RADIATION RESISTANCE R3=";R3;'0hmn PRINT "ELECTRIC COUPLING COEFF. WITH EXTERNALCAPACIT. K=";K PRINT 'FIGURE OF MERIT OF EQUIV. NETW. WITH EXTERNALCAPACIT. Q=";Q

.I Continued

468

APPENDIX A

PRINT"STAT. CAPACIT. OF EQUIV. NET. WITH EXTERN. CAPACIT CO=";CO;"F" REM STOP PRINT "LCR RESONANT FREQ. WITH EXTERN. CAPACIT. FO=";FO;"Hz" PRINT "UPSHIFTED PIEZOEL.TRANSD. RESONANT FREQ. F7=";F7;"Hz" DO=U 1/2/F7 PRINT "PIEZOELEM. THICKNESS WITHOUT BOND DO=";DO;"m* L2=1/( (2*PI*FO)"2*CO) GOTO 930 PRINT "CORRECTIVE INDUCTANCE PARALLEL TO CO =";L2;"H" 930 K9=1 PRINT "INDUCTANCE INCREASE RATIO K9=";K9 L3=L2/K9 PRINT 'CORRECTIVE INDUCTANCE PARAL. TO LOAD TRANS. LINE=';L3;"HU PRINT "LOAD TRANSM. LINE CHARACTERISTIC IMPEDANCE -";ZO;"Ohm" PRINT 'DIELECTRIC CONSTANT E=2.1' L5=3E+ 1 1/SQ R(2.1 )/F0/4 PRINT "Q-W TRANSFORMER LENGTH (GENERAT.TRANSM.LINE)=";L5;"mm" 0 5 =1 PRINT "Q-W TRANSFORMER SHORTENING RATIO 05=";05 L5=L5*05 PRINT 'SHORTENED Q-W TRANSF. LENGTH (GENERAT.TRANSM.LINE)=";L5;"mm" U3=3E+1 lISQR(2.1) U4=2*PI*FO M3=( U3/U4)*ATN( l/(K9*U4*CO*ZO)) PRINT 'INDUCTIVE STUB LENGTH ZO=';M3;"mm' Q6=2* PI*L9*L8/( NO*(U7/F0)"2) PRINT "KLEIN-COOK PARAMETER Q6=';Q6 A=l.451 E-12 PRINT 'ACOUSTIC ATENUATION PARAMETER A=";A;'Np/sec" M2=3.43E-17 PRINT 'A0 FIGURE OF MERIT M2=';M2;'sec**3/gM S0=(1.23*M2*L8/H)*l E+18 PRINT "DIFFRACTION EFFICIENCY SO=';SO;"%NVt" GOTO 1240 T5=SQR( 1-SIN( L9*F9/2/U7)"2) PRINT 'BRAGG ANGLE COSINE T5=';T5 Q7=( P P 2 "M2* 1E+07*MO*X7)/(H*( L9*.0 1*T5)"2)/4 PRINT 'Q7=';Q7 QO=Q7* S IN(P I*X7/(2*N9))/( PI*X7/N9/2) PRINT 'DIFFR. EFFIC. WITH BRAGG ANGLE ADJUSTMENT QO=";QO;"YooNVt' AF=FFO*FFF 1240 REM IF N = 0 GOTO 2080 PRINT #1 ELECTROOPTICAL FRECUENCY RESPONSE FOR AOD" PRINT #1 WITH MATCHING NETWORK BASED ON" 11"

Figure A.l

Continued

APPENDIX A

469

GOTO 1290 PRINT #1,," LUMPED INDUCTANCE AT LOAD TRANSMISSION LINE INPUT" REM GOTO 1310 1290 PRINT #1,," SHORTENED INDUCTIVE STUB AT LOAD TRANSMISSION LINE" GOTO 1320 AND EXTERNAL SERAL AND PARALLEL CAPACITANCES" 1310 PRINT #l,," 1320 PRINT #1,," AND QUARTER-WAVE TRANSFORMER WITH FREQUENCY RESPONSES" PRINT #1,," A 0 INTERACTION AND ACOUSTIC AlTENUATION" PRINT #1,," LiNbO3 => Te02 [OOl] AOM : MARK [TENZOR 901" PRINT #l,," SIGNAL PARAMETERS" PRINT #1,,"Central frequency .......................................................... =';FO;'Hz' PRINT #1 ,,"Time aperture ................................................................. ='. T;"sec" PRINT #1,,"Relative bandwidth ........................................................ =';FFF PRINT #l,," Bandwidth.......................................................................... =".FFl PRINT #1,," ACOUSTO OPTIC SUBSTRATE" PRINT #1,,'Te02 N[001], U[OOl], E- perpendicular to [OOl]" PRINT #1,,'Acoustic wave direction..................................................... - [OOl]" PRINT #1,,"Optical wave polarity................. = perpendicular to [OOl]" PRINT #1,,'Optical wave direction...................................................... [lOO]" PRINT #1,,"Acousto optic interaction................................ isotropic" PRINT #1,,"Acoustic velocity (longitudinal) ......................... =';U7;'m/sec' PRINT #1,,"Acoustic wave attenuation....................................... =';A;'Np/sec' PRINT #1,,'Klein Cook parameter (without mismatch).........=';Q6 PRINT #1,,'Bragg angle mismatch........................................................ =";P PRINT #1 ,,'Acousto optic figure of merit ................................ =';M2;'sec*'3/gU PRINT # 1,,'Diffraction efficiency (without losses). .............. ..=';SO;'%/Wt" PRINT #1,,'Optical aperture................................................................... =';D9;'m' GOTO 1610 PRINT #1,,'Diffrac. eff. with Bragg angle adjustement...............=';QO;'%/Bt" 1610 PRINT #1,,' PIEZOELEKTRIC TRANSDUCER" PRINT #l,,'LiNb03 Y+36 deg.' PRINT #1 ,,'Dielectric constant with constant strain...................... =';E PRINT #l,, 'ElectromechaniCal coupling coefficient......................... =';KO PRINT #1,,'Electric coupling coeff. for equvalent network =';K6 PRINT #1,,'Figure of merit of LCR circuit...................................... =';Q9 PRINT #l,,'Top electrode width.............................................................=' ;H;"m" PRINT #l,,'Top electrode length.............................................................. =' ;L8;"mN PRINT #1,,'Static capacitance of clamped transduser =';C9;"Fm PRINT # 1,,"Radiation resistanse................................................................ =';RS;"Ohm" PRINT #1 ,,'Acoustic velocity with constant strain .......................... =';U1 ;'m/sec' PRINT #1,, 'PIEZOEL.TRANSD.PARAMETERWITH FEEDER AND EXTER.CAPAIT.' PRINT #1,,* Piezoel.transd. feeder capacitance.................................... =";C2;'F' PRINT #1,,'Capacit.parall.to load transm.line input........................... =";CCO;'F" REM PRINT #1,,"Exter.capacit.ser.to piezoel.transd.+feeder........=";C4;"F" PRINT #1,,"Electric coupl.coeff. with parallel capacit. ...............=';K

-

-

-

-

-

-

...................

Figure A.l

Continued

APPENDIX A

470

PRINT #1,;LCR figure of merit with exter. capacit. ......................=' ;Q PRINT #l,;Stat. capacit. of piezoel.transd. + exter.capacit.';CO;'F" PRINT # l ,,'Radiat.resistance with exter. capacit. =';R3;'0hm' IF C4=0 THEN 1900 PRINT #l,,'Central frequency FO= ...........';FO;'HZ' PRINT # l ,,'Piezoelectric transducerresonant frequency' PRINT # l ,,'upshifted due to external capacitance =';F7;'HZ' ;DO;'m' 1900 PRINT #l,,'Piezoelement thickness without bond DO PRINT # l ,,' Matching network parameters' PRINT #l,,'Generator impedance for Q-W transformer =';R6;'Ohm' GOTO1960 PRINT # l ,,'Corrective inductance parallel to CO+C2+C3 =';L2;'H' 1960 PRINT #l,,'Correct.induct. paralleltoload trans.linein. ..=';L3;'Hm GOTO1990 PRINT #l,,'Corrective inductan............................................. lumped' REM GOTO 2000 1990 PRINT # l ,,'Corrective inductance shorted inductive stub' 2000 PRINT #l,,'lnductance increase ratio =';K9 =';Ll;'m' PRINT # l ,,'Load transmssion line length PRINT #l,,'Normalized load transmission line wavelength =';L0 PRINT # l ,,'Transmission linedielectrcs teflon,diel.const. ..=2.1' 05=0 THEN 2050 PRINT # l ,,'@W transformer shortening ratio =';05 2050 PRINT # l ,,'Q-W transformer width =';LS;'mm' ST0 P 2080 REM PUT CALL TO PLOT SETUP ROUTINE HERE FOR F=.5 TO 1.501 STEP .0125 GOSUB 3100 WRITE # l , F,13 NEXT F FOR F=.5 TO 1.501 STEP .0125 GOSUB 3010 WRITE #2, F, M9 NEXT F FOR 2-1.25 TO 1.75 STEP .25 R5=ZO'Z GOTO 2160 PRINT 'Loadtransmission line input impedance =';R5;'0hm' 2160 Z4=SQR(R6'R5) REM IF N=O GOTO 2250 PRINT #l,,'Gener.impedance to load transm.charac.impedance ratio 7 PRINT # l ,,'Q-W transf. charac.' impedance =';Z4;'0hm" REM IF N=O GOTO 2250 PRINT #l,,'lnductive stub charact. impedance =';ZO;'Ohm'

...................

.....................

...............

...........=' ......

.....

............................ ........................ ...................

...........................

...................................

................ ...........

Continued

.....

APPENDIX

471

PRINT # l ,,'Inductive stub length with charac. impedance ZO....=" ;M3;'mm' 2250 FOR F=.5 TO 1.5 STEP .0125 GOSUB 2950 GOSUB 2620 TT=2'PI'F'.25'05 A4=ZO'R B4=ZO9X+Z4'TAN(TT) C4=Z4-ZO'X'TAN(TT) D4=ZO'R'TAN(TT) C44=C4*C4+D4'D4 R4=(A4'C4+B4'D4)IC44 X4=(B4'C4-A4'D4)IC44 KK1 l=(Z4'R4-R6)*(Z4'R4-R6) KK12=(Z4'X4'X4'Z4) Kl=KKll+KK12 KKl3=(Z4'R4+R6)'(Z4'R4+R6) K2=KK13+KK12 G4=1-KllK2 REM G4=(1-6"2) GOSUB 3010 M5=G4'M9 GOSUB

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REM B1 Electroopt.freq.response normalized by Klein Cook parameter M6=M5'13 F1.01 THEN 2540 GO=SQR(Kl/K2) N=O GOTO 2540 SO=(l+ABS(GO))/(l-ABS(G0)) PRINT #l,,'Reflection coefficent at frequency F=l........... =';GO PRINT #l,.'VSWR at frequency F=l =';SO 2540 XX1=1 THEN 2565 IF Z=1.25 THEN WRITE F,M6 Z=1.5 THEN WRITE #4, F,M6 IF Z=1.75 THEN WRITE #5, F,M6 GOTO 2570 2565 Z=1.25 THEN WRITE #6, F,G4 Z=1.5 THEN WRITE #7, F,G4 Z=1.75 THEN WRITE #8, F,G4 2570 REM NEXT F REM last statement 2470 next NEXT Z CLOSE # l CLOSE #2 CLOSE

.........................

Continued

472

APPENDIX

CLOSE #4 CLOSE CLOSE #6 CLOSE #7 CLOSE END func 2620 NN=F-l/F G5=1+Q'Q'NN8NN BO=R5'2'PI'FO'CO/Z Gl=BO'K'Q/G5 REM 'Inductance parallel to CO add '=-1/F' to B1 REM Inductive stub parallel to CO add '-Tl' to B1 B1=(F'G5-K0NN'Q"2)/G5 B2=BO'B1 REM Denormalized G8=G1 & B8=B2 G8=GlR0 B8=B2/ZO B5=2'PI'F'LO B3=B2+SlN(BS)/COS(BS) C=l-B2*SIN(B5)/COS(B5) D=Gl'SIN(B5)/COS(BS) GS=C*C+D*D G=(Gl'C+B3*D)/G9 R E M 'Inductance parallel to load trans. line input add '-KS'BOIF' to B R E M 'Induc.stubparal. toload trans.line input add 'f'2'pi'fO*zO*ccO'to B R E M Inductive stub parallel to load trans. line input add '-BO'Tl' to B B=(B3'C-G1'D)/G9-BO'T1+F'2'PI'FO'ZO*CCO REM *Denonnaked compon. of input conduc. of load tran. line P9=G & D9=B P9=G/ZO DS=B/ZO R=G/(G'G+B'B) X=-B/(G'G+B'B) REM 'Denormalized components of load trans. line input imped. & X9=X R9=R'ZO X9=X'ZO RETURN 2950 REM Reactive conductance of shorted stub 71' AO=U4'M3/U3 AAl=SIN(AO'F)/COS(AO'F) AA12=U4*CO'ZO'AAl T1=1/AA12 RETURN 3010 REM Acoustic attenuation frequencyresponse FF=FO'F

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Continued

APPENDIX Al=A'T'FF'FF IF A1>100 THEN 3070 MS=(l-EXP(-Al))/Al GOTO 3080 M9=1 3080 RETURN 3090 REM A0 interaction frequencyresponse 3100 ll=.25'Q6*(F*F-PgF) ll=O THEN 3135 12=SIN(ll) l3=(l2/ll)*(l2/ll) GOTO 3140 3135 13=1 3140 RETURN REM Transversal dimensions of rectangular coaxial line H=.3 PRINT 'Width of central conductor';H;'mm' H1=.2 PRINT 'Dielectric thickness';Hl;'mm' H2=H+2'Hl PRINT 'Facewidth';H2;'mmm L8=2 PR1NT 'Length of central conductor';L8;'mm' Z0=18.5 PRINT 'Characteristic impedance';ZO;'Ohm' E9=2.1 PRINT 'Dielectric constant of waveguidedielectrics';E9 Wl=H2'(EXP(ZO*SQR(E9)/59.952)'(L8/H2+H/H2)-1) PRINT 'Face1ength';Wl;'mm' PRINT PRINTTransversal dimensions of microcoaxial rectangular' GOTO 3370 PRINT 'loadtransmissionline' PRINT Q-W transformer' 3370 PRINT 'shorted inductive stub' PRINT PRINT 'characteristic impedance';ZO;'Ohm' PRINT 'Dielectricc teflon ';E9 PRINT PRINT 'Width of central conductor';H;'mm' PRINT 'Length of central conductor0;L8;'mm' PRINT 'Facewidthm;H2;'mm' PRINT 'Face1ength';Wl;'mm' END 3470 REM & Q of PT equivalentnetwork with external serial capacit.

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Continued

APPENDIX

474

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* C4 externalcapacitanceserial C7=C8'( 1 IF C4=0 THEN 3520 GOTO 3540 3520 U=O GOTO 3550 3540 U=C7/C4 3550 1+U) Q5=SQR((l+K8)'(l+U)/(l+K8+U)) Q=Q9'Q5 FO=F9'Q5 F9=FO/Q5 F7=FO/Q5 C6=C7/K8 C5=C7/( 1+U) CO=C5*CS/(C5+CS) RETURN

to CO

Continued

interaction geometries.) The program calculates an optimized transducer height that no losses are associated with diffraction. The program can be used interactively to design an electrical impedancematching network given user-supplied values of the equivalent network of the piezoelectric transducer. An electrical equivalent circuit for a typical A 0 deflector transducer is shown inChapter in Fig.20. The user supplies the electrical coupling coefficient k ( = C,&,), the figure of meiit = l/ooCAR),and the series resonant frequency of the equivalent circuit. A simple two-stage matching network connected to the transducer via a transmission line is designed (similar to that shown in Chapter in Fig. 21) which resonates the parallel-plate capacitor with an inductor (Lo)followed in series by quarter-wave transformer [24]. Once the circuit is designed, the user can vary 2,the ratio of the load impedance R, to thetransmission line impedance The program in Fig. A . l is configured to calculate the diffraction efficiency of a longitudinal mode 100-MHz bandwidth, 3-psec timeaperture TeOzdeflector. RF power is delivered to the device via a microcoaxial waveguide structure with an internal conductor cross section equal to the piezoelectric transducer electrode size (2.5 X 0.4 mm). The output from the program providing all of the design information is shown in Fig. A.2. The program also provides calculated values for the parametersin Eq. (A.l) as a function of frequency. The program can be interfaced to a

APPENLIIX A

476

0.60

0.70 0.90 1.00 1.10 1.20 1.30 Relative Frequency (FC=3OOMHz)

1.40 1.50

Relative transducer efficiency vs. relative frequency for 1OO-MHz bandwidth, 3-hsec time-aperture deflector using different Z values.

0.60

0.90 1.00 RelativeFrequency

0.70

1.10

1.20 1.30 MHz)

1.50

Relative device efficiency vs. relative frequency for 1OO"Hz bandwidth, 3-hsec time-aperture deflector using different Z values.

APPENDIX A

477

graphics routine which allows the user to interactively design the A 0 deflector and electrical impedance-matching network to achieve a desired frequency response. Figure A.3 shows composite plot of qa, and for this device. Three curves are shown for corresponding to different values of the impedance ratio 2.Figure shows the composite diffraction efficiency q for this device using the three curves from the previous plot. The most uniform bandshape is that with Z = 1.50. A few of the many A 0 devices designed at the St. Petersburg State Academy of Aerospace Instrumentation are shown in Fig. A S .

A 0 devices designed and fabricatedat the St. Petersburg State Academy of Aerospace Instrumentation.

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A Computer Program for the Analysis and Design of Transducer Structures P. Goutzoulis Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

! ! ! ! !

DESIGN.FOR

T H I S I S A TRANSDUCERDESIGN PROGRAM THAT I S BASED ON THE THEORY D E S C R I B E D I N CHAPTER 5. I T USESTHESUBROUTINES T L I M PT, R A I M P , AND CONEFF I N ORDER TO CALCULATETHEIMPEDANCE ! O F AT R A N S M I S S I O NL I N ET, H EI M P E D A N C E O F THE TRANSDUCER, AND ! THETRANSDUCERCONVERSIONLOSS,ALSOACCORDINGTOTHETHEORY ! I T CALCULATESTHECOMPLEXIMPEDANCE(Z2RR+jZ2211) FOR ! A TOPELECTRODEWITHUPTO 2 L A Y E R S( T 2 AND TA),ANDTHE ! COMPLEX IMPEDANCE O F THEBOTTOMELECTRODECZ3RR*)Z31I)WITH ! UP TO 5 D E L A YL A Y E R S( T 3T, 4 , 75, T 6 T, 7 ) I. TT H E NU S E ST R A I M P ! TOCALCULATETHEFINALIMPEDANCE FOR THE INPUT TRANSDUCER. ! THEUSERCANADD AS MANY LAYERS AS NEEDED OR BYPASSTHE ONE ! NOTNEEDED B Y USINGZEROTHICKNESS.ATTHEEND O F THE ! CALCULATIONSTHEUSERNEEDSA l - DP L O TR O U T I N E TO I N S P E C T ! THECONVERSIONLOSS(CLL),ANDTHEREAL A PARTS O F THE ! INPUTIMPEDANCE CZAR AND Z A I ) AS A F U N C T I O N OF FREQUENCY. ! THE PROGRAM I S ! SETUPFOR A T L 3 A s S 4E X A M P L EW I T H [ L 1 L I N b O 3 TRANSDUCER, ! 1 0 0A OF CR AT EACH TRANSDUCER FACE AND ON THE A 0 CRYSTAL, ! Sn AS T H EB O N D I N GM E D I U M( L / 4 @ 3 0 0 MHt.2.8 AND ! A u A S THE TOP ELECTRODE. THE FREQUENCY RANGE O F INTEREST ! I S2 0 0 - 4 0 0M H z T . HE PROGRAM COVERS T H E1 0 0 - 5 0 0M H z RANGE. ! D O U B L EP R E C I S I O N KK,RSE,PI,Ul,U2,U3,U4,US,U6,U7,A2,A3,A4,A5, 1 Z2C,Z3C,Z4C,Z5C,Z6C,Z7C,ZAO,ZOO,Tl,T2,T3,T4,T5,T6,T7,

2

OFO,AO,EO,EV,CO,RO,FFO,FF,FFI,B2,B3,B4,B5,B6,B7,

3 4

22RR,Z211,Z3RR,Z311,Z4RR,Z411,Z5RR,2511,~6RR,~611,~7RR,~711,

6

OF,ZARR,ZAII,TKC3,DPZ

THO,ZTR,ZTI,CL,RG,TAA,ZAC,TA,UA,BA,Tll,A6,A7,T22,T55, !

APPENDIX B REAL !

COMPLEX Cl,C2,C3,C4,CS,CIN,COUT,CA,CB,CC,CD,CE !

PI-3.14159265 ! ! SOURCE bND WIRE SERIES IMPEDANCE (Ohms)

RG-50.0 RSE-0.5 ! ! TRANSDUCER COUPLING COEFFICIENT (Squared) KK-.49+0.49 ! ! VELOCITIES (m/aec)

U1-7400.0 U2-3378.0 U3-6650.2 U493320.0 US-2250.0 U6-U3 u7-u3

UA-U3 ! ! ATTENUATION COEFFICIENTS

42-0.0 A390.0 A4-0.0 AS-0.0

6610.0 A790.0 DPZ 0.0

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! ! MECHANICRL IMPEDANCES (gr/acc.m*+2)

Z2C-65.2E9 23Cg47.2E9 Z4C-24.6E9 ZSC-Z3C Z6C=Z3C 27C-23C ZAC-ZJC ! CRYSTAL IMPEDANCE Cgr/aec.m++21 ZAO-13.3E9 ! TRANSDUCER IMPEDANCE (gr/sec.m+*2) 200-34.8E9 ! ! NORMALIZATION OF IMPEDANCES

zAc-zAc/zoo z2c-z2c/z00 Z3C-Z3C/ZOO Z4C-Z4C/ZOO zsc-z5c/zoo Z6C-Z6C/ZOO Z7C-Z7C/ZOO

ZAO-ZAO/ZOO ! ! THICKNESS ( m )

11-10.OE-6 T292000.1 €-l 0 13-1 0O.OE-l0

APPENDIX B

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481

(mxm)

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TLIMP