Laser-Induced Damage of Optical Materials (Series in Optics and Optoelectronics)

Laser-Induced Damage of Optical Materials Series in Optics and Optoelectronics Series Editors: R G W Brown, University...

Author: Roger M. Wood

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Laser-Induced Damage of Optical Materials

Series in Optics and Optoelectronics Series Editors: R G W Brown, University of Nottingham, UK E R Pike, Kings College, London, UK

Other titles in the series Applications of Silicon–Germanium Heterostructure Devices C K Maiti and G A Armstrong Optical Fibre Devices J-P Goure and I Verrier Optical Applications of Liquid Crystals L R M Vicari (Ed)

Forthcoming titles in the series Stimulated Brillouin Scattering: Theory and Applications M Damzen, V I Vlad, V Babin and A Mocofanescu Diode Lasers D Sands High Aperture Focusing of Electromagnetic Waves and Applications in Optical Microscopy C J R Sheppard and P Torok The Handbook of Moire Measurement C A Walker (Ed) High Speed Photonic Devices N Dagli (Ed)

Other titles of interest Thin-Film Optical Filters (Third Edition) H Angus Macleod

Laser-Induced Damage of Optical Materials

Roger M Wood

Institute of Physics Publishing Bristol and Philadelphia

# IOP Publishing Ltd 2003 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreement with Universities UK (UUK). British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN 0 7503 0845 1 Library of Congress Cataloging-in-Publication Data are available

Commissioning Editor: Tom Spicer Production Editor: Simon Laurenson Production Control: Sarah Plenty Cover Design: Victoria Le Billon Marketing: Nicola Newey and Verity Cooke Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK US Office: Institute of Physics Publishing, The Public Ledger Building, Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106, USA Typeset by Academic+Technical Typesetting, Bristol Printed in the UK by MPG Books Ltd, Bodmin, Cornwall

Contents

Preface 1 Introduction

ix 1

2 Optical effects at low power/energy levels 2.1 Introduction 2.2 Electromagnetic theory 2.3 Dispersion 2.4 Reflectance and transmittance 2.5 Reflectance and absorptance of a conducting surface 2.6 Molecular polarizability 2.7 Absorption 2.8 Scatter 2.9 Analysis of R, T, A and S measurements

7 7 7 9 15 22 23 24 27 32

3 Optical effects at medium power/energy levels 3.1 Introduction 3.2 Absorption 3.3 Raman scattering 3.4 Brillouin scattering 3.5 Harmonic generation 3.6 Self-focusing

41 41 41 44 46 47 48

4 Damage theory 4.1 Introduction 4.2 Thermal mechanisms 4.2.1 Transmitting materials 4.2.2 Absorbing materials 4.2.3 Heat flow in transmitting windows 4.2.4 Thermal distortion 4.3 Dielectric processes 4.3.1 Electron avalanche breakdown theories

54 54 62 63 70 78 79 84 86 v

vi

Contents 4.4 4.5 4.6

4.3.2 LIDT versus pulse length and beam diameter Testing regimes Time of damage Damage morphology 4.6.1 Definition of damage 4.6.2 Damage morphology

88 91 94 97 97 99

5

Surfaces and sub-surfaces 5.1 Introduction 5.2 Surfaces 5.2.1 Polishing 5.2.2 Cleaning 5.2.3 Surface imperfections 5.2.4 Measurement of surface roughness 5.2.5 Surface measurement techniques 5.2.6 Surface absorption 5.2.7 Surface damage thresholds 5.3 Sub-surface

110 110 112 112 117 118 119 120 122 124 131

6

Coatings 6.1 Introduction 6.2 Coating technology 6.3 Measurements and morphology of coated surfaces 6.4 Coating design 6.5 Damage to dielectric coatings

137 137 139 143 145 153

7

Special topics 7.1 Ambient atmosphere/gases 7.2 Liquids 7.3 Photodetectors 7.4 Fibre optics 7.5 Scaling laws 7.5.1 Variation of damage threshold with wavelength 7.6 Significance of the units of measurement

157 157 161 163 165 170 174 174

8

Measurement techniques 8.1 Introduction 8.2 Measurement of power, power density, energy, and energy density 8.2.1 Beam divergence and spot size 8.2.1.1 Avizonis’ method 8.2.1.2 Aperture method 8.2.1.3 Knife-edge method 8.2.1.4 Slit method

177 177 178 182 184 184 187 188

8.3

8.4

8.5 8.6

Contents

vii

8.2.1.5 Saito’s method 8.2.1.6 Linear arrays 8.2.1.7 Discussion 8.2.2 Laser temporal profile 8.2.3 Power, power density/energy and energy density measurement Laser-induced damage threshold 8.3.1 Single-shot damage testing 8.3.2 Repetitive testing 8.3.3 Power/energy handling capability Measurement of optical characteristics 8.4.1 Measurement of reflectance and transmittance 8.4.2 Measurement of absorption 8.4.3 Measurement of scatter Surface measurement and specification Other measurements 8.6.1 Measurement of distortion 8.6.2 Measurement of birefringence 8.6.3 Other issues

188 189 189 190 191 192 192 193 195 196 196 198 207 209 212 212 212 213

Appendices 1 Dielectric breakdown fields 2 Summary of literature surveys of typical damage threshold in MW mm2 under 10 ns Q-switched 1.06 mm irradiation 3 Damage thresholds measured at the GEC Hirst Research Centre (MW mm2 ) 1.064 mm irradiation, 10 ns 4(a) Summary of LIDT measurements made at 10.6 mm at the GEC Hirst Research Centre on infrared window substrates and coatings (pulsewidth, ¼ 100 ns) 4(b) Summary of LIDT measurements made at 10.6 mm at the GEC Hirst Research Centre on metal mirrors 5 Summary of LIDTs of infrared transmitting materials 6 LIDTs of metal mirrors 7 LIDTs of coated substrates 8 Summary of the LIDTs of ultraviolet transmitting materials 9 Summary of damage thresholds under HF/DF laser irradiation 10 Continuous wave laser damage, 10.6 mm 11 Comparison of the LIDTs of /4 single-layer coatings on fused silica

215 215

References

232

Index

239

217 218

219 220 221 224 226 227 228 229 230

Preface

When I wrote my previous book Laser Damage in Optical Materials (Adam Hilger 1986) I expressed my fear that while more and more is known about less and less, much of the factual evidence gets buried under the mass of paperwork and the lessons painstakingly learned get forgotten. Having now lived to the turn of the millennium I have found not only that this is true but also that many of the research workers in the field of high-power lasers have now either retired or moved on to other work. The new generation of workers in the field of high-power lasers are therefore frequently having to replicate the work we, the earlier generation, did many years ago. For instance, the subject of laser-induced damage in laser glass has come to the fore at least three times, to my recollection, at the annual Boulder Damage Symposia. This has resulted in my being asked to run courses on the subject for both the Institute of Physics in the UK and for SPIE in the USA. I have also been very involved on behalf of the British Standards Institution with the ISO conferences on standardizing laser-based measurements. In writing this present book I am attempting to update the previous book by adding more complete theory together with more rigorous mathematical treatment and supporting data. This book also extends the previous book in that I am covering the whole field of the power/energy handling capability of materials, components and systems. In doing so I am attempting to show how knowledge of the subject of high power interactions can be used to advantage. When low-intensity light passes through a transparent substrate, falls on a reflecting surface or passes into an absorbing medium little or no extraneous effect is observed. When the intensity of the beam is increased a range of reversible interactions come into action. These range from absorption, through temperature rise to distortion, nonlinear absorption/transmission and reflectance. These effects also include electro-optic effects, second and third harmonic generation, parametric oscillation and self-focusing. Many of these effects can be used to advantage in optical engineering (generation of new wavelengths, optical limitation etc.). When the intensity of light is increased still further these phenomena give way to non-reversible ix

x

Preface

changes in the material or component: cracking, pitting, melting, vaporization and violent shattering. A knowledge of the precise levels at which these take place is necessary for laser machining (drilling, welding, cutting—both of engineering materials and for laser surgery), for laser cavity design and for materials research (spectroscopy etc.). I cannot pretend that I would have got as far as publishing the earlier book or edited the SPIE Milestone book on laser damage to optical materials (1990) without interaction with the many workers in the field. I first need to thank my colleagues at GEC Hirst Research Centre, Wembley, for their collaboration for over 28 years. I would particularly like to thank the organizers of the annual Boulder Damage Conferences for all their encouragement, and most of all for continuing to organize this series of symposia. I would also like to thank my fellow members of ISO/TC 172 for their part in writing the measurement standards discussed later in this book. I also need to make a general acknowledgement of all the workers in the laser field who have published data that could be used to augment my own, particularly at wavelengths, pulse lengths and power levels beyond those at which I have made measurements. These have allowed me to check and verify that it is possible, even if problematical and error ridden, to scale across large differences in these parameters. Roger M Wood

Chapter 1 Introduction When a low-intensity light beam passes through a transparent substrate or falls on a reflecting mirror or on an absorbing medium, little or no effect may be observed. When the intensity of the beam is increased, however, a whole range of reversible interactions may become obvious. These include temperature rise, expansion, distortion, strain, nonlinear transmittance and absorption, electro-optic effects, second-harmonic generation, optical parametric oscillation and self-focusing. When the intensity of the beam is increased further these phenomena give way to non-reversible changes in the material or component. These effects include surface and bulk annealing, surface melting, material softening and bending, cracking, pitting, bulk melting, vaporization and violent shattering. Although these effects will occur whenever a light beam is powerful enough (either in average or peak energy or power density) the advent of the laser has given prominence to them as common occurrences. It will be assumed, for the rest of this book, that the radiation source is a laser. This will make it easier to calculate the magnitude of the effects since laser beams are usually monochromatic and have precise temporal and spatial characteristics. The main limitation in the design and utilization of lasers (and in particular miniaturization) is the tendency of the high laser flux generated in the laser cavity to change the optical performance characteristics of the internal optical components. The change in the optical performance of individual components, from those measured as free-standing components, may be due to any one of a number of factors. These effects may be either individual or cumulative. They may limit the transmission of the system, degrade the performance or may lead to laser-induced damage. The change in component performance may be due to: thermally induced strain and distortion of the optical elements, a change in the beam divergence of the transmitted beam due to thermal lensing, melting, in particular of the dielectric coatings, laser-induced damage of absorbing specks in the optical materials (e.g. Pt speck in laser glass), 1

2

Introduction self-focusing in the optical elements, laser-induced damage of the optical element surfaces due to weak coatings, contaminated surfaces and coatings, or digs/scratches on the coatings/surfaces.

These problems have been experienced over the whole range of laser wavelengths and pulse duration. For example they are well known in the following. Diode lasers—Most diode lasers exhibit a change of divergence with input power. Degradation of the laser output characteristic occurs due to damage to the internal facets because of a drift of internal defects and impurity ions. Low-power He/Ne lasers—There is a gradual diminution of the power output with time because of a build-up of contamination on the mirrors leading to a change in the window characteristics with time. Medium/high-power Nd:YAG lasers—Birefringence effects affect the design of both the laser resonator and the system. The life and output of the laser is usually limited by damage to the anti-reflectance and highreflectance coatings. There is usually a change of output beam divergence with input power and nonlinear input/output characteristics. Optically complicated SHG and dye laser systems—Reflections and multiple beams affect the design of these systems. High-power pulsed and continuous wave CO2 lasers—Melting, contamination/degradation of the mirror surfaces, distortion/birefringence and change of the beam divergence with input power are all affected by the design, construction and specifications. Ultra-high-power, short-pulse lasers—Multi-photon ionization and selffocusing limit the energy per pulse. The highest laser powers/energies are found inside the laser oscillators and amplifiers (until the output powers are focused on a workpiece or target). It is therefore clear that knowledge of the laser-induced damage thresholds of the individual laser and optical materials making up the resonator is necessary before a laser system can be contracted to a minimum size. It is also necessary to ensure that these irradiation levels, including those pertaining to air-breakdown, do not occur before the laser beam reaches its target. In order to gain this knowledge it has been necessary to measure, reliably, the component power and energy handling capabilities of the optical materials involved in a laser resonator and subsequent optical system. Only when this was done could the design of damage-resistant laser/optical systems be finalized. One of the most pertinent aspects of laser system design and deployment is that of the specification of the optical components which make up the

Introduction

3

optical system. It is hoped that this treatise will make it clear that both the mounting configuration and the overall design of the system affect the specifications of the individual components. It should also be clear that unless the system designers understand the reasons why they put certain restrictions on the specification they are likely to find inconsistency in the overall operation of the laser system. A system may work well as constructed but when, as happens to all high-power systems, laser-induced damage or even simple degradation of the output occurs, the operator may have problems in obtaining components which allow the original specification to be reached. The replacement components may be to the nominal specification put on by the original laser manufacturer but inferior characteristics and even laser-induced damage may occur. This may be due to an incomplete specification or, as has been seen in many cases, may be the result of the component manufacturer complying with the laser manufacturer’s specification to too high a tolerance. One example of this is taken from the supply of focusing lenses for a 10.6 mm, CO2 continuous wave (cw) laser. The original laser had operated well but with a slowly degraded output for over a year. It was finally decided to refurbish the laser system and when it was stripped down it was obvious that the final focusing lens was damaged and its transmission was degraded. A replacement lens was ordered from a reputable component manufacturer, delivered and fitted into the system. The laser power to the workpiece was momentarily restored to something approaching its original level although there was some doubt as to the power density delivered to the workpiece. After only a short time of operation the lens cracked. After a considerable amount of recrimination and investigation it was found that, if the component supplier finished the lens diameter to the minimum in the specification (as opposed to the naturally inclined maximum), the lens worked perfectly and the full output power and the original focused power density could be obtained. Subsequent investigation indicated that the tightness of the fit and the consequent differential expansions of the lens and the lens holder caused strain and distortion in the lens. This resulted in a degradation of the lens focusing characteristic (larger focused spot size), the necessity for a slightly higher input energy and a resultant strain in the component that led to catastrophic damage. Thermally induced distortion of the optical components comprising the resonator can degrade the optical performance at powers well below those required to melt or fracture the optical component. This subject is one of the main problems confronting system designers. The problem comprises the twin effects of a change in the optical figure of the window or lens and the introduction of both birefringence and extra beam divergence. The necessity for measuring and improving the power handling capacity of optical materials in order to construct more compact laser systems, comes:

4

Introduction

1. in the military context, where the deployment of equipment depends critically on its ability to fit into a constricted space and on its input power demands, 2. in the industrial and medical contexts where large systems are cumbersome and where downtime is a serious issue, and 3. in the extreme cases, such as laser-induced fusion, where such high powers need to be generated and the system costs are so enormous that a constant search has to be made to identify components that can handle the high peak powers and energies involved. The output characteristics of a laser system are affected by the design of the complete system. This means that the temporal and spatial output characteristics are a function of not only the basic resonator design but also the temperature of the system and the input power level. This makes it necessary either to always use a laser system at a constant input power level or to measure and adapt the laser output to the application. Any effect that modifies the output of a laser is important in ensuring the optimum use of the laser in its particular application. These effects include absorption, distortion and laser-induced damage. Experience shows that most lasers are subject to at least one of these effects and if they are to be run for an extended period then care must be taken to minimize all three. Non-uniform absorption of the laser beam and consequent nonlinear or differential expansion by a component or component holder leads to wavefront distortion, the production of extraneous modes, changing beam divergence, strain and cracking. Running a laser resonator even at low output levels can lead to contamination of the mirror and windows, alteration of the resonator conditions and either cessation of lasing or catastrophic damage to the optical components. Running a laser at high output levels can lead to immediate single-shot damage and running a laser over an extended period or at a high pulse repetition frequency can lead to cumulative or pulserepetition frequency (prf )-dependent laser-induced damage. This book has been written in order to help engineers, managers etc. to understand that they cannot expect to generate increasingly high powers and energies from their laser systems without coming to some sort of compromise between these powers/energies and the laser system characteristics. The first laser systems were bulky and yielded what today would be regarded as ridiculously low outputs. The size and inferior output characteristics of these systems inhibited the use of these lasers in many industrial and military applications. The limitations of these lasers pressurized the system manufacturers both to increase efficiency and to reduce system size. The developments over the years have led to an impressive range of laser types, wavelengths, powers and energies and there are now relatively small systems that generate enough power/energy to fulfil a range of applications. These applications include laser-induced fusion, cutting, welding and drilling of engineering

Introduction

5

materials, medical, communications, and military (see chapter 8 for a summary of these). However, the sheer success of the engineering effort put into laser development has resulted, in many cases, in a series of ‘black boxes’ and it has been noticeable that there is now a new generation of laser engineers ‘who knew not Joseph’ (The Bible, Exodus 1 v 8). The engineers who developed the present laser systems had to overcome or live with the constraints inherent with generating high laser powers and energies. In many cases the present generation have come to accept the engineering benefits without understanding why the detail is so important. There is now growing up two series of laser engineers, those who understand the laser systems and those who use the same systems. This book is designed to be a bridge between these two schools of engineers. It has been said that the history of a man begins with his father and mother. Similarly the mechanisms and morphology of laser-induced damage in optical materials can be traced back to the electronic and physical parameters of these materials. The book therefore starts by considering the geometrical and physical properties of optical and laser materials. These include the origin of the wavelength dependent absorption as well as the many other sources of light absorption, which lead to a change in the material optical and thermal characteristics. Chapter 3 includes a discussion of the optical nonlinear mechanisms, which occur at medium power levels below the threshold for laser-induced damage. Nonlinear effects, whilst not necessarily leading directly to laserinduced damage, may however lead to increased absorption and local temperature rise. All materials exhibit some absorption and, if the incident energy/power is high enough, will melt. The threshold at which this will occur is both pulse length and wavelength dependent as well as being a function of the material and laser spot sizes and the ambient temperature. The pertinent material parameters will be the absorption, at the laser wavelength, the specific heat, the conductivity and the melting temperature. If the laser pulse is high powered but of short duration then avalanche ionization and/or multiphoton absorption may take place. These effects, which are only experienced under short-pulse, high-power conditions, may in fact occur at lower irradiation levels than those required for melting. However this is only observed in the case of low-absorption, highly transparent optical materials. Chapter 4 describes the processes by which laser-induced damage occurs and generates the expressions that can lead to the calculation of the laser-induced damage threshold (LIDT) of a material. Chapter 5 then goes on to describe the material optical quality parameters which lower this LIDT below the theoretical value. These parameters include bulk, sub-surface and surface quality. This chapter includes the methods and techniques that have been developed to minimize this damage.

6

Introduction

Chapter 6 emphasizes the contribution which dielectric coatings have in increasing the transmission of a laser system. This includes comments on the role of dielectric coatings in minimizing laser-induced damage. Chapter 7 covers a range of important topics, such as the LIDT of gases and liquids, the power handling capacity of fibre-optics, the significance of the units of measurement and scaling laws. Chapter 8 covers the measurement techniques for measuring the relevant material characteristics and the various ISO standards that have been developed over the past 10 years. A series of appendices lists just some of the range of LIDTs of optical materials over a range of wavelengths and pulse lengths that have been made over the past 30 years. It is hoped that these will be useful to those who need to know what maximum power/energies their optical materials, components or systems can withstand. They should also indicate that there is a great gulf between the theoretical and measured performance for many materials. It is hoped that by the time the reader gets to look at these appendices that he/she will understand the reasons for the discrepancies. I commented in the previous version of this book that there is a plethora of research papers and conference reports relating to the subject of laserinduced damage. Much of this, albeit very worthy in its own context, goes unnoticed because of the very magnitude of the data. In many cases the lessons of the past have gone unlearned because there is just so much detail that it takes a post-doctoral dissertation to even summarize it. At the same time the understanding of the subject is still increasing and my earlier book on the subject (Wood 1986) is now slightly out of date and incomplete. Much of the literature on the subject is to be found in the mainstream scientific publications and mention should be especially made of the Proceedings of the Annual Boulder Damage Symposia. The earlier years’ proceedings were published as NBS Special Publications and more lately as SPIE Proceeding reports. It is also possible to approach the subject via the SPIE Milestone Series of selected papers on laser-induced damage in optical materials (Wood 1990). However, although the committed student will find these publications invaluable I have thought it sensible to write this book as a summary of what has been done and to point those interested in going farther back to the key literature without drowning them in the minutiae of the subject. I unreservedly acknowledge my debt to my earlier colleagues at GEC Hirst Research Centre, Wembley, UK, where we had fruitful collaboration in the subject for over 30 years, to the sponsors of that work from the UK Ministry of Defence, to my international colleagues and in particular the organizers of the Boulder Damage Symposia and more latterly to my colleagues involved under ISO TC 172 in the formulation of international standards for laser and laser-related measurements. In particular I acknowledge the debt that I have to those whose results I have quoted (and hopefully have adequately acknowledged) in order to illustrate and augment my own measurements.

Chapter 2 Optical effects at low power/energy levels 2.1

Introduction

It was mentioned, in chapter 1, that the physical and chemical parameters, which determine the optical properties of a material and determine the susceptibility of that material to laser-induced damage, can be traced back to the electronic and physical structure of the material. This chapter aims to look at the origin of the optical characteristics of materials in order to lay the foundation for the calculation of the irradiation thresholds at which first nonlinear effects and then irreversible effects occur. It is understood that the majority of the readers of this book will find this chapter slightly irrelevant at this stage and will go straight on to the chapters on laser-induced damage mechanisms. However, for the sake of completeness, the basic physics involved in the optical and laser properties of materials are set out in this chapter. It is hoped that the reader will subsequently realize the reason for including this chapter and come to acknowledge its usefulness.

2.2

Electromagnetic theory

All electromagnetic phenomena are governed by Maxwell’s equations. This is not the time and place to derive these (see Jenkins and White 1957, Ditchburn 1958, Born and Wolf 1975, Ghatak and Thyagarajan 1989, and Olver 1992 for good introductions to the subject) but the following series of equations have their derivations in the fundamental equations. The statement that light is an electromagnetic wave is taken to be fundamental and has the implication that it is associated with transverse oscillations of the associated electric (E) and magnetic (H) fields. These fields are subject to the laws of conservation of energy and this in turn allows us to predict and quantify the interaction of light with both bulk materials and the interfaces between materials. 7

8

Optical effects at low power/energy levels

The velocity of light within a medium, v, is related to the velocity of light in vacuo, c, by the refractive index, n. c ¼ vn

ð2:1Þ

This in turn is related, through the bulk dielectric Ke and magnetic Km constants to the dielectric permittivity ", magnetic permeability and the conductivity of the medium such that c ¼ ð0 "0 Þ1=2 ;

v ¼ ð"Þ1=2

ð2:2Þ

2

where Ke ¼ "="0 , Km ¼ =0 , p ¼ Km Ke , and p is the complex refractive index ¼ n þ ik. The wave impedance of the medium, =" (¼z2 ), is a constant for the medium and is related to the oscillating electric, E, and magnetic, H, fields by the equations Ex ¼ z0 Hy

ð2:3Þ

and Ex Hx þ Ey Hy ¼ 0;

Ez Hz ¼ 0:

ð2:4Þ

The solutions for the electric and magnetic components are of the form Ex ¼ A eiwðtþpz=cÞ

ð2:5Þ

where A is a constant. By substitution we find that Ex eiwðtnz=cÞ ewkz=c :

ð2:6Þ

The first term in this equation is a sine wave and the second is an exponential damping decay. By further substitution we find that p2 ¼ "c2 ðc2 =!Þ ¼ Km Ke IðKm =!"0 Þ ¼ n2 2nik:

ð2:7Þ

The complex wave impedance of the medium z0 , can be split into resistive and reactive components: z0 ¼

Ex c cðn þ ikÞ ¼ 2 ¼ p Hy n þ k2

cn ick ¼ 2 þ 2 2 n þk n þ k2

ð2:8Þ

with a phase angle of tan ¼ k=n between Ex and Hy . Km ¼ =0 1 for all insulators and therefore the dielectric constant Ke n2 . The dielectric constant varies with frequency and results in dispersion of the electromagnetic wave.

9

Dispersion In the case of a dielectric ¼ 0, and therefore k ¼ 0 and n2 ¼ Km Ke . In the case of a metal 1 and n2 12 Km . Ke ="! k2 .

2.3

Dispersion

An electron bound to a nucleus orbits that nucleus at a frequency that is dependent on the electronic structure of the atom. When an externally applied electromagnetic wave is incident on this atom or molecule, the periodic electric force of the wave sets the bound charges into an oscillatory motion at the same frequency as the wave. The phase of this motion relative to that of the impressed electric force will depend on the impressed frequency and will vary with the difference between the impressed frequency and the natural frequency of the bound charges. When a light beam traverses the medium the amount of light scattered laterally is small because the scattered wavelets have their phases so arranged that there is practically complete destructive interference. On the other hand, the secondary waves travelling in the same direction as the original beam do not cancel out, but combine to form sets of waves moving parallel to the original waves. The amplitudes of the secondary waves must be added to the primary ones and the resulting amplitudes will depend on the phase difference between the two sets of waves, thus modifying the phase of the primary waves equivalent to a change in their wave velocity. Since the wave velocity is the velocity at which a condition of equal phase is propagated, an alteration of the phase, by inference, changes the velocity of the transmission of light through the medium. As the phase of the individual oscillators, and hence of the secondary waves, depends on the impressed frequency so the velocity of the radiation through the medium varies with the frequency of the probe light. If it is assumed that a material medium contains particles bound by elastic forces so that they are constrained to vibrate with a certain definite frequency, 0 , then it is possible to postulate the shape of the dispersion (change of refractive index with frequency) curve. The passage of the light wave through the medium exerts a periodic force on the particles causing them to vibrate. If the frequency of the radiation, , does not agree with 0 then the vibrations will only be forced vibrations and hence of low amplitude. As the frequency of the radiation approaches 0 the response of the particles will be greater and a very large-amplitude vibration will occur when ¼ 0 . An equation relating the refractive index, n, and the wavelength, , has been obtained (Sellmeier): n2 ¼

1 þ A2 : 2 20

ð2:9Þ

In this expression the constant A is a material parameter and is proportional to the number of oscillators capable of vibrating at frequency 0 , and

10


0 is related to the natural frequency of the particles by the equation 0 0 ¼ c, where c is the velocity of light. There is, of course, the possibility that the medium contains a number of different particles all having their own natural frequencies. Cauchy derived the following equation for the refractive index of a composite medium: N ¼Pþ

Q R þ þ 2 4

ð2:10Þ

where P, Q, and R are material constants. Although Sellmeier’s equation represents the dispersion curve very successfully in the transmission region of the medium it is not so successful at wavelengths where the material has appreciable absorption. The difference between the Sellmeier curve and the experimentally measured curve has been shown to be due to the fact that it is necessary to take account of the energy absorption mechanism. This was done by Helmholtz, who assumed that both absorption of energy and a frictional resistance to the vibration occurred. At the same time it should be remembered that a typical material contains a number of different molecules, all having their own natural frequencies. Thus each molecule has its own absorption, ai , at wavelength i , thus defining an absorption constant, k0 , where k0 ¼ ai i =4 and the frictional force is gi : n2 k20 ¼ 1 þ

X i

2nk0 ¼

ai 2 ð2 2i Þ þ gi 2 =ð2 2i Þ

X i

ai =gi 3 : ð2 2i Þ2 þ gi 2

ð2:11Þ ð2:12Þ

Although the curve of the refractive index against wavelength is different for every different material, the curves for all optically transparent media possess certain general features in common. This is illustrated in figure 2.1,

Figure 2.1. Variation of refractive index with wavelength.

Dispersion

11

which shows the variation of the refractive index, n, from ¼ 0 to several kilometres for a hypothetical substance. At ¼ 0, n ¼ 1. For very short waves (gamma and hard X-rays) n < 1. An absorption is encountered in the X-ray region at a wavelength depending on the atomic weight of the heaviest element in the material. The refractive index rises sharply and then falls (the K absorption limit of the element). At higher wavelengths there are other absorption discontinuities, L, M etc., as well as the K, L, M absorption limits of other elements present in the material. These absorptions are attributable to the innermost electrons in the atoms (the K, L, M, . . . shells) which are of decreasing energy (increasing distance from the nucleus). These absorption discontinuities are sharp because as these electrons are deep within the atom, they are shielded from the effect of collisions and electric fields due to neighbouring atoms. The refractive index continues to drop throughout the soft X-ray region until it reaches a broad absorption region in the ultraviolet, 1 . This is due to the interaction of the light with the outer electrons of the atoms and molecules that make up the material. As these are not shielded the corresponding absorption band is broad. In the case of molecular gases the bands consist of sharp individual rotational bands which are collectively unresolved. After the absorption peaks the refractive index drops again (but is now >1). The nearer the ultraviolet absorption peak is to the visible the greater the dispersion (dn=d) in this region. In the near infrared the refractive index again begins to drop more steeply until it runs into an absorption band centred at 2 . This band is associated with the natural frequency of the lightest atoms in the material. These possess lower vibrational frequencies than those associated with the electrons since the nuclei are appreciably heavier. Beyond this band there are usually others which are associated with even heavier molecules. The index of refraction increases each time these bands are passed and thus the index will be higher in the far infrared than in the visible. At wavelengths beyond all the infrared absorption bands the index decreases very slowly until it reaches a limiting valuepffiffifor ffi very long wavelengths. The limiting value of the refractive index is ", the ordinary dielectric constant of the medium. Figure 2.2 shows a generalized picture of the resultant transmission spectrum, shown as a function of the probe wavelength. It is possible to calculate the position of the absorption edges using the following arguments. On the short-wavelength side, transmission is restricted by electronic excitation and at long wavelengths by atomic vibrations and rotations. The width of the transparent spectral range increases as the energy for electronic excitation is increased and that for atomic vibration decreased (i.e. heavier atoms).

12


Figure 2.2. Generalized transmittance versus wavelength spectrum.

For ionic crystals the energy of electronic excitation is given by Ae2 þ Ea I ð2:13Þ r where h is Planck’s constant, ¼ c= is the frequency, A is Madelung’s constant, e is the electronic charge, r is the interionic distance, Ea is the electronic affinity of negative ions, and I is the ionization potential of positive ions. This equation can be used to calculate the value of the low-wavelength absorption edge and shows that materials with strong bonding are transparent in the ultraviolet. Table 2.1 lists the absorption edges of a number of commonly used optical transmissive materials. This absorption edge is affected by the temperature as it is influenced both by the shift of the absorption peak (to longer wavelengths) and by broadening of the absorption band (Smakula 1962). There are nowadays many more optical materials, particularly in the infrared transmission region. These materials have been developed in particular for thermal imaging applications (Savage 1985, Zhang 2002). The properties of many of these are similar to but usually slightly better than the simpler materials shown in table 2.1. In covalent materials the position of the absorption edge, , is determined by the effective, m , and the free, m, electron masses and the refractive index, n: m ¼ const: 4 : ð2:14Þ nm h

Chemical formula

BaF2 CaF2 MgF2 NaF NaCl KCl KBr SiO2 Al2 O3 Y3 Al5 O2 ZnS ZnSe Si Ge GaAs CdTe

Material

Barium fluoride Calcium fluoride Magnesium fluoride Sodium fluoride Sodium chloride Potassium chloride Potassium bromide Quartz Sapphire Garnet Zinc sulphide Zinc selenide Silicon Germanium Gallium arsenide Cadmium telluride

1.47 1.45 1.38 1.3 1.54 1.45 1.53 1.45 1.75 1.82 2.26 2.45 3.4 4.0 3.3 2.70

0.3 0.3 0.2 0.12 0.17 0.18 0.3 0.25 0.3 0.4 0.3 0.5 1.3 1.8 1.0 1.0

9.0 9.5 6.0 10.0 14.5 23.0 25.0 1.25 4.0 1.3 11.0 16.0 6.0 16.0 20.0 2.0

Refractive Wavelength index (n) 1 mm 2 mm " 7.32 6.81 – – 5.9 4.8 – 3.7 10.15 – 8.37 9.1 11.7 16.0 12.8 10.6

n2 (m2 Vÿ2 ) 1:12 10ÿ22 7 10ÿ23 – – 7:18 10ÿ22 3:68 10ÿ22 – 1:5 10ÿ22 1:44 10ÿ22 3:51 10ÿ22 – – – – – –

Table 2.1 Physical parameters of commonly used optical materials.

3.6 3.4 2.5 1.6 4.5 3.4 4.4 3.4 7.3 20.3 15.0 17.6 30.0 36.0 28.3 21.1

1280 1360 1498 1270 801 776 1003 1600 2015 1970 1830 1520 1410 938 1238 1090

Reflectance MP (R%) (8C) 65–82 120–200 415 60 15 7.2 7 461 1705 1215 355 100–150 1150 190 750 45

Hardness (Knoop) 4.89 3.18 3.18 2.79 2.17 1.99 2.75 2.21 3.986 4.55 4.09 5.27 2.33 5.32 5.31 5.85

Density (g cmÿ3 )

0.12 0.0016 0.008 4.2 hygroscopic hygroscopic 65.2 insoluble 9:8 10ÿ5 insoluble insoluble insoluble insoluble insoluble insoluble insoluble

Solubility (g per 100 g)

Dispersion 13

14


Figure 2.3. Short-wavelength absorption edges and refractive indices of covalent elements and compounds.

Figure 2.3 shows the position of the short-wavelength edge as a function of the refractive index for a number of covalent materials. The infrared absorption edge is set by the vibration of the dipole moments of the atoms. The binding forces of the ions are of the same order as those of the electrons, but as their masses are 104 times greater the vibrational frequencies are 102 smaller. ¼ const: M=f

ð2:15Þ

where f is a force constant and M is the reduced mass, given by 1 1 1 ¼ þ M M1 M2

ð2:16Þ

where M1 and M2 are the masses of ions with opposite charges. These equations indicate that in order for materials to be transparent over a wide range of the infrared they must have weak binding and large atomic mass. The infrared absorption edge shifts towards longer wavelengths with increasing atomic mass (and also a decrease of the melting point). The intensity of the vibrational band is much weaker in partially ionic crystals than in pure ionic crystals and they are therefore transparent farther into the infrared. Pure covalent crystals of monatomic elements should, in theory, not exhibit any longwave absorption. The longwave absorptions are included in table 2.1, indicating that there is either a certain amount of ionic bonding or lattice distortion in these crystals. As has been shown, the refractive indices of a material, being bound up in the structure of the material, are not constant but change with the wavelength of the probe light. A typical plot of refractive index versus

Reflectance and transmittance

15

Figure 2.4. Refractive index versus wavelength, ZnSe.

wavelength is shown for zinc selenide in figure 2.4. In this plot, the transmissive region, where p ¼ n, is bounded at each end by an absorbing region, where p ¼ n þ ik. As most materials used in optics and laser applications are used in the transmissive region we are therefore mainly concerned with real values of the refractive indices and the complex part is taken to be small. In this regime ¼ 0, k ¼ 0, p ¼ n and n2 ¼ Km Ke . In the case of materials where the structure is not isotropic (i.e. the molecular spacing is different in different planes) the electromagnetic interaction will be different depending on the direction of the wave vector and the refractive indices will be different in the various directions. The transmission characteristics of the material will then change depending on the direction of the wave vector and the material will be said to be birefringent and the transmitted light beam will become polarized. At high electric fields most materials exhibit optical nonlinearity.

2.4


The equation for an electromagnetic wave has been defined as Ex ¼ ei!ðtnz=cÞ e!kz=c ;

ð2:17Þ

saying that the wave is transmitted through the material with an associated electromagnetic field of period nz=c and with an exponential absorption of e!kz=c . When the wave falls at normal incidence on to the surface between two media (see figure 2.5) the boundary conditions are that the normal components of the magnetic induction vector and the displacement vector are continuous, and that the tangential components of the electric and magnetic

16


Figure 2.5. Interaction between electromagnetic waves at a surface.

field vectors are also continuous, i.e. Ey þ Ey00 ¼ Ey0 ; 0

0

00

Hx þ Hx00 ¼ Hx0 ;

ð2:18Þ

00

where E, H, E , H , E , H are the electric and magnetic field vectors appropriate to the incident, transmitted, and reflected waves (as defined in figure 2.5) at the surface between the two media (with refractive indices n0 and n1 respectively). Since Ey0 ¼ z0 ; Hx0

Ey ¼ z; Hx

Ey00 ¼ z Hx00

ð2:19Þ

then Ey00 z0 z ¼ 0 z þz Ey Ey00 n n1 ¼ 0 Ey n0 þ n1 Ey0 2n0 ¼ Ey n0 þ n1 and the energy propagated in the wave (Poynting’s vector) is ð"=Þ1=2 ¼ n1 E 2 :

ð2:20Þ

The proportion of the energy which is reflected is therefore (Fresnel’s Law) R¼

n0 Ey002 ¼ ðn0 n1 Þ2 : n0 Ey2

ð2:21Þ


17

Figure 2.6. Ray diagram at an interface.

The proportion of the energy which is transmitted is T¼

n1 Ey02 4n0 n1 ¼ n0 Ey2 ðn0 þ n1 Þ2

ð2:22Þ

and R þ T ¼ 1 as energy is conserved. Note that both R and T are symmetrical and therefore the proportion transmitted or reflected is constant and does not depend on the direction of the incoming wave. Also, if n1 > n0 then Ey00 =Ey is negative and the

Figure 2.7. Normal incidence reflectance, R%, for an air (n0 ¼ 1)/material (n1 ) interface as a function of the material refractive index, n1 .

18


phase of the reflected wave is exactly out of phase with the incident wave. If n1 < n0 then Ey00 =Ey is positive and both the reflected and the transmitted waves have the same phase. Extension of the same theory leads to the derivation of all the laws of physical optics. The equation defining the relationship between the angle of incidence, i, and the angle of refraction, r, as a ray passes from a medium of refractive index n0 into one with a refractive index n1 is (using the terminology of figure 2.6) Snell’s Law:

n0 sin i ¼ n1 sin r:

ð2:23Þ

Figure 2.7 shows a plot of the reflectance, at normal incidence, in air at the surface of a medium of refractive index n1 , for a range of values of n1 . When the incident ray is at non-normal incidence Fresnel’s law has to be modified to take account of the angle of the material plane to the two plane

Figure 2.8. Reflectance, R%, versus angle of incidence, i, for an air/glass (n0 :n1 ¼ 1 :1:5) interface.


19

polarized components of the incident polarized light. These components are termed s and p (vibrations perpendicular and parallel to the plane of incidence respectively). Fresnel’s laws may be rewritten as n0 cos i n1 cos r 2 sin2 ði rÞ R? ¼ Rs ¼ or ð2:24Þ n0 cos i þ n1 cos r sin2 ði þ rÞ n1 cos r n0 cos i 2 4 sin2 r cos2 i Rjj ¼ Rp ¼ or ð2:25Þ n0 cos i þ n1 cos r sin2 ði þ rÞ cos2 ði rÞ and similarly tan2 ði rÞ tan2 ði þ rÞ

ð2:26Þ

4 sin2 r cos2 i : sin2 ði þ rÞ cos2 ði rÞ

ð2:27Þ

Ts ¼ Tp ¼

Figure 2.9. Reflectance, R%, versus angle of incidence, i, for an air/germanium (n0 :n1 ¼ 1 :4) interface.

20


The total reflection and transmission coefficients for the medium, assuming an unpolarized beam, is given by combining the appropriate equations: R ¼ 12 ðR? þ Rjj Þ ¼ 12 ðRs þ Rp Þ T ¼ 12 ðT? þ Tjj Þ ¼ 12 ðTs þ Tp Þ:

ð2:28Þ

These equations predict that at normal incidence (i ¼ r ¼ 0), the reflection coefficients, Rs and Rp are equal and are governed by the refractive indices of the media. At glancing incidence (i ¼ 908) Rs ! Rp ! 1, irrespective of the refractive indices of the media. For the special case where i þ r ¼ =2 (where iB is termed the Brewster angle) then Rp ¼ 0. In the case of a dense-to-rare, internal, reflection a critical angle, ic , exists. This is defined as the angle at which all the light is reflected and none transmitted. Examples of the reflectance at (a) an air/glass interface (n0 ¼ 1, n1 ¼ 1:5) and (b) an air/germanium interface (n0 ¼ 1, n1 ¼ 4) are shown in figures 2.8 and 2.9 respectively. The Brewster and critical angles are illustrated in these

Figure 2.10. Brewster angle, iB , at an interface (n0 :n1 ) and the internal reflectance critical angle, ic , at an interface (n1 : n0 ) as a function of the material refractive index ratio n1 =n0 .

21


figures and also in figure 2.10, where they are plotted as a function of the material refractive index ratios. If the medium is strongly absorbing then the refractive index n1 is replaced by a complex quantity: p ¼ n1 þ k 1

ð2:29Þ

where k1 is the absorption coefficient of the medium. For the special case of normal incidence, the Fresnel equations give R¼

ðn1 n0 Þ2 þ ðn1 k1 Þ2 : ðn1 þ n0 Þ2 þ ðn1 k1 Þ2

ð2:30Þ

Figure 2.11. Normal reflectance versus refractive index. (a) Bare surface, refractive index n1 . (b) Surface of refractive index n2 with =4 dielectric coating of refractive index n1 .

22


It is possible, by extending the theory, to calculate the reflectance of a surface with a dielectric coating, refractive index n1 on a medium of index n2 : 2 n1 n0 n2 2 R¼ : ð2:31Þ n21 þ n0 n2 The reflectance of a quarter-wave dielectric coating, index n1 , on a medium, of index n2 , is compared with the reflectance of the bare substrate, with refractive index n1 , in figure 2.11. Ellipsometry and broadband spectrometry can be used, by combining the reflectance and transmitting properties of the optical material in question, to calculate the wavelength-dependent variation of the index of refraction, n, and the extinction coefficient, k (Bloomer and Mirsky 2002, Forouhi and Bloomer 1986, 1988). It is also possible, by making a series of measurements, to separate out the various parameters involved (see section 2.9).

2.5

Reflectance and absorptance of a conducting surface

When a light beam is incident on a conducting surface a small amount of radiation penetrates it to a distance, termed the skin depth, which is in turn a function of the electrical conductivity, . A good, relatively simple explanation of this effect can be found in the literature of the subject (Prokhorov et al 1990). The easiest way to calculate both the reflectance and the absorptance of the surface is to calculate the value of the complex refractive index, k. p2 ¼ n2 k2 2ink ¼ Km Ke

iKm : !"0

ð2:32Þ

For a metal n2 k2 =ð2!"Þ 1, R¼1A¼1

4n 2ð2!"Þ1=2 : 1 1 þ 2n þ n2 k2

ð2:33Þ

The complex refractive index can also be calculated using Drude theory (Bennett and Bennett 1966) : n2 k 2 ¼

1 !2p ; !2 þ t2 e

2nk ¼

!2p !te ð!2 þ t2 e Þ

ð2:34Þ

where !p is the electron plasma frequency, equal to ðNe2 Þ1=2 =ðm "0 Þ, te is the mean time between collisions, m =Ne2 , and Ne is the free electron concentration leading to R1

2 ; !p t e

A

2 : !p t e

ð2:35Þ

Molecular polarizability

23

Table 2.2. Values relating theoretical and experimental absorptance.

Metal

Mean Debye Plasma collision temp., frequency, !p time, te TD (1016 rad s1 ) (1014 s) (K)

Experimental dR=dT, Theoretical absorptivity A1 absorptivity (minimum) ð105 K1 Þ (%) (%)

Silver Aluminium Gold Copper Lead

1.40 2.23 1.34 1.18 1.12

1.62 3.20 2.35 3.88 –

3.57 0.81 2.46 1.9 0.34

1273 1173 – – –

0.46 1.1 0.8 0.8 4.42

0.5 1.3 0.8 0.4 –

There is a temperature dependence of both the reflectance and the absorption, which arises through the change in the relaxation time with temperature, which can be described from changes in the d.c. conductivity, : AðTÞ ¼

!p ðÞ ¼ A0 þ A1 T: 2

ð2:36Þ

This approximates to A1 T for T TD =3 where TD is the Debye temperature. Assuming (Plass et al 1994) that 1=T then d=dT ¼ =T and dR 2 1 ¼ dT !p T R¼1þ

dR T: dT

ð2:37Þ ð2:38Þ

It will be seen from these expressions that the reflectance of a metal mirror decreases markedly with temperature (A1 105 K1 ). Values for some typical metal mirror materials are given in table 2.2. Optical constants for a range of 12 different metals were presented in a useful paper on the subject by Ordal et al (1983) and a fuller treatment of the whole subject was published by Prokhorov et al (1990).

2.6

Molecular polarizability

The magnitude of the induced dipole moment, p, of an atomic bond increases linearly with the electric field strength, E, and can be represented by the equation p ¼ E where is called the deformability or polarizability.

ð2:39Þ

24


The total polarization, P, per unit volume (containing N molecules) in the presence of the external field, E, is given by P ¼ NE:

ð2:40Þ

The polarization, P, is also connected with Maxwell’s displacement vector, D, by the relationships D ¼ E þ 4P

and

D ¼ "E;

ð2:41Þ

where " is the dielectric constant and therefore, in a gas (to a first approximation), " ¼ 1 þ 4N: ð2:42Þ In a solid the presence of the surrounding molecules will have an effect on the displacement of the electron cloud around the nuclei. In general, molecules with symmetrical structure have no dipole moment while asymmetric molecules do possess one. In addition the arrangement of the molecules with relation to their nearest neighbours can also enhance or negate the dipole-moment effect. The effect of the molecular structure/lattice and the ambient temperature can be described by " ¼ 1 þ 4Nð þ p20 =3kTÞ ¼ "0 þ 4Np20 =3kT

ð2:43Þ

where "0 is the dielectric constant for the case of a vanishing permanent dipole moment, p0 ¼ 0, and k is Boltzmann’s constant. n ! ð"0 Þ1=2 ¼ ð1 þ 4NÞ1=2

ð2:44Þ

where n is the refractive index of the material.

2.7

Absorption

Absorption of the optical radiation comes from a number of mechanisms and is the main cause of unavoidable loss and ultimately of laser-induced damage for long pulse and cw sources. In general the absorption coefficient measured for thin films of material is greater than that measured for the bulk material. The causes are summarized below, although discussion of the effects is more suitably located in later sections. 1. Bulk absorption The origin of this permanent absorption has already been shown (section 2.3) as being rooted in the electronic structure and ensuing electronic orbits of the material. In the transmitting region of the spectrum the absorption is made up of two parts. The first is free carrier absorption, which is intrinsic, and the second is extrinsic impurity absorption. The transmission of an absorbing material is described by I ¼ I0 ex :

ð2:45Þ

Absorption

25

In crystals, and in glasses of near-ideal structure, the small residual absorption due to impurities, dislocations etc. (which may be individually too small to cause damage) can be considered as a superposition of the absorption from each imperfection or defectP(Hellwarth 1972). There is therefore an additional absorption of ð!Þ ¼ i Ni i ð!Þ where the sum is over all the various types of imperfection, whose densities are Ni and absorption cross sections are i . 2. Colour centre absorption All crystals contain a number of lattice defects (vacancies, aggregates of vacancies, interstitials, dislocations and extrinsic impurities). The presence of these defects alters the charge distribution and therefore modifies the electronic levels in the vicinity of the defects (Dekker 1960). The positive or negative ion vacancies so formed act as negative/positive ion traps (F and V centres). Such centres are usually observed in crystals that have been irradiated using long-wavelength (high-energy) radiation (e.g. ultraviolet). These are commonly termed colour centres as they usually exhibit extra absorption in the transmission region of the spectral curve (e.g. LiF looks pink, KCl looks violet and NaCl looks brown–yellow). The main research into these has been done using the alkali halide materials (these having cubic structure and being transparent in the visible). In general the induced absorption can be eliminated by appropriate thermal treatment in appropriate atmospheres. Colour centres have also been identified in Nd:YAG laser crystal, LiNbO3 electro-optic crystal and in fused silica (Escobas 1998). 3. Transient absorption It has been shown that when some materials containing colour centres are irradiated at even moderate power levels an excited state absorption arises [ruby (Bliss 1970, Glass and Guenther 1972), Nd:YAG (Wood 1986) and quartz glass (Takke 1999)]. This excited state exists for about the same length of time that the irradiation lasts and, unless special experiments are made, cannot be proven by ordinary spectroscopy. Figure 2.12 shows the results of such an experiment made by measuring the transmittance of an Nd:YAG laser rod when it was irradiated using a flash-tube. In the case of Nd:YAG the lifetime of the excited state is of the order of microseconds, whilst for quartz glass the effect lasts for minutes. 4. Localized absorption Most materials contain absorbing impurities. These may originate either from the raw materials or from the fabrication processes and can be minimized using appropriate fabrication technology. Although most fabrication processes aim to purify the melt it is also possible to introduce even more damaging material into the lattice from the fabrication process itself. For example, many papers have been published on the presence and effect of platinum defects in melted Nd:glass (Taylor and Wood 1974).

26


Figure 2.12. Nd:YAG transient absorption.

These microscopic Pt particles come from the Pt crucible and are dispersed throughout the glass. Appropriate gas treatment has been shown to eliminate or melt these particles into even smaller particles. If the particle is large enough (>100 of irradiation) the particle will heat up, add to the absorption coefficient and act as a scattering centre. If the particle size is between 10 and 0.1 the particle will absorb and strain the lattice. If the particle size is lower than 0:1 then it will only add to the absorption but not lead to either the scatter or the strain in the lattice (Bliss 1971, Hopper and Uhlmann 1970, Duthler and Sparks 1973). A lot of work has gone on over many years on the source and the damage mechanisms of coating inclusions in dielectric coatings (e.g. Staggs et al 1992, Lange et al 1983, 1994, Stolz and Kozlowski 1994). This subject will be considered in detail in chapter 6. 5. Free-electron absorption Some materials suffer from nonlinear absorption, which affects both the absorption at high irradiation levels and lowers the effective melting point of the material. This occurs mainly in semiconducting materials (Wood et al 1982a) and will be discussed in chapter 3. 6. Conduction electron absorption As has already been shown, in section 2.5 (Bennett and Bennett 1966), the conduction electrons in a metal absorb a portion of the irradiation. This absorption is temperature dependent and results in metals having increasingly lower reflectivity until the point where the metal melts. In

Scatter

27

general a molten metal has an extremely high reflectance. This change in the absorption/reflectance characteristics is one of the main problems which has to be overcome in laser welding and cutting (see chapter 9). 7. Surface absorption Scratches, digs, contaminants etc. all add to the absorption/scatter/ transmission loss characteristics of a material (Bloembergen 1973, Foley et al 1980, Newman et al 1979, Braunstein et al 1980). This will be further developed in chapter 5. 8. Sub-surface absorption All machined surfaces contain a machined/polish-damaged layer. The depth of this layer depends on the precise fabrication technique and can be anything from 10 nm to 0.5 mm depth (Sharma et al 1977, Wood 1990b). The evidence for and the subsequent effect of this layer is given in chapter 5. 9. Nonlinear absorption Many optical materials have optically nonlinear properties, the deployment of which depends on the irradiation level. The relevant nonlinear properties include second harmonic generation and Raman and Brillouin scattering, all of which invoke the generation of different wavelengths and the possibility of extra absorption. This subject will be enlarged on in chapter 3.

2.8

Scatter

The amount of scatter produced in a material or on the surface of that material depends on a number of factors but can be summarized as being due to the interaction of the irradiation with point defects. When you are concerned with high power/energies and/or when scatter levels of 0:6 x > 0:6 x > 0:7 x > 1:0 x > 2:0

beam. At low power densities the scattering behaviour may be explained in terms of (Menzel 2001): Rayleigh scattering—for particles/defects ; the magnitude of this effect is 4 . Rayleigh–Gans scattering—for particles/defects , the magnitude being 2 . Mie scattering—for particles/defects ; the magnitude of this effect is 0 . The relative values of these effects may be illustrated by considering the defect radius and type causing scattering at a wavelength of 5 mm in As2 S3 glass (see table 2.3, Hewak 1998). The amount of scatter produced depends on the particle/defect dimensions or surface roughness (and hence the surface finish) relative to the wavelength of the incident radiation. To a first approximation, neglecting the influence of absorption, scatter decreases linearly with increasing probe measurement wavelength. For clean surfaces the scatter can be equated with large-angle specular reflectance and an estimate of the expected scatter can be made from a measurement of the surface finish. The intensity of scatter, I, as a function of angle, , is given by (see figure 2.13) I ¼ Is cos2 RI0 cos ;

ð2:46Þ

where is the angle of measurement, Is is the maximum scatter (at the angle of incidence, ’), R is the surface reflectance, and I0 is the incident intensity. The equation for the percentage of the light scattered from a beam at normal incidence (Is when ’ ¼ ¼ 08), is given by (Bennett 1977) S¼

Pscattered Pscattered þ reflected

¼

ð4 Þ2 :

ð2:47Þ

Interesting effects occur at large angles of incidence (glancing angle). For example, inferior diamond turning leaves parallel curves, which allow calculation of the lead screw pitch and of the motor frequency.

Scatter

29

Figure 2.13. Specular and scattered intensity versus angle of measurement.

Bulk scatter may be caused by the presence of voids, by impurities or from microscopic damage sites. It is relatively easy to detect large (>10 mm) scatter points using optical inspection techniques (e.g. by shining an He/Ne laser beam through a component under dark field conditions). However, although high-powered microscopic inspection can detect scatter points on the surface of a component down to 0:5 mm it can be very difficult to locate scatter points in the bulk material except by catastrophic damage testing. The scattering from density fluctuations is given by S¼

83 8 2 n p c KB Tg 34

ð2:48Þ

where n is the refractive index, p is the photoelastic constant, c is the isothermal compressibility (at Tg ), KB is Boltzmann’s constant, and Tg is the glass transition temperature. It is also relevant to note that there is a direct correlation between the value of the scatter, the number and size of the surface defects and the reflectivity of the surface. Figure 2.14 contains data gained from a series of coated and uncoated substrates irradiated with an He/Ne laser beam at normal incidence. The parameter C is a function of the number of defects on the surface of the coating, the average defect size and the reflectance of the surface. During this investigation it was confirmed that a nearly defect-free

30


Figure 2.14. Measured scatter versus density of defects, defect dimensions, coating reflectance, and beam diameter (Wood 1982e).

coating could be deposited on a defect-free substrate and that this gave the lowest scatter values. It was also found that no evaporation process would lessen the number of defect points. Scatter is an important parameter in many laser-based applications not only as a loss mechanism but also as an actual performance limiting parameter. Perhaps the application that is most sensitive to the scatter loss of its optical components is that of laser-based communication systems. In this application it is vitally necessary that the optical system should not contain scatter points or that frequency changes do not occur. The parameter of interest for a laser communication receiver is that of point source rejection (PSR). This is the ratio of the energy reaching the receiver detector to the energy entering the telescope aperture from off-axis scattered light. This parameter is angular dependent and PSR values of log1 1010 are usually required. This has been well discussed by Lambert and Casey (1995) for the primary mirror of such a system as it has been found that the polish finish of the reflecting mirrors is crucial in terms of the rejection of the off-axis energy. It is therefore been found necessary to establish which optical finishing technique (and on what substrate) can realize these ultra-low scatter levels.

Scatter

31

Table 2.4. Point source rejection ratio for a range of mirror finishes (Lambert and Casey 1995). Point source rejection ratio (log10 ) roughness, r.m.s. (A˚) Angle (degrees)

Dt. Al 120

Vac. Be 30

Al/Ni coat 10

S/p FS 3

1 5 10 15 20

7.4 8.1 9.2 10.6 11.0

8.1 10.8 10.1 11.3 12.5

9.2 11.0 11.1 12.3 13.8

10.2 12.9 12.1 13.2 14.5

Dt. Al ¼ diamond turned aluminium. This is a standard high-quality mirror substrate. Vac. Be ¼ vacuum-deposited beryllium. Although there are hazard problems with beryllium dust, beryllium is very attractive as a lightweight mirror. Al/Ni coat ¼ aluminium substrate overcoated with electrodeposited nickel. Electrodeposited nickel yields a very smooth surface. S/p FS ¼ super-polished fused silica. Although this surface usually has to be dielectric coated it is probably the smoothest surface which has been generated.

Table 2.4 gives an indication of the surface roughness finish which can be achieved for a selection of mirror surfaces and of the point source rejection ratios which these finishes yield as a function of the measuring angle. It will be observed that the best surface, but not the highest reflectance, is that for a super-polished fused silica blank. These measured values were the maximum rejection ratios obtained for clean surfaces under ultra-clean measurement conditions. Degradation of the surface occurs due to dust and atmospheric contamination. The subject of the measurement of surface roughness is discussed in chapter 5. A small number of very small defects or impurities may not lead to a high scatter loss but even one scatter point with a diameter above the wavelength of the irradiation source can lead to catastrophic damage, particularly when high-power pulsed lasers are used as the source of radiation. This is because a void (or a scratch on the surface) acts as an electric field concentrator (like inserting a lens inside the material). The shape of the void has a distinct bearing on the amount of local enhancement of the electric field. This was realized very early on (Bloembergen 1973). In figure 2.15 E0 and E are the electric fields associated with the incident beam and the local intensity at the defect respectively. As the intensity in the beam is proportional to E 2 the effects are proportional to n4 . This enhancement is therefore most serious for high refractive index materials. A more recent treatment of this subject has been given by Genin et al (2001).

32


Figure 2.15. Local enhancement of the electric field (Bloembergen 1973).

2.9

Analysis of R, T, A and S measurements

In order to characterize an optical component thoroughly it is necessary to measure the four basic physical optical parameters, where A þ R þ T þ S ¼ 1:0:

ð2:49Þ

It is possible to define scatter as the amount of non-specular reflected and transmitted radiation and the absorption as the non-transmitted amount. In a good quality optical material both A and S will be small and the relationship between R and T will depend upon the refractive index of the material and/or the design of any coatings. It is perhaps fortuitous that in the visible there is an abundance of materials with very low absorption coefficients and that in the infrared, where absorption coefficients become appreciable, scatter becomes less. In the case of uncoated substrates it is relatively easy to make accurate measurements of each parameter (see chapter 8 for a summary of the recommended measurement techniques). It is even possible to make accurate measurements of the absorptance, separating the surface absorption from the bulk absorption by making a series of measurements using different thickness samples (or wedged samples). Surface absorption may then be subdivided into removable (e.g. water absorption and grease) and bound states (impurities bound into the lattice by the free electrons from the distorted surface lattice). The issue of surface water absorption is well illustrated by the measurements made at the GEC Hirst Research Centre (Wood et al 1982a) which are summarized in figure 2.16. This figure plots the change of the absorption coefficient


33

Figure 2.16. Absorption coefficient of n-type germanium as a function of resistivity.

(measured at 10.6 mm) for n-type germanium as a function of the resistivity. The resistivity is in turn a function of the doping concentration. It will be seen from the graph that the lowest absorption material at 10.6 mm is about 9 cm1 . It is interesting to note that the theoretical minimum absorption does not agree with the theoretical absorption limit (0.006 cm1 ). The figure contains both the theoretical variation and the results of a series of measurements made on a series of slices of n-type silicon, all cut from the same boule. As the experimental boule was grown from a small melt the concentration of n-type material changed fairly fast along the boule length. This made it perfect for the experiment envisaged, which was to confirm the Capron–Brill (1973) theory as to the optimum resistivity for 10.6 mm laser window material. The boule was diced with a diamond saw and polished (Syton) and then submitted for 10.6 mm absorption measurements. These measurements were undertaken in an apparatus which could either be used with an air surround or evacuated (2 105 Torr). The vacuum apparatus was constructed mainly because it was felt that the temperature measurement would be more stable if any convection was eliminated. In fact the main application proved to be for the measurement of the surface absorption of various gases by infrared transmitting materials. Although neither the air-based measurements nor those made in vacuo showed the smooth variation with resistivity predicted by

34


Capron and Brill, the trend was the same. The two sets of experimental measurements varied by an average absorption of 0.66%. This was ratified as being the correct value by a separate measurement of the amount of water that could be driven off under evacuated conditions. This amounted to an average thickness of water of 50 A˚. When this absorption is deducted from the Capron–Brill theory (shown in figure 2.16) the minimum absorption is nearly the same as the theoretical phonon absorption limit. In the case of ‘real’ laser windows it becomes necessary to ensure that one face is partially reflecting and the other is anti-reflection (AR) coated. It is also important that both these coatings are non-absorbing at the wavelength of interest. In order to ensure that components meet their specification, to understand the physics of the processes involved and to minimize the onset of laser damage, it is useful to measure, or at least calculate, the physical characteristics of the window. It has proved possible to separate the coating reflectances and to make estimates of the magnitude and location of absorbing layers by making R, T and A measurements from both directions through the window (Wood et al 1982e). It is obviously easier if the scatter can be neglected and this, in most cases, can be lumped together with the absorption as a ‘loss’. In order to gain a full understanding of the loss etc. it is necessary to use ellipsometry, which measures the reflectance, transmittance and the loss as a function of the wavelength. Take the simple case of a substrate with an absorption A, coated each side with a non-absorbing coating, one side with parameters R1 , T1 , and the other with parameters R2 , T2 . Measurements of the reflectance, transmittance and absorption are made first from one side, side A (measurements RA , TA , AA ), and then from the other side, side R (measurements RR , TR , AR ). The schematic diagram for these measurements is shown in figure 2.17 and the equations governing the process are given below.

Figure 2.17. Schematic of reflectance, transmittance, and absorptance of a coated window.


35

The intensities of the different rays, when the substrate is irradiated by a laser beam, intensity I0 , incident on side 1 are given by: I1 ¼ I0 R1 I2 ¼ I0 T1 I20 ¼ I2 ð1 AÞ ¼ I0 ð1 AÞT1 I3 ¼ I20 T2 ¼ I0 ð1 AÞT1 T2 I4 ¼ I20 R2 I40 ¼ I4 ð1 AÞ I5 ¼ I40 T1 ¼ I0 ð1 AÞ2 T12 R2 I6 ¼ I40 R1

ð2:50Þ

I60 ¼ I6 ð1 AÞ I7 ¼ I60 T2 ¼ I0 ð1 AÞ3 T1 T2 R1 R2 I8 ¼ I60 R2 I80 ¼ I8 ð1 AÞ I9 ¼ I80 T1 ¼ I0 ð1 AÞ4 T12 R1 R22 I10 ¼ I80 R1 0 I10 ¼ I10 ð1 AÞ 0 T2 ¼ I0 ð1 AÞ5 T1 T2 R21 R22 : I11 ¼ I10

Therefore R ¼ R1 þ T12 R2 ð1 AÞ2 þ R21 R1 R22 ð1 AÞ4 þ þ T12 Rn1 2 2Rn2 ð1 AÞ2n 2 R1 þ T12 R2 ð1 AÞ2

ð2:51Þ

TM ¼ T1 T2 ð1 AÞ þ T1 T2 R1 R2 ð1 AÞ3 þ T1 T2 R21 R22 ð1 AÞ5 þ þ T1 T2 Rn1 1 R2n 1 ð1 AÞ2n 1 T1 T2 ð1 AÞ

ð2:52Þ

A ¼ AT1 þ AT1 R2 ð1 AÞ þ AT1 R1 R2 ð1 AÞ2 þ AT1 R1 R22 ð1 AÞ3 þ AT1 R21 R22 ð1 AÞ4 jn=2 1j

þ þ AT1 R1

jn=2 1j

R2

AR1 þ AT1 R2 ð1 AÞ:

ð1 AÞn 1 ð2:53Þ

36


Table 2.5. Numerical solutions of the measured transmittance, reflectance, and absorption characteristics of coated transmitting optics. R1

R2

A

RR

AR

TM

RA

AA

1.00

0 0 0 0.05 0.05 0.05 0.1 0.1 0.1

0.1 0.5 0.01 0.1 0.05 0.01 0.1 0.05 0.01

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0.81 0.9025 0.9801 0.8106 0.9013 0.9779 0.8092 0.897 0.9717

0.19 0.0975 0.0199 0.1878 0.0968 0.0198 0.1849 0.0957 0.0197

0 0 0 0.05 0.05 0.05 0.1 0.1 0.1

0.1 0.05 0.01 0.1 0.05 0.01 0.1 0.05 0.01

0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99

0.001 0.0005 0.0001 0.001 0.0005 0.0005 0.0012 0.0006 0.0001

0.009 0.0095 0.0099 0.0089 0.0095 0.0095 0.0088 0.0094 0.0099

0.8019 0.8935 0.9703 0.8027 0.8924 0.8924 0.8016 0.8884 0.9622

0.1891 0.097 0.0998 0.1868 0.0963 0.0963 0.1838 0.0951 0.0196

0 0 0 0.05 0.05 0.05 0.1 0.1 0.1

0.1 0.05 0.01 0.1 0.05 0.01 0.1 0.05 0.01

0.9 0.9 0.9 0.9004 0.9005 0.9005 0.9009 0.901 0.9011

0.01 0.005 0.001 0.0108 0.0011 0.0055 0.0117 0.0059 0.0012

0.09 0.095 0.099 0.0887 0.0984 0.094 0.0873 0.0931 0.0977

0.729 0.8122 0.8821 0.7319 0.8812 0.8128 0.7335 0.8114 0.8775

0.181 0.0928 0.0189 0.1782 0.0188 0.0917 0.1748 0.0903 0.0185

0 0 0 0.05 0.05 0.05 0.1 0.1 0.1

0.1 0.05 0.01 0.1 0.05 0.01 0.1 0.05 0.01

0.8 0.8 0.8 0.8017 0.8019 0.802 0.8034 0.8039 0.8042

0.02 0.01 0.002 0.0216 0.0109 0.0022 0.0232 0.0117 0.0024

0.18 0.19 0.198 0.1767 0.1872 0.1958 0.1732 0.1842 0.1933

0.648 0.722 0.7841 0.6538 0.7251 0.7854 0.6589 0.727 0.7849

0.172 0.088 0.0179 0.1687 0.0866 0.0177 0.1648 0.0849 0.0174

1.0

1.0

0.99

0.99

0.99

0.9

0.9

0.9

0.8

0.8

0.8

37

Analysis of R, T, A and S measurements Table 2.5. Continued R1

R2

A

RR

AR

TM

RA

AA

0.7

0 0 0 0.05 0.05 0.05 0.1 0.1 0.1

0.1 0.05 0.01 0.1 0.05 0.01 0.1 0.05 0.01

0.7 0.7 0.7 0.7037 0.7042 0.7046 0.7077 0.7086 0.7094

0.03 0.015 0.003 0.322 0.0162 0.0033 0.0346 0.0175 0.0035

0.27 0.285 0.297 0.264 0.2796 0.2921 0.2576 0.2739 0.2869

0.567 0.6318 0.6861 0.5762 0.6382 0.6904 0.5853 0.6440 0.6938

0.163 0.0832 0.0189 0.1592 0.0816 0.0166 0.1550 0.0797 0.0163

0.7

0.7

R1 ¼ Reflectance of coating 1 (high-reflectance component). R2 ¼ Reflectance of coating 2 (lowreflectance component). A ¼ Absorption of bulk material. RR ¼ Measured reflectance (side 1 towards laser). RA ¼ Measured reflectance (side 2 towards laser). TM ¼ Measured transmittance. AR ¼ Measured absorption (side 1 towards laser). AA ¼ Measured absorption (side 2 towards laser).

The measured parameters, making measurements with first one side (RA , TA , AA ) and then the other side (RR , TR , AR ) towards the laser, give us five equations with three variables (since TA ¼ TR ¼ TM , T1 ¼ 1 R1 and T2 ¼ 1 R2 for non-absorbing coatings). Numerical solutions for the measured parameters, using typical values for R1 , R2 and A, are given in table 2.5. Figures 2.18(a)–(f) show six cases illustrating the relationship between the reflectance measurements made in two different directions (subscript R for reflecting side first and subscript A for the anti-reflectance side first) for a range of values for the anti-reflectance value, R2 , and substrate absorption, A. Figures 2.19(a)–(c) show a similar set of graphs relating AA and AR for varying R1 and R2 . The computations show that, to a first approximation, the measured reflectance, RR , is the reflectance of the higher reflecting component if R1 > 0:7 and R2 < 0:3. For non-zero substrate absorption the measured reflectance, RA , is considerably less than the measured reflectance RR . A significant feature of these graphs is that the curves all meet at RR ¼ RA when R1 ¼ R2 and that they terminate at RA ¼ R2 . The absorption, AA , is considerably higher than AR except whenR1 R2 . The usefulness of this analysis can be demonstrated by reference to tables 2.5 and 2.6. Table 2.5 lists the calculated values of RA , RR , TM , AR and AA for typical values of R1 , R2 , and A. In table 2.6 the experimentally made measurements on a series of partly reflecting germanium output windows are summarized together with the calculated parameters and the absorptions which satisfy the theory. The first seven samples in this table

38


Figure 2.18. (a)–(f) Theoretical computation of the relationship between the measured reflectances of a dielectric-coated germanium window.

were a batch of good output couplers. The forward reflectance, RR , and the transmittance, TM , were measured on all these windows and the backward reflectance, RA , was measured for most of these windows. Both the individual reflectances, R1 and R2 , and the absorptances, AA and AR , both of

Figures 2.19. (a)–(c) Theoretical computation of the relationship between the measured absorptions of a dielectric-coated germanium output window.

84.1 – –

78.9

13.6 13.0 14.0

19.3

13.5

28.3

64.8† 67.0†

83.5

23.0

74.4

29.8

25.1

69.6†

68.6

TM

RA

* Assumed. † Calculated. ‡ Absorption, surface of R1 only. n Nominal (manufacturer).

W 201 W 231 W 232

W 200

W 199

W 198

W 197

85.3 85n 79.3 80n 85.7 85.0 85.0

74.1 74n 69.8 70n 75.8 77.5n 70.5 72.5n

W 195

W 196

RR

Ref. No.

Measured values (%)

85.5 86.0 86.0

78.6

85.0

70.5 70.5

75.2

69.7

74.1

R1

8.9 0 0

15.0

14.6

0 2.1

9.7

1.2

3.0

R2

0.22 1.98 1.75

0.26

0.8* 0.7n 0.29 0.47n 0.45 0.44n 1.2* 0.6* 0.57n 0.34

AR

2.3 1.52 0.65

1.6

3.1

6.9 3.3

2.6

1.6

5.3

AA

R

99.5 100.0 100.7

98.9

99.2

100.0 99.4

99.3

99.9

100.0

P

Calculated values (%) A

100.0 – –

100.0

100.1

100.0 98.6

100.0

100.0

100.0

P

Table 2.6. Summary of the measured and calculated characteristics of dielectric-coated germanium windows.

0.014 – –

0.011

0.02

0.041 0.02

0.0165

0.0096

0.31

A

0.035 0.02 0.01

0.028

0.05

0.102 0.05

0.041

0.024

0.078

cm1

Calculated absorption

0.010 0.011‡ 0.009‡

0.007

0.016

0.037 0.016

0.013

0.006

0.027

2AS

Analysis of R, T, A and S measurements 39

40


which could have been measured, have been calculated together with the summed absorptance, A, of the coating and the substrate. It will be noted from both tables that the absorption AR is always considerably lower than the absorption AA . It should also be noted that the calculated value of the anti-reflectance coating may be negligible. Whilst this might be true it should be recognized that this could also point towards absorption in the coatings themselves. Table 2.6 also includes a ‘summed’ absorption coefficient, cm1 , and a total surface absorption (2AS , where the absorption of each surface is AS ). This was calculated assuming that the true bulk absorption of the 10 cm1 resistivity germanium was 0.01 cm1 . The agreement and consistency of the calculations can be seen by the summations X X R ¼ RR þ TM þ AR ; A ¼ RA þ TM þ AA ; ð2:54Þ and the agreement with the suppliers’ absorption values. The theory used so far assumes that the absorption does not affect the reflectance of the coatings (i.e. that the absorption is either in the substrate or on the substrate/coating interface). It will be seen that the surface absorptions calculated (2AS ) range from 0.6 to 3.7%. These are in the experimentally deduced range. If the surface absorption is not on the surface but in the coating then anomalous results can be obtained. This can be illustrated by reference to samples 8 and 9 in table 2.6. These substrates were supplied as having large coating absorption. The calculations give nonsensical solutions if all the absorption is lumped together with the germanium bulk absorption. If, however, the assumption is made that the absorption is in the coatings then reasonable solutions can be gained. It would appear that the partly reflecting coating contained most of the absorption (greater than 1%) whilst the anti-reflectance coating contained a non-negligible amount (approximately 0.4%).

Chapter 3 Optical effects at medium power/energy levels 3.1

Introduction

At moderate and high optical power densities a number of nonlinear interactions come into play. Most of these have well defined thresholds. In comparison to linear (low-power) optics both the real and the imaginary part of the refractive index (the conventional refractive index, n, and the absorption coefficient, ) become functions of the incident light intensity, I, or electric field, Eðr; ; t; ’Þ. The refractive indices and the absorption therefore become functions of space, wavelength, time and polarization.

3.2

Absorption

It is possible for an electron in the conduction band of a material to be accelerated by the laser field to an energy greater than the band gap and hence lead to an electron avalanche. For this to occur the lifetime of the electrons in the conduction band must be long enough and the field strong enough to produce sufficient electrons with greater than the band gap energy. All the III–VI semiconducting materials meet this criterion and as a consequence exhibit nonlinear absorption and thermal runaway. This phenomenon is best understood in the germanium crystal, which is widely used as a window material in infrared laser systems because of its low dispersion and absorption at room temperature in the 2–12 mm wavelength range. Below 2 mm the free-carrier absorption increases more rapidly as more and more electrons are excited across the 0.785 eV band gap. The 12 mm upper limit marks the onset of absorption by the crystal lattice, which is characterized by an extremely complex series of absorption peaks. Infrared absorption in the transparent region is a strong function of the free carrier concentration (see figure 2.16) (Wood et al 1982a). This figure 41

42

Optical effects at medium power/energy levels

shows the measured absorption at 10.6 mm as a function of the resistivity of the material for a number of samples cut from an experimentally grown crystal boule. The figure also shows the surface water contribution to the absorption.

Figure 3.1. Measured transmission and calculated absorption versus temperature, AR/AR coated germanium single crystal.

Absorption

43

Figure 3.2. Absorption coefficient versus temperature for Ge and ZnSe.

The small band gap gives rise to a relatively large population of intrinsic carriers at room temperature and causes irradiated samples to exhibit ‘thermal runaway’ at room temperatures in excess of about 50 8C (see figures 3.1 and 3.2). All semiconducting materials will, by their very nature and composition, exhibit free carrier absorption but due to their differences in band gap, thermal conductivity etc. the precise temperatures at which thermal runaway is self-generating will be different. These parameters also affect the precise shapes of the laser-induced damage threshold versus pulse repetition frequency curves (see chapter 4). Plots of the absorption coefficient versus temperature for both germanium and zinc selenide are shown in figure 3.2 and a list of thermal runaway temperatures is given in table 3.1. Table 3.1. Comparison of thermal runaway and melting points for a range of semiconducting single crystals.

Material Germanium, Ge Gallium arsenide, GaAs Zinc sulphide, ZnS Zinc selenide, ZnSe Cadmium telluride, CdTe Silicon, Si

Thermal runaway temperature (K)

Melting point (K)

370 500 700 700

937 1238 1830 1520 1090 1410

44

3.3


Raman scattering

When the power density in an electromagnetic beam exceeds a well-defined value, stimulated Raman scattering starts to take place. Raman scattering occurs as a result of the interaction of the light wave with vibrational transitions of the medium. Raman scattering is caused either by the incident light photon emitting a phonon and re-radiating the remaining energy as another photon or by a phonon being absorbed and the energy added to the incident photon energy and re-emitted as a scattered photon. The spectrum of the scattered light includes spectral lines shifted to lower frequencies (Stokes lines), or to higher frequencies but with much less intensity (anti-Stokes lines). The process requires a sufficient interaction of the lightwave electric field with the material vibrations via the nonresonant interaction of the electrons in the medium and is therefore inversely power density dependent. Only a few vibrations of matter satisfy the full conditions and only a few of these show detectable intensities. However, in those materials which do fulfil the requisite conditions the process results in a very useful technique for frequency conversion and is becoming widely used as a narrow-band spectroscopic source. For a fuller treatment of the subject, see Menzel (2001). Some typical Raman thresholds, gained for a range of commonly used electro-optic crystals, are listed in table 3.2. The values indicate that the stimulated Raman scattering (SRS) threshold rises as the pulse length decreases. SRS results in power being moved from the fundamental into both Stokes and anti-Stokes lines at equal frequency shifts with decreasing efficiency (see table 3.3). In long lengths of electro-optic material (e.g. fibre-optic cable) these stimulated frequencies will in turn stimulate further frequency shifts and Table 3.2. Stimulated Raman scattering thresholds at 532 nm (Dmitriev et al 1999).

Crystal KDP LiIO3 LiNbO3 -HIO3

Threshold power density, Pthr (109 W cm2 )

Pulse length, (ps)

22 44 0.015 0.7 1.2 5 0.3 1.4 6

30 4 30 000 30 30 4 35 30 4

Raman scattering

45

Table 3.3 Stimulated Raman scattering in -HIO3 (Dmitriev et al 1999). Measurements made at 532 nm, I0 ¼ 1 GW cm2 , ¼ 35 ps.

SRS component

(cm1 )

(nm)

Efficiency (%)

1st Stokes 2nd Stokes 3rd Stokes 4th Stokes 1st anti-Stokes 2nd anti-Stokes

790 1580 2370 3160 790 1580

555.2 580.7 608.6 640.2 510.5 490.7

21 7 0.95 0.1 1 0.1

the resulting spectrum ends up as a series of lines with powers just below the SRS threshold. The stimulated process results in a serious limitation of the power handling capacity of optical fibre, especially in telecommunication applications where the Raman threshold effectively marks the limit at which incoherent detection techniques can be used. The shift to lower frequencies of the forward Raman travelling wave can result in added dispersion in the fibre. The primary effect may or may not be deleterious in the high-power-handling scenario where the total energy is only slightly modified. The stimulated Raman threshold, PR , is given by PR ¼ 16

A gR L

ð3:1Þ

Table 3.4. Raman shifted wavelengths in silica fibre (Chinlon Lin and Glodis 1982). Measurements made at 650 kW input power using 180 m fibre length. Line

Wavelength, (A˚)

Frequency shift, (cm1 )

L S1 S2 S3 S4 S5 S6 S7 S8 S9

3079–3081 3124 3167 3208 3253 3299 3347 3395 (3445) (3491)

– 463 431 403 430 428 434 428 (428) (383)

46

Optical effects at medium power/energy levels Table 3.5. Calculated values of the fibre length necessary to allow the generation of the maximum Stokes’ intensity as a function of the input laser power (Pini et al 1983). Laser power (kW)

250

500

750

1000

S1 S2 S3 S4

130 m – – –

30 m 150 m – –

11 m 35 m 100 m –

8m 19 m 50 m 110 m

max max max max

where gR is the Raman gain coefficient [440 mW for a 10 mm diameter fibre (Stolen 1979)], A is the fibre cross-sectional area, and L is the effective interaction length ð1 expðlÞÞ where l is the fibre length. The effective interaction lengths have been measured in fluoride fibres with core diameters of 30 mm and are of the order of metres. Critical powers of 3 kW peak, 12 mW mean have been measured. It must be realized that the effect is power density dependent and that the fibre diameter is one of the parameters which affects the power handling capability of optical fibres. Table 3.4 shows the wavelengths and frequency shifts measured when 650 kW of laser power at a wavelength of approximately 3080 A˚ were passed through a 180 m length of silica fibre. It was commented that the different Stokes lines stimulated each other. Table 3.5 illustrates the fact that increasingly longer material interaction lengths are necessary to allow the generation of the higher-order Stokes lines.

3.4

Brillouin scattering

This occurs when the incident photon is scattered by an acoustic phonon. This effect does occur at low optical power but becomes increasingly serious at high optical powers as stimulated Brillouin scattering transfers energy into the backward travelling wave. SBS has been observed in a wide range of gases, liquids and solids (Menzel 2001). SBS is especially serious in singlemode fibre (where it may occur at input levels of a few mW) and measurements of the reflected fraction have been measured to be as high as 60%. The SBS threshold, PB , is given by PB ¼ 21

A gB L

ð3:2Þ

where A is the fibre cross-sectional area, gB is the Brillouin gain coefficient, and L is the fibre length. PB 1:2 mW for a 10 mm diameter fibre of 4 km length (Stolen 1979); PB 2:4 kW for a 1 mm diameter fibre of 2 m length.

Harmonic generation

47

SBS can be detrimental in a number of ways, e.g. by introducing additional attenuation, by causing multiple frequency shifts or by adding backward coupling into the laser medium. It is particularly limiting in telecommunication applications as it limits the power available for coherent detection techniques. In high-power transmission applications the main problem is straightforward attenuation leading to the power loading and lowering of the laser-induced damage threshold. At high power levels damage occurs from the mechanical stresses associated with the acoustic wave. For long pulse lengths, high pulse repetition frequency (prf) pulse trains and continuous wave (cw) laser beams steady-state scattering is reached and damage occurs at constant linear energy density (see chapter 4). For Q-switched pulses the laser power density is inversely proportional to the pulse length, . For single mode-locked pulses the energy density needed for damage is expected to increase as the pulse length decreases since there is less time for the acoustic wave to build up (t expðPD Þ1=2 ¼ constant) (Bliss 1971).

3.5

Harmonic generation

The interaction of matter with the electric field of the incident light, Eðr; tÞ, can be described by the polarization, Pðr; tÞ: Pðr; tÞ ¼ "0 ð1Þ Eðr; tÞ þ "0 ð2Þ E2 ðr; tÞ þ "0 ð3Þ E3 ðr; tÞ þ ¼ Plinear ðr; tÞ þ Pnonlinear ðr; tÞ: The nonlinear part of this equation describes the progressive nonlinearity of the interaction with increasing power of the electric field. The nonlinear susceptibilities ðmÞ are, in general, functions of the material and the frequencies of the applied light waves. Harmonic generation occurs when two different light waves superimpose and generate the nonlinear polarization. In the simplest case, that of two equal monochromatic light waves with the same polarization, frequency and direction, the second-order polarization is determined by the product of the two electric fields. In this case a wave is generated with a frequency twice that of the incident wave (second-harmonic generation, SHG). Similarly it is possible to generate even higher harmonics in suitable media. For nonlinear and electro-optic effects to occur the tensors must contain non-vanishing elements in the electric dipole approximation. For second-order effects this only occurs for non-centrosymmetric and crystalline structures. No symmetry requirements are imposed for third-order nonlinear optical effects. For a full treatment of the subject of nonlinear optics it is sensible to consult specialist textbooks on the subject (Dmitriev et al 1999, Gunter 1999, Menzel 2001). This section, however, has been written to stress that a light beam in the transmitting window of a material may, under the correct

48


polarization, temperature and angle conditions, generate wavelengths that lie in the absorbing region. If this happens nonlinear absorption with a corresponding nonlinear temperature rise will occur. This may result in anomalously high temperatures and correspondingly low damage thresholds being attained. Although ð2Þ phenomena are usually absent in glasses and glass fibres because of the natural inversion symmetry in the lattice, SHG has been demonstrated, using suitable pump wavelengths, by passing sufficiently high power down an optical fibre. This has been observed after either cw or semicontinuous pulse trains have been passed down germanium- or phosphorus-doped fibre. No SHG has been reported using pure silica cored fibre. The SHG apparently arises from a reorientation of the molecules resulting in a non-centrosymmetric core. The phase matching criteria are apparently met by the phenomenon of quasi-phase matching (alteration of the sign of the ð2Þ nonlinearity) with the right periodicity to compensate for the mismatch in wavevectors. The present reported maximum efficiency of conversion is 13%, from a peak-input power of 900 W at 1.064 mm.

3.6

Self-focusing

Self-focusing is a reduction of the laser beam diameter below the value predicted by the refractive indices of the unirradiated material and details of the focusing optics. It can result from any process that leads to an increase in the index of refraction with increasing light intensity and/or temperature (see figure 3.3(a)). The degree of self-focusing will depend on the transmitted power and on the length of the sample. If the transmitted power is high enough and the consequent focusing is tight enough the lattice may damage catastrophically. Laser-induced damage thresholds for self-focusing will consequently vary with material length (Martinelli 1966, Hopper and Uhlmann 1970). In practice the laser-induced damage occurs in filaments (see figures 3.3(b) and (c)). The filamentary damage threshold (Davit 1968) is related to a selffocusing length which is a function of the nonlinear refractive index, n2 . When the sample under irradiation is longer than this self-focusing length the filamentary damage threshold is a minimum. The list of possible self-focusing mechanisms stretches from absorption heating through to electrostriction, electronic distortion, molecular distortion and molecular libration. Thermal self-focusing occurs in materials due to refractive index changes with temperature which are given by the equation @n @n @ n ¼ þ dT ð3:4Þ @T d dT

Self-focusing

49

Figure 3.3. (a)–(c) Self-focusing.

where @n=@T is the refractive index change with temperature at constant volume and is associated with higher populations in lower-lying states close to the absorption edge. The sign of this effect is positive and it occurs instantaneously. The second term,

@n d ; d dT

is the refractive index change due to thermal expansion and dilution of the density. The sign of this effect is negative and takes time to build up (acoustic relaxation time).

50

Optical effects at medium power/energy levels Alternatively n can be expressed as n ¼ n dn ¼

nPD ¼ nT PD ¼ nT Ep C

ð3:5Þ

where dn is the conventionally defined refractive index change with temperature, PD is the power density of the laser beam, is the laser pulse length, is the absorption coefficient, C is the specific heat, and NT is the energy-dependent refractive index factor. The self-focusing length, Zfoc , can be calculated as the point where the hot (slower) ray travelling along the beam axis meets in phase with the cold (faster) ray arriving from the edge of the beam (radius r). r2 n Zfoc ¼ pffiffiffi : 2nT PD

ð3:6Þ

Because Fresnel diffraction also takes place, trapping of the beam is defined as occurring when Zfoc (the focusing distance) is less than or equal to the Fresnel length (where diffraction doubles the beam diameter). The power in the beam necessary for focusing at the Fresnel length can therefore be defined as Pc : Pc ¼

ð1:22Þ2 n : 32nT

ð3:7Þ

Taking a typical example, for glass n ¼ 1:5, nT ¼ 109 , and Ep ¼ Pc ¼ 2 J. The pulse energy to trap the beam is a constant, independent of pulselength, therefore Pc ¼ 108 W

for ¼ 20 ns

Pc ¼ 106 W

for ¼ 2 ms:

Electrostriction would occur in a dielectric material under the influence of laser irradiation, as the net electrostrictive force at a point is proportional to the square of the electric field at that point. Thus, a radially symmetric beam would lead to a radially symmetric stress with an associated change in the refractive index leading to self-focusing. As the acousto-optical interaction involves a radially propagating compression wave driven by the light intensity gradient, beam focusing is caused by the compressional increase in the refractive index along the beam axis and electrostrictive self-focusing can occur even in non-absorbing glass (Kerr 1971). Thus, n ¼ nE V 2 ¼

B ðn2 1Þðn2 þ 2Þ 2 V 16n 3

ð3:8Þ

where B is the compressibility ¼ 1=v2 , V is the electric field in the medium, v is the velocity of sound, and nE is the electrostrictive coefficient. This leads

Self-focusing

51

to the equation Pc ¼

107 ð1:22Þ2 v: 256nnE

ð3:9Þ

Again, taking glass as a typical example, n ¼ 1:5, ¼ 2:2 g cm3 , v ¼ 3 105 cm s1 and ¼ 1:06 mm. This gives a value of the critical pulse power for electrostriction to occur as Pc ¼ 4:6 105 W: It will be seen from a comparison of these two critical pulse powers that, for a material with an absorption less than a few percent per cm, the electrostrictive focusing threshold power is lower than the thermal focusing threshold for pulse lengths shorter than microseconds. Acoustic relaxation must take place before electrostrictive focusing can occur. The time taken for the acoustic response to develop is of the order of 1010 s (Bliss 1971). For pulse lengths longer than this the threshold power density for self-focusing is independent of pulselength (Quelle 1969). For a single mode-locked pulse the power density necessary for damage increases with decreasing pulselength. A mode-locked train, however, does give the acoustic response time to develop and damage (see chapter 4) and damage therefore occurs at similar power densities to the longer pulses. Other self-focusing processes, such as electronic distortion and molecular libration, have extremely short relaxation times and affect the refractive index even for picosecond pulses and consequently the damage thresholds are independent of pulselength. With very short pulses there is not time for acoustic relaxation to occur across the whole beam diameter to permit trapping. In this case parallel lines of self-focusing damage occur (see figure 3.3). Trapping power must occur in an area, A, such that a sound wave can traverse it during the pulse duration. This area can be estimated as A ¼ r2 ¼ ðvÞ2

ð3:10Þ

and therefore Pfil ¼

Pc P ¼ 2c 2 ; A v

Efil ¼

Pc P ¼ 2c ; 2 2 v v

ð3:11Þ

where Pfil and Efil are the power and energy density respectively in the trapped filaments. The acoustic relaxation then leads to a 1= dependence of the energy density for filament formation. For example, if ¼ 30 ns, Efil 50 J cm2 and Zfoc 3 cm then, for pulses longer than the acoustic transit time, the power threshold for trap formation is constant and the pulse energy required increases linearly with the pulselength Efil ¼

Pc : r2

ð3:12Þ

52


Heating at the laser frequency will lead to thermal self-focusing if the sign of dn/dT is positive (Budin and Ruffy 1966, Hopper and Uhlmann 1970). If the sign of dn/dT is negative it can contribute to local increases in power density but not to self-focusing (Zverev and Pashkev 1970, Bliss 1971). The threshold power density for damage due to thermal self-focusing is inversely proportional to the pulselength provided that the latter is small compared with the acoustic relaxation time. Thus the electronic distortion and molecular libration mechanisms dominate at very short pulselengths, electrostriction dominates for Q-switched pulses and thermal self-focusing dominates for free lasing pulse trains and cw beams. When the laser is focused inside the material or component under test a standing wave is formed at the rear material/air interface. This standing wave gives rise to periodic internal electric fields which propagate back through the component. These periodically varying fields can give rise to electric field strengths twice as high as the electric field strengths associated with the forward travelling beam (Boling et al 1973, Klein 1993). This means that the irradiance may be enhanced up to a factor of four. As the incident energy increases this effect results in a series of damage spots travelling back through the material under test. Damage occurs at intervals where the enhanced irradiance reaches the LIDT of the material and the measured LIDT is therefore reduced by a factor which depends on the refractive index of the material under test: ED ¼ EM ð1 RÞ

ð3:13Þ

where is the irradiance enhancement factor and R ¼ ðn 1Þ2 =ðn þ 1Þ2 , which is the entrance surface reflectivity. The importance of the enhancement factor, , arises when it is hoped to make comparisons between measurements made using different spot sizes and sample dimensions. This is because the sample length/spot size ratio is important, particularly when focusing to ultra-small spot sizes. The higher this ratio the more likely that self-focusing will occur. In long lengths of material (such as optical amplifiers) self-focusing of the light leads to high-intensity spots on-axis thus leading to high peak power densities and eventually to dielectric breakdown (Soileau et al 1980). This author confidently states that no-one has ever measured the true breakdown threshold even of a bulk material because self-focusing always dominates at the high power densities involved. The refractive index of the material can be expressed as n ¼ n0 þ n 2 E 2 þ

ð3:14Þ

where n0 is the first-order power-independent refractive index and n2 is the second-order power-dependent refractive index. At some critical intensity or power a phase shift will occur affecting parts of the spatially resolved pulse causing frequency broadening or dispersion.

Self-focusing

53

The critical threshold power is given by Ps ¼

C n0 A 3 4 2 n2 L c

ð3:15Þ

where Lc is the critical interaction length. It should be noted that this effect is proportional to the pulse wavelength.

Chapter 4 Damage theory 4.1

Introduction

When the irradiation level reaches a high enough level, commonly termed the laser-induced damage threshold (LIDT), of the material, one of a number of irreversible, catastrophic interactions occurs. These interactions may occur whenever the irradiation is powerful enough, although the advent of the laser has given them prominence as common occurrences that must be considered whenever the specifications of high-power optical/laser systems are considered. Laser-induced damage may occur at the faces of the optical component (front or rear depending on the direction of the laser beam), at interfaces between components (especially if they are in contact) or in the bulk of the component. Damage to systems may occur due to reflections between components. It is important to know both the material and component physical parameters and the way they are integrated into a system before it is possible to make predictions as to the likelihood of laser-induced damage. The study of the theory, mechanisms, measurement and amelioration of the LIDT has been a major research topic in the laser community for well over 30 years. There is a lot of literature on the subject as evidenced by the Proceedings of the Annual Boulder Damage Conference (originally published as Special Publications of the US National Bureau of Standards and more recently by SPIE), the literature published by the Laser Institute of America, and that published in the mainstream scientific journals. Those who wish to start from a slightly lesser threshold would be advised start with this book or the SPIE Selected Papers on Laser Damage in Optical Materials (Wood 1990a). There are three main classes of mechanism which give rise to laserinduced damage. The first are thermal processes, which arise from absorption of the laser energy in the material, and in general apply for continuous wave (cw) operation, long pulse lengths and high-pulse-repetition-frequency pulse trains. The second class are dielectric processes, which arise when the electric field density is high enough to strip electrons from the lattice. 54

Introduction

55

These apply when the pulse lengths are short enough for avalanche ionization to take place and when the thermal absorption is low enough for the avalanche threshold to be below the thermal threshold. A third mechanism, which is usually classed as a special case of the second, is multiphoton ionization. This occurs when the energy is delivered at such a high intensity that electrons are stripped from the lattice and are raised to higher energy levels instantaneously. This effect occurs for femtosecond pulse lengths. Both the former classes of mechanism can be subdivided in order to describe the correct cause but in general their results are the same.

Dielectric breakdown

Thermal absorption

Bulk effects Surface effects Enhancement by scratches, voids and particles Raman scattering Brillouin scattering Self-focusing

Bulk effects Surface effects Localized absorption Conduction and free electron absorption Transient absorption Stress

Laser-induced damage may arise from single mechanisms or from a number of the above mechanisms acting in concert. There is no one value for the damage threshold for any particular material irrespective of the wavelength, pulse duration, beam size or shape. It should also be recognized that at the micrometre level all samples of material may be slightly different and that these differences may affect the measured LIDTs. Damage thresholds are therefore component specific and it is not enough to state that the damage threshold is x MW cm2 (or any other unit) without specifying the wavelength, pulse duration and the test spot dimensions (Wood 1997). Damage may be initiated in a single laser pulse, (1-on-1) measurement testing, by repeated irradiation at a single point, (S-on-1) measurement testing, and by high-repetition-rate testing/cumulative damage, (R-on-1) measurement testing. Each type of testing, although having similar logic and components to the others, is different inasmuch as each gives different information about the materials, components, and systems under test. It is necessary to know and understand the material characteristics and the test laser parameters before it is possible to assign provisional values to the LIDT of particular materials. It is also necessary to know the configuration and mounting particulars before it is worth trying to work out the power/energy handling capability of a specific material or component in any given system. Since the LIDTs are affected by the laser wavelength, spot size and irradiation duration (both pulse length and pulse repetition frequency) it can be difficult to predict what the power handling capacity

56

Damage theory

of a material would be under one set of irradiation parameters from data gained at another. It is necessary to emphasize at the outset of this chapter that the measurement of the LIDT and, in particular, any attempt at working out the scaling laws between LIDTs gained under different measurement conditions, even on identical samples, depends critically on knowing the spatial and temporal characteristics of the laser beam at the point of maximum irradiance. Laser beam profile characteristics come in a bewildering array and seemingly slight differences in the uniformity and distribution of the irradiation can make large differences in the irradiation level which causes laser-induced damage. Damage may correlate with 1. 2. 3. 4. 5. 6. 7. 8.

peak power (spatial and temporal) in the laser pulse maximum energy density (spatial) in the laser pulse average energy density in the pulse spike average energy density in a pulse with both a spike and a tail total energy density in a pulse train average power density in a pulse train cw power density (energy in a given time) linear power density in a long pulse

and a laser pulse may consist of 1. a single spike with a defined temporal shape 2. a train of spikes, each with a specific pulse width, at some given pulse repetition frequency 3. a spike plus a tail, which may contain an appreciable amount of energy but no appreciable power 4. a burst of energy with some fairly random temporal distribution 5. a cw, or chopped cw, beam. The spatial distribution may vary from a perfect Gaussian or a semiGaussian through some complicated mode structure to a random intensity profile. A number of oscilloscope traces showing some of the many variations in the laser beam and pulse profiles are shown in figure 4.1. Figure 4.1(a) shows the temporal profile of a single longitudinal TEM00 mode using fast detection. It will be noted that even this trace indicates slight residual energy emission outside the envelope of the main pulse. This is a common problem even with electro-optic switching. It is possible, however, to use separate electro-optic switching to cut the tail off and to reduce the pulse to something more like a single spike (figure 4.1(b)). The use of a fast detector is recommended/mandatory since, unless the detector speed is fast enough to resolve the temporal structure in the pulse, it may look as if the pulse is longer and has less peak power than it really has. Figures 4.1(c) and (d) show the temporal profile of a pulse, which has several

Introduction

57

distinct modes, first using fast detection and then using slow detection. The peak powers in each of the separate mode-locked spikes were in the region of ten times more than in the apparent envelope. This has occurred in the past and led to extremely low estimates of the LIDTs of optical materials (Wood 1978). It might be said that the use of slow detection slowed the acceptance of standard values for the LIDTs of a range of materials for several years. It is interesting to note that if the laser runs a sufficient number of modes, such that even using fast detection they are not resolvable, then the average envelope can be used without loss of accuracy (figure 4.1(e)). Each laser type has typical temporal behaviour. Figure 4.1(f) shows the single gain-switched spike from an ultraviolet-preionized 10.6 mm CO2 TEA laser. Figure 4.1(g) shows the gain-switched spike plus tail from a trigger-wire 10.6 mm CO2 TEA laser. Up to two-thirds of the energy may be in the tail, which may last up to 2 ms. Figure 4.1(h) shows the beam profile of both the TEA section and the hybrid TEA laser, indicating that the tail gains amplitude from the cw section of the laser. The TEA laser pulse consists of an envelope of short mode-locked spikes, while the hybrid section both smoothes out the spikes and amplifies the energy content in the pulse. In this case the gain-switched spike is almost dwarfed by the tail. In case the foregoing evidence leads the reader to feel that only CO2 lasers exhibit problems figures 4.1(i) and (j) include traces taken from HF (2.7 mm) and DF (3.8 mm) laser pulses. The importance of these remarks will be clearer after the sections covering laser-induced damage mechanisms (sections 4.2, 4.3) and particularly the ‘time of damage’ (section 4.5). The spatial distribution of the power also deviates from the optimum for many laser systems. The measurement aspects of this subject will be covered in chapter 8. For accurate measurement of the laser-induced damage threshold it is advisable to have either a ‘top-hat’ profile or a Gaussian profile. However, many laser systems do not have either of these clean-cut profiles. Whilst it is not impossible to make useful measurements with other spatial distributions it is hard to make comparative measurements and to compare measurement with theory. Practical profiles may vary from those with clean cut-offs (figure 4.1(k)), through those with extra energy in the wings (at low energy density but fairly large total energy) to beams with irregular multi-transverse profiles (figure 4.1(l)). The energy profile from a raw beam may be somewhat problematical (figure 4.1(m)). This figure shows a contour map of the energy density distribution in the beam of an Nd3þ :YAG Q-switched laser. It was shown that the gain of the system was such that the lasing medium was able to sustain several, parallel ‘fundamental’ modes which, when focused or homogenized, coalesced into a single Gaussian profile. The energy distribution across a good single-mode beam can be accurately quantified in terms of simple geometric parameters, such as the 1=e2 beam diameter at the focus of a lens or by measurement of the beam divergence. Many laser beams, however, have spatial profiles which do not

58

Damage theory

Figure 4.1. Temporal and spatial beam profiles. (a) Single longitudinal TEM00 using fast detection: Nd:YAG. (b) Electro-optic modulated pulse with decay tail cut off, CO2 . (c) Pulse with 1 < m < 10 modes (fast detection), Nd:YAG. (d) Pulse with 1 < m < 10 modes (slow detection) Nd:YAG. (e) Multi-longitudinal mode pulse, Nd:YAG. (f ) Gain-switched spike, ultraviolet preionized CO2 TEA laser.

Introduction

59

(h)

Figure 4.1. (g) Gain-switched spike plus tail, trigger-wire CO2 TEA laser. (h) Gainswitched spike plus tail, hybrid TEA CO2 laser.

conform to this and their energy distributions are a function of the distance of the measurement plane from the laser output window. In order to calculate the irradiance at any point in a generalized beam it becomes necessary to measure the beam propagation factor, K, or the related times-diffractionlimit factor, M 2 . The measurement of these factors will be discussed in chapter 8.

60

Damage theory

(i)

( j)

Figure 4.1. (i) Gain-switched spike plus tail, HF laser at 2.7 mm. ( j) Gain-switched spike plus tail, DF laser at 3.8 mm.

Introduction

61

(m)

Figure 4.1. (k) Spatial profile, near Gaussian beam profile. (l) Spatial profile, multi-transverse mode. (m) Contour map of the energy density distribution in the beam of a Nd:YAG Q-switched laser beam.

62

Damage theory

It should not be hard to accept that unless the laser beam characteristics can be measured sensibly and consistently no sense can be made of the irradiation levels which cause damage. This being so, it is not hard to accept that wide ranges of measured values have been published. However, it is to the credit of the laser measurement community that there is now a fairly well established idea of what the LIDT levels for particular materials are. High energy density, particularly when contained in short pulse durations, leads to high peak power in the beam, to high power densities incident and transmitted through optical components and to appreciable amounts of energy being absorbed in a short time in those optical materials and components. The effects outlined may occur in any material, however good it may be. It should be noted, however, that any discontinuities/ inhomogeneities in the optical materials irradiated will usually aggravate any problems arising. For repetitive short-pulse, long-pulse and cw laser beams the choice of failure mode is between cracking (because of undue strain) and melting (because the centre of the component reaches the melting point). Failure in unrestrained components is usually by melting, but when a component is held rigidly there is every likelihood that the whole component will shatter because of the induced strain. For single-shot and low-pulse-repetitionfrequency (prf) short-pulse-duration radiation the damage mechanism is dominated by either melting or dielectric breakdown. The absorption of the material at the wavelength of interest is the crucial factor in deciding which mechanism overrides the other. The following treatment first analyses the effect of varying the levels of uniform absorption and then goes on to look at the influence of absorbing inclusions and scratches. It must be recognized that the limit to damage by thermal mechanisms alone occurs at pulse lengths longer than 1013 s. At pulse lengths shorter than this, multiphoton and avalanche ionization gradually become more dominant. Damage arising from irradiation by single pulses with pulse lengths shorter than 1 ps can almost certainly be credited to multi-photon ionization. For ease of reference, pulses shorter than 1013 s are termed ultra-short in the rest of this text.

4.2

Thermal mechanisms

When a light beam is incident upon a material some of the energy is absorbed in the form of heat. The interaction depends markedly on both the relative sizes of the beam and the component under test, on the ambient conditions, on the mounting conditions and on the optical, mechanical and thermal properties of the material or component irradiated. A simplified schematic of the variation of the maximum temperature obtained as a function of the pulse temporal shape and pulse repetition frequency is given in figures 4.2(a)(e).

Thermal mechanisms

63

Figure 4.2. Laser beam intensity, I, and material temperature, T, versus time, t.

For short pulses, figure 4.2(a), the maximum temperature, at the centre of the beam, occurs after the peak of the temporal spike. For long pulses (figure 4.2(b)) the maximum temperature is close to the end of the pulse. For a low-repetition series of pulses (figure 4.2(c)) the temperature oscillates in line with the repetition temperature of the sample and gradually rises. For a high-prf train of pulses the temperature at the centre of the sample gradually rises (figure 4.2(d)), and apart from being slightly more spiky is very much the same as the temperature rise measured for a cw beam (figure 4.2(e)). In all these figures I stands for the laser beam intensity envelope and T stands for the temperature reached at the centre of the material. 4.2.1

Transmitting materials

Absorption of energy may give rise to a rise in temperature, leading to thermal expansion, strain, distortion, birefringence, movement of internal defects, cracking, melting, and catastrophic shattering.

64

Damage theory

High peak power densities also give rise to the advent of nonlinear absorption and transmittance, electro-optic effects, second-harmonic generation, optical parametric oscillation, and self-focusing. These effects may add to the amount of energy absorbed. The combination of mechanisms add up to change the beam shape, induce birefringence, and shatter or melt the component. They can also be put to use to cut, drill, weld and anneal. When laser radiation is absorbed in a transmitting medium it is absorbed in a cylinder passing through the material on the axis of the laser beam. It causes both a temperature rise at the centre of this cylinder and a radial strain between this centre line and the edge of the component. The temperature rise, the spread of the heat and the radial strain depend not only upon the material properties and the amount of heat absorbed but also on the beam diameter, the component diameter and the laser pulse duration. It is possible to define a diffusion length, L, the distance the heat will travel out from the centre of the beam in the duration of the laser pulse, such that L2 ¼ 4D

ð4:1Þ

where D is the diffusivity (¼=C), is the laser pulse duration, is the thermal conductivity, is the material density, and C is the heat capacity of the component. Unless the beam radius, r, is larger than this, i.e. 2r L, there is negligible spread of the energy in the pulse duration. If the centre of the beam reaches the melting point of the material under test, Tm , a damage threshold can be defined: ED ¼ C dT=

ð4:2Þ

where dT ¼ Tm Ta and Ta is the ambient temperature. A threshold for catastrophic cracking can similarly be defined: ED ¼ CS=

ð4:3Þ

where S is the damaging stress and is the volume expansion coefficient. In this short-pulse time regime, the damage threshold is a constant value if expressed in terms of the peak power density, i.e. in units of J cm2 . The expected LIDT for thermal damage in the above regime can be calculated from the material parameters. Table 4.1 lists the expected LIDT for a range of commonly used laser window materials. It will be seen, from inspection of this table, that many of the materials suffer laser-induced damage without being heated to their melting points. Many of the materials used suffer from other deleterious effects below their true melting points. For example, most glasses soften at temperatures below the melting point; chlorides, sulphides and selenides dissociate; diamond graphitizes and all

0.69 0.88 0.49

0.3

0.44 0.86 0.27

0.18

0.31

0.71 0.15

KCl NaCl ZnS

ZnSe

BaF2 CaF2 GaAs

CdTe

Ge

Si HgCdTe

2.33 7.6

5.32

5.85

4.89 3.18 5.31

5.27

1.99 2.17 4.09

370 tr 937 m 1410 m 930 m

1610 s 719 s 1170 m 2015 m 1000 g 2000 m 776 d 801 d 700 tr 1830 d 700 tr 1520 d 1280 m 1360 m 800 tr 800 tr 1238 m 1090 m 0.055 0.035 0.33

0.41 1.02 0.09

102 102 2 103 102 102 103 102 2 102 102 103

0.070

0.11

0.047 0.034 0.86

104 104 0.24 0.2

0.0075 0.0051 0.015 0.16 1.03

104 103 102 2 104 104

1.1 107 4 105 5 104 7 106 6 107 1.5 108 3 106 4 106 8 102 3 103 7 102 2 103 4 104 105 7 102 104 2 104 101 104 5 102 104 8 10 101

Temperature, Tm Absorption coefficient Thermal diffusivity, D LIDT, CdT= (8C) (cm1 ) (cm2 s1 ) (J cm2 )

m ¼ melting point, s ¼ softening point, d ¼ dissociation point, g ¼ graphitization point, tr ¼ onset of thermal runaway.

1.68 0.10

0.67

0.075

0.11 0.095 0.48

0.17

0.07 0.065 1.72

2.21 2.51 4.64 3.99 3.51

0.81 0.86 0.61 0.72 6.1

Fused silica BK7 LiNbO3 Al2 O3 Diamond

0.014 0.011 0.046 0.46 22.0

Specific heat, Cp Conductivity, K Density, (J g1 K1 ) (W cm1 K1 ) (g cm3 )

Material

Table 4.1. Physical characteristics and LIDT data for a range of laser window materials.

Thermal mechanisms 65

66

Damage theory

semiconducting materials suffer from thermal runaway (see chapter 3). The temperatures at which these effects occur are therefore the relevant ones to be inserted in the thermal damage equation. It will then be seen that these effects commonly lower the energy density at which a material should be expected to be damaged by a large factor. Another variable, which is entirely relevant, is the precise absorption at the wavelength of interest. This point is illustrated by comparing the C dT= values for semiconductor detector materials in their transmission windows and in the conduction band. When the thermal conduction out of the irradiated area becomes nonnegligible, i.e. when r2 = D < R2 =, where r is the laser spot radius and R is the component radius, then the illuminated region can be treated as a continuous line source (Carslaw and Jaegar 1947). The energy densities required for melting or catastrophic strain are then given by ED ¼

4DC dT ln ð4D=r2 Þ 2 r

ð4:4Þ

4CDS : r2

ð4:5Þ

or ED ¼

It will be seen from these equations that in this regime the damage threshold will be dependent on power rather than on energy density or even on the more conventionally quoted power density. In the case of long irradiation times (long-pulse, multiple-pulsing, and cw irradiation) the component temperature gradually rises to a maximum and the equation for the temperature rise reduces to Tm Ta ¼ dT ¼

P ; 2CrD

ð4:6Þ

i.e. this is the steady state profile in a semi-infinite solid (see figures 4.2(d) and (e)). It will be noted that in this regime the damage threshold is proportional to W cm1 . The damage threshold versus pulse length and the laser spot diameter is plotted in figures 4.3 and 4.4 using different abscissa units for zinc selenide. In figure 4.3, where the damage threshold is quoted in terms of the energy density (J cm2 ), it will be seen that the threshold, LIDT, is constant at short pulse lengths, and dependent on pulse length and spot size at longer pulse lengths. Figure 4.4, where the damage threshold is plotted in terms of the linear power density (W cm1 ), apparently indicates the opposite. These two figures show that it is useful, in displaying the damage thresholds of optical components, to be aware that the thermomechanical properties of

Thermal mechanisms

67

Figure 4.3. LIDT (J cm2 ) versus pulse length and spot size, ZnSe.

the materials change the relationships. It is also not too early to emphasize that when the LIDTs of different samples, even of the same material, are compared the wavelength, spot size and pulse length must be known and compensated for.

Figure 4.4. LIDT (W cm1 ) versus pulse length and spot size, ZnSe.

68

Damage theory

Table 4.2. Thermal nonlinear break point. Thermal diffusivity, D

Uniform beam radius or Gaussian beam 1=e diameter; pulse length, (s)

(cm2 s1 )

10 mm

100 mm

1 mm

1 cm

103 102 101 100

103 101 105 106

101 102 103 104

101 100 101 102

103 102 101 100

In following the above discussion it is necessary to know where the break point (between the conduction-limited effects) come in. The transition point between the pulse-length-dependent (equation (4.4)) and the pulselength-independent (equation (4.2)) sections of the energy density versus pulse duration graphs for thermal damage is given by ¼ r2 =D. This transition point has been calculated for a range of spot radii and thermal diffusivity values and these are listed in table 4.2. It should be noted that although the equations have been derived assuming a square-topped spatial energy density profile of radius r, they are still correct if the value of the 1=e diameter of a Gaussian beam is substituted. Figure 4.5 depicts the LIDT versus pulse length for a number of common optical materials, showing the break point. It should be noted that the break point is idealized as in practice the transition is much more curved. It must be emphasized, however, that this graph does not allow for the differences in absorption with wavelength, i.e. these values are to be expected in the transmission range of the materials only. For all the semiconductor materials, which form the main class of infrared transmitting materials (e.g. germanium, zinc selenide, zinc sulphide, gallium arsenide, mercury, cadmium telluride, etc.) it should be noted that thermal runaway occurs at fairly low temperatures compared with the melting temperature (see table 3.1). In practice this means that the value for Tm in the previous equations is a low value, the point at which nonlinear absorption starts, and not the melting point of the material. Figure 3.3 illustrated the change of absorption in both germanium and zinc selenide as a function of the ambient temperature. It should be noted that the only common infrared transmitting materials that do not suffer from thermal runaway are the halides. As long as these are kept in a strictly dry environment they exhibit relatively high LIDTs which do not drop with laser pulse repetition frequency. However they are all hygroscopic and, if left in the open, absorb water vapour, which then both dissolves the substrate and absorbs infrared radiation.

Thermal mechanisms

69

Figure 4.5. Thermally induced LIDT versus pulse duration.

A much more complex situation occurs when absorbing inclusions inside a transmitting matrix absorb laser energy. These inclusions may be, for example, platinum specks inside Nd:laser glass, absorbing crystallites inside a KDP electro-optic crystal or carbon particles inside a diamond film. In each of these cases the damage observed is critically dependent on the size of the particle. The damage is associated with melting and expansion in each case but the damage morphology varies. In the case of a Pt speck (originating from the melt crucible) damage occurs (shattering the glass matrix) only over a limited range of particle diameter. If the particle size is too small (less than 0:1 mm) it is too small to absorb much energy and damage does not occur. If the particle size is large (>50 mm diameter) the periphery melts but the heat is mainly absorbed in the bulk. In between these extremes the platinum melts, expands and causes strain, which shatters the glass matrix. In the case of dust, misoriented crystallites or other absorbing material in KDP, the expansion of the absorbing inclusion shatters the crystal along its growth planes. In the case of diamond and diamond films, carbon particles in the diamond matrix vaporize, form plasma and then interact

70

Damage theory

with the diamond itself. Research is ongoing in the growth and deposition processes in all three materials to eliminate the absorbing particles. 4.2.2

Absorbing materials

When a laser beam is incident on a non-transmitting surface a small amount of radiation penetrates it to a distance called the skin depth, which is in turn a function of the electrical conductivity. Subsequent absorption of this radiation by free carriers within the material raises the temperature of the surface. As the temperature rises, stress and distortion of the surface will occur. In the limit, catastrophic damage may occur due to mechanical failure, to melting of the surface, or to a combination of both. The temperature rise due to the absorption of energy may be calculated using a one-dimensional heat flow calculation. At the centre of the beam the temperature rise, T, is given by t x Tðx; tÞ ¼ 2I0 ierfc pffiffiffiffiffiffiffiffiffiffiffiffiffi ð4:7Þ kC 2 kt=C where t is the irradiation time, is the absorption, I0 is the intensity of the beam, k is the thermal conductivity, is the density, and x is the depth at which the measurement takes place (x ¼ 0 at the surface). As long as the function ierfc(y) is small (y > 2) a sample thickness of pffiffiffiffiffiffiffiffiffiffiffiffiffi x > 4 kt=C is effectively infinitely thick as regards the effect on the maximum surface temperature. This leads to the expression pffiffi 2I0 t TðtÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffi ð4:8Þ kC at x ¼ 0. If damage is due to surface melting, then T ¼ Tm Ta

ð4:9Þ

where Tm is the melting temperature of the irradiated surface and Ta is the ambient temperature. pffiffiffiffiffiffiffiffiffi The expression ðTm Ta Þ kC may be regarded as a figure of merit for laser-induced damage (although it is modified by the absorption of the sample at the wavelength of interest). A table containing this figure of merit (FOM), for a range of metal mirror candidates for use at 10.6 mm, is shown as table 4.3. It must be stressed that the FOM may be modified drastically by the absorption, . It must also be recognized that all the constants involved are temperature dependent. In the case of a coated substrate (e.g. apgold-coated copper mirror), if the coating thickness, z, is ffiffiffiffiffiffiffiffiffiffiffiffiffiffi much less than k=C , then the values for k, and C are determined by the substrate material whilst the value for is that of the coating and Tm is p the ffiffi lowest melting point of the two materials. Equation (4.9) also indicates a t dependence of the damage threshold with pulse length.

Thermal mechanisms

71

Table 4.3. Figure of merit for 10 mm mirror candidate materials (Lide 1994).

Element

Tm (8C)

(W cm1 K1 )

(g cm3 )

C (J g 1 K1 )

Figure of merit with respect to copper

Copper Aluminium Beryllium Chromium Gold Hafnium Molybdenum Nickel Niobium Osmium Palladium Platinum Rhenium Rhodium Ruthenium Silver Tantalum Titanium Zirconium

1084 660 1287 1907 1064 2233 2623 1455 2477 3033 1555 1768 3186 1964 2334 962 3017 1668 1855

4.01 0.243 2.00 0.937 3.17 0.230 1.38 0.907 0.537 0.876 0.718 0.716 0.479 1.50 1.17 4.29 0.575 0.219 0.227

8.96 2.7 1.85 7.15 19.3 13.3 10.2 8.9 8.57 22.5 12.0 21.5 20.8 12.4 12.1 10.5 16.4 4.5 6.52

0.385 0.90 1.825 0.449 0.129 0.144 0.251 0.444 0.265 0.130 0.246 0.133 0.137 0.243 0.238 0.235 0.140 0.523 0.278

1.000 0.124 0.832 0.827 0.741 0.371 1.236 0.400 0.234 1.219 0.565 0.632 0.934 1.044 1.356 0.774 0.870 0.299 0.324

Taking into account the correction that has to be made if the laser pulse is not square, the LIDT is given by I0 Tm Ta ¼ dT ¼ pffiffiffiffiffiffiffiffiffiffiffiffi f ðtÞ 2 C

ð4:10Þ

where f ðtÞ is a time-dependent function, the precise form of which is determined by the input pulse shape. It is possible to evaluate the value of f ðtÞ for different pulse shapes. Figure 4.6 contains a plot of the relative input power necessary (as a function of the beam spot and the sample diameters) for the sample to reach a specified temperature at the beam centre. This figure shows, for instance, that the maximum temperature rise produced by a typical CO2 TEA Gaussian laser pulse is 50% greater than that due to a square topped, uniform pulse of equal peak intensity and pulsewidth. Figure 4.7 shows the correlation between the experimentally measured and the theoretically calculated damage thresholds for a range of metal mirrors (for a 50 ns FWHM CO2 laser pulse). The measured values quoted are the maximum values gained as the LIDT may be lowered appreciably by scratches, blemishes etc. Note that the damage threshold is inversely proportional to the temperature of the material and that it can easily be raised by back-cooling the metal substrate.

72

Damage theory

Figure 4.6. Relative power versus beam diameter for a specified temperature at the beam centre.

Although diamond-turned metal mirrors usually give superior performance to conventionally polished mirrors, it has been shown that it is possible to conventionally polish copper surfaces to the same degree of finish. This experiment (Wood 1986) illustrated that the main drawback to obtaining high LIDTs from conventionally polished metals was associated with the micrometre-sized scratches associated with finishing a mirror surface. Finishing the surfaces to a finer finish not only raised the LIDT but, as expected, lowered the absorption. This is illustrated in figure 4.8 where the measured absorption

Figure 4.7. Calculated and measured LIDTs for metal mirrors. Measurements made using a 50 ns FWHM CO2 TEA laser.

Thermal mechanisms

73

Figure 4.8. The effect of absorptivity on the measured LIDTs for six conventionally polished copper mirrors. 50 ns FWHM, 10.6 mm CO2 TEA laser.

for six conventionally finished copper mirrors is plotted against the measured LIDT (50 ns FWHM pulses from a 10.6 mm CO2 TEA laser). The calculated and measured values of the laser-induced damage threshold, made under identical conditions, for a series of different metal mirrors are shown in figure 4.7 and in table 4.4. These measurements were all undertaken at the same facility employing a 50 ns CO2 TEA laser focused to a 100 mm 1=e2 diameter focused spot. A separate table comparing measurements made at a number of different laboratories is shown in table 4.5. These measurements were all made using CO2 lasers but with different pulse widths. Table 4.5 includes a column showing the normalized LIDT. In order to complete the temperature analysis it is necessary to calculate the temperature distribution well after the laser pulse. From the heat flow equation r2 T ¼

1 T D t

ð4:11Þ

where D is the diffusivity, with the boundary conditions that the incident radiation is absorbed in a hemisphere of radius r, where r is much less than the radius of the sample. The solution can then be approximated to T ¼

E 3=2

4CðDtÞ

expðr2 =4DtÞ:

ð4:12Þ

1083 1083 1062† 1062 1062† 660 1455 961 1890 2620

Mirror

Dt Cu Dt Cu Dt Cu/Au Dt Au Au/Ni/Cu Al (d) Ni (d) Ag (d) Cr (d) Mo (d)

0.92 0.92 0.92x 0.70 0.13‡ 0.50 0.13 1.00 0.21 0.35

Thermal conductivity, (cal/s cm 8C) 8.92 8.92 8.92x 17.0 8.9‡ 2.7 8.9 10.5 7.2 10.2

Density, (g cm3 ) 0.092 0.092 0.092x 0.031 0.106‡ 0.215 0.106 0.057 0.107 0.060

Specific heat, C (cal g1 ) 0.4 0.8 1.0† 1.0 1.0 2.0 2.0 1.0 0.5 3.0

Absorption, A (%) 2.0 1.0 0.78 0.54 0.30 0.08 0.02 0.64 1.2 0.34

LIDT, relative to Cu

120 60 47 32.5 18 5 1.2 38.5 70 20.5

LIDT calculated (J cm2 )

90 60 40 37.5 15 3.3 – 40 – 23

Highest measured (J cm2 )

Standard, † Au, ‡ Ni, x Cu. Measurements made using 50 ns CO2 TEA laser. Dt ¼ diamond turned. Dt Cu/Au ¼ gold plated layer on a diamond-turned copper substrate. Au/Ni/Cu ¼ gold-plated layer on a nickel-coated polished copper substrate. (d) ¼ diamond-polished substrates.

Melting point, Tm (8C)

Table 4.4. Calculated and measured values of the LIDT for a series of metal mirrors.

74 Damage theory

75

Thermal mechanisms Table 4.5. Damage thresholds of metal mirrors; comparison of published values.

Absorption, A (%)

LIDT (J cm2 )

Pulse width (ns)

Normalized LIDT (J cm2 )

Centre

90 60 55 10.1 67 290 40 kW pffiffiffi 4 105 – 25

50 50 50 1.7 58 600 10 s range – 1.7

90 60 55 55 62 83.7 89 98 – 135

GEC, HRC GEC, HRC GEC, HRC Los Alamos Los Alamos Hughes RL Kirtland Spawr Dussledorf Los Alamos

50 50 –

40 50 –

GEC, HRC GEC, HRC USNWC

1.7 58 50 cw 50

29 23 12.5 30 30

Los Alamos Los Alamos GEC, HRC Spawr Osaka Un.

Material

Finish

Copper

Dt Dt Pol Pol Pol Dt Dt Dt Dt Single crystal

0.4 0.8 0.6 0.9 0.9 0.8 0.8 0.8 0.8 –

Cu/Au

Dt Pol Dt

1.0 0.56 0.6

Mo

Pol Pol Pol Dt e.b.

1.9 1.9 3.0 1.7 1.7

Al

Pol Dt Dt Pol

10.4 2.1 1.1 1.1–7

0.34 0.62 – –

1.7 1.7 – –

1.8 3.3 – –

Los Alamos Los Alamos USNWC Dussledorf

Stainless steel

Pol Pol

10.2 10.2

0.9 4.6

1.7 58

4.9 4.3

Los Alamos Los Alamos

Silver

Pol Dt

1.0 0.5

40 –

50 –

40 50 – 5.3 25 12.5 pffiffiffi 3 105 30

40 –

GEC, HRC USNWC

Measured values normalized to 50 ns FWHM pulse length.

If a second pulse is incident on the mirror before the temperature rise from the first pulse is completely dissipated, then the temperature profile (given by equation (4.10)) has to incorporate this heat flow equation. Each incident pulse would generate a steplike temperature profile (as illustrated in figure 4.2(d)), resulting in a staircase-like temperature–time curve with the tread as its repetition rate and the riser as the peak pulse temperature. In materials with good thermal conductivity the decay time drastically reduces the temperature between each pulse.

76

Damage theory

Figure 4.9. LIDT (J cm2 ) versus pulse length and spot size. OFHC copper at 10.6 mm.

The ‘average temperature’ is relevant to the case of both high prfs and cw beams. The equation of this curve can be approximated by T ¼

P r erfc pffiffiffi 2CrD 4Dt

ð4:13Þ

which, for large values of t, reduces to T ¼

P 2CrD

ð4:14Þ

which, again, is the steady state radial profile of the temperature in a semiinfinite solid. It will be further recognized that the temperature is inversely proportional to the radial distance, r, from the centre of the beam. When the pulse duration is longer than the material heat diffusion constant, i.e. when the heat has time to diffuse out of the irradiated spot, the damage threshold becomes proportional to W cm1 . As discussed in the previous section, the damage threshold can be plotted in a number of ways. The most pertinent are shown in figures 4.9 and 4.10. As already discussed, the optimum choice of units for expressing the damage threshold depends on the pulse length, spot size and the thermal conductivity of the material. The actual value of the LIDT is, however, mainly decided by the absorption, conductivity and the specific heat of the material.

Thermal mechanisms

77

Figure 4.10. LIDT (W cm1 ) versus pulse length and spot size. OFHC copper at 10.6 mm.

There is a problem in calculating the melting points and corresponding LIDTs for laser pulses with non-uniform pulse shapes. Porteus et al (1981) reported a detailed study of the LIDTs of Cu, Ag and Au diamond-turned surfaces at five different wavelengths. The calculated and measured LIDTs agreed well in the 9 ns, 1.064 mm, and 200 ns, 10.6 mm short pulse cases. The calculated values were slightly high for the hybrid-TEA 10.6 mm laser and high for the 3.8 mm, HF, and 2.7 mm, DF, lasers which both had narrow spikes plus a long tail (see figures 4.1(i) and (j)). The paper reported thresholds for slip, melting, crater damage and light emission. In all cases the thresholds for slip were lower than the other three phenomena. The thresholds for these were all fairly similar although there were slight variations. There was some evidence that the surface roughness was important at the shorter wavelengths. This paper included a good summary of previously published results on metal mirror damage thresholds. A good example of a study aimed at measuring the LIDTs of single point diamond-turned OFHC copper mirrors (Spawr and Pierce 1981) showed that it pwas possible to gain a fairly consistent value of ffiffiffi 2 4:4 105 J cm over a wide range of wavelengths and pulse lengths as long as the reflectance was taken into account. It will be seen, by reference to table 4.5, that this, when normalized to a 50 ns pulse width, correlates with an LIDT of 98.3 J cm1 . Similarly a measurement on a diamondturned molybdenum surface yielded a normalized result of 30 J cm2 . Both

78

Damage theory

these results are in line with the other measurements collated from other sources and reported in table 4.5. 4.2.3

Heat flow in transmitting windows

When a pulsed or cw beam passes through a semi-transparent material the absorption results in a cylinder of heated material. The precise temperature distribution will depend on the temporal and spatial characteristics of the laser beam. Several workers have made analyses of the temperature gradients etc. in mirror and window components (Jaspese and Gianio 1972, Sparks 1971, Apollonov et al 1974). In the case of a normal thin, l mm thick, window the energy Ep is absorbed in a cylinder of radius r (cylindrical volume of 22 l). Unless the beam radius is comparable with the diffusion length, L (where L ¼ 2ðDÞ1=2 ), there is negligible lateral spread of the energy in the pulse time, . The peak temperature rise at the centre of this cylinder is approximately (for a Gaussian profile) Tp ¼

4Ep : Cr2 l

ð4:15Þ

For a typical germanium window with l ¼ 4 mm, ¼ 5:46 g3 , C ¼ 0:376 J g1 8C1 , ¼ 1% and Ep ¼ 50 mJ. The temperature rise is 37.6 8C for r ¼ 50 mm and 0.15 8C for r ¼ 2:5 mm. As in the case of surface absorption, the peak temperature will drop exponentially with both time and radius (assuming only radial heat flow according to equation (4.12)): T ¼

E 4CðDtÞ

3=2

expðr2 =4DtÞ:

ð4:16Þ

In the case of repetitive irradiation the temperature excursions will mirror those shown in figure 4.2(e). The peak temperature can be quantified by summing up the temperature excursions due to each pulse. If the laser repetition frequency, f ¼ 1=t1 , then the peak temperature reached during the mth pulse is given by Tp ¼

m X

E 3=2

n¼1

4CðDmt1 Þ

expðr2 =Dnt1 Þ:

ð4:17Þ

For the case of a germanium sample irradiated with 50 mJ pulses at 1 Hz in a 100 mm spot, the peak temperature rise for a single pulse would be 37.6 8C and, during the 11th pulse, 38 8C. In the case of cw irradiation, where t1 ! 0, the temperature again tends to a steady state, as given by equation (4.14) and in the experiment outlined in section 4.2.4 the temperature at the centre of the irradiated spot would

Thermal mechanisms

79

reach 49.5 8C after 7.8 s (assuming linear absorption). As germanium suffers markedly from nonlinear absorption at 50 8C it is not surprising that catastrophic damage should occur at this irradiation level. 4.2.4

Thermal distortion

Thermal distortion is particularly severe in the output windows of high mean power and cw lasers. Lensing occurs, usually before catastrophic damage, and both the laser output power and the beam shape are affected (Sparks 1971, Detrio and Petty 1975, Loomis and Bernal 1975). In the case of non-uniformly heated metal mirrors it has been shown to be possible to keep the surface shape constant by back-cooling. In the case of a uniformly irradiated edge-cooled window, or a window having a larger incident radiant intensity at its centre than at its edge, there is a radial temperature gradient across the window. The thermal expansion of the material (positive d=dT) causes the window or lens to become more convex. The radial temperature gradient also causes a gradient in the refractive index, dn=dT, since the value of n is a function of the temperature. The sign of dn=dT is negative for ionic crystals and positive for covalent crystals (Sparks 1971). The net optical figure change is therefore positive for covalent crystals but may be positive, negative or negligible for ionic crystals. The angle through which a normally incident ray is bent is a measure of the distortion induced by the optical change. In general this angle is a complicated function of the radial coordinate as all rays do not cross the optic axis at the same point. An added complication is that the thermally induced stresses cause the local values of n to be different for different polarizations; thus the window may become birefringent. The stresses result from the partial constraint of the expansion of the warm centre of the window by the cooler edge. Sparks (1971) developed figures of merit for a range of laser window materials, for use at 10.6 mm, and made an estimate of the temperature difference, Tcrit , between the centre and edge of a window which causes a given reduction in the target intensity. Table 4.6 lists the relevant material parameters, the calculated Tcrit and the figures of merit for cw operation, fcw , and for pulsed operation, fpulse , which cause a halving of the diffraction-limited target intensity in an arbitrary system. It will be seen from inspection of this table that, although there are several good candidates for pulsed operation, the range of suitable window materials drops markedly for cw operation. The problem with the results of this analysis is that it demands that either the alkali halide windows are protected from the atmosphere or that the optical window (and consequently the laser system) diameter is larger than strictly necessary from the considerations of the material LIDT. The precise degree of distortion, both in terms of optical non-uniformity and in terms of acceptable loss of system performance, is critically dependent

1.39 1.32 1.54 1.49 1.52 1.67 1.66 1.79 2.06 1.38 1.43 1.40 2.37 1.66 1.78 1.54 2.20 2.43 2.67 3.30 2.42 3.41 4.0 2.41 2.93 2.60

LiF NaF NaCl KCl KBr KI CsBr CsI AgCl MgF2 CaF2 BaF2 TlBr–TlI MgO Al2 O3 Crystal quartz ZnS ZnSe CdTe GaAs Diamond Si Ge As2 S3 glass Si25 As25 Te50 Ge28 Sb12 Se60

1.27 1.6 3.65 3.4 4.0 5.0 6.3 10.0 6.1 0.19 0.77 0.9 23.5 1.89 1.41 0.539 7.5 4.8 11.75 18.7 0.98 16.2 26.8 0.86 2.0 7.9

dn=dT 10 (8C1 ) 32.3 31 38.9 36 43 38 47 47 30 10.7 20 18.4 58 9.8 4.9 10.933 6.7 7.7 4.5 5.7 1.1 4.2 6 25 13 16

Coefficient of thermal expansion, a 106 (8C1 )

2.715

3.3

8 103

2.5 0.036

1.25

2.646 1.224 1.420 1.561 1.58 1.652

3.1285 2.999 2.084

1.171 0.9094 1.984

4:4 103 1:3 103 0.01

5 103 60 15 150 0.38 6 103 est 1:2 103 1:2 102

4.12 3.04 1.845 1.347 1.197

Volume specific heat, C (J cm3 8C1 )

50 0.37 1:34 103 4:83 104 5 105 est

Absorption coefficient, at 10.6 mm (cm1 )

0.3

9.7 11.7 0.54 25 25 6.21, 10.7 26 13 7 37 151 120 59

11.3 10 6.5 6.5 4.8 3.1 0.96 1.13 1.15

Thermal conductivity, 102 1 (W cm1 8C ) 34 41 15 12 12 7.5 5.7 2.5 6.6 18 36.4 229 1.0 5.2 6.8 56 1.6 2.1 1.0 0.64 11 0.74 0.45 3.5 2.5 1.2

Tcrit (8C)

1.44

0.003 0.12

2.0 8:2 104 0.0045 0.0038 0.04 3.5 8.5 0.53

0.066

13.0 19 6.6

0.0045 1.13 149 359 4.5 102

cw FoM, fcw (W cm2 )

180

0.47 20

3:48 103 1:04 103 75

0.26 1.36 0.79

17.8

1:52 103 1:76 103 1:31 103

1.85 345 27:5 103 47:1 103 546 103

Pulsed FoM, fpulse (W cm2 )

The values of Tcrit , fcw , and fpulse correspond to halving the target intensity for the case defined by Sparks (1971). Not all these materials are good candidates for operation at 10.6 mm.

Refractive index, n

Material

5

Table 4.6. Values of the optical and physical parameters for a range of laser windows materials and the critical temperature and figures of merit for cw and pulsed operation (Sparks 1971).

80 Damage theory

Thermal mechanisms

81

on such system parameters as wavelength, spot and substrate diameters, cooling conditions and on considerations of the optical performance. There are several analyses of these factors (Bennett 1976) and they emphasize that in many respects systems are usually over-tightly specified in terms of surface figure and that although multi-mode effects can take place, the far-field pattern is not necessarily disastrously affected. Analyses of the temperature gradients etc. due to single laser pulses, pulse trains and cw beams have been presented in the previous section. The close relationship between lasing action failure, distortion and cracking may be illustrated by the following experiment. The distortion of different components under irradiation was studied using a Mach–Zehnder interferometer consisting of an He–Ne laser source and four flat mirrors, one of these being the component under test. The output of the interferometer was in the form of fringes, which could either be photographed or the movement of which could be displayed on an oscilloscope or chart recorder. A 500 W cw CO2 laser was used as the component probe, reproducing the internal peak power density conditions in a 100 W laser cavity. Traces of the fringes recorded during the distortion measurements performed first on an 85% R/AR (side one reflecting, side two anti-reflecting) germanium window and then on a copper fully reflecting mirror are shown in figures 4.11(a) and (b). Figure 4.11(a) shows the fringe movement which occurred when a flat 85% R/AR germanium output coupler was irradiated at a peak power density of 0.84 W mm2 (the typical internal conditions prevailing in a compact laser cavity). The fringe pattern indicated that the flat window started to act as a lens, diverting the beam power into a wider spot and out of the detector. After 7.8 s the window cracked catastrophically. Figure 4.11(b) shows the fringe movement when a fully reflecting copper mirror was irradiated at the same cw power density. In this case the mirror did not crack but did distort badly, defocusing the He–Ne laser beam off the detector. In a practical case the distortion would be more likely to lead to cavity detuning and loss of output power. This usually, but not always, prevents catastrophic damage to the component. Most laser systems have low divergences (of the order of 1 mrad). This divergence is a function of the resonator construction, the average number of double transits that a photon makes through the laser resonator and the optical shape of the lasing medium. In the case of a solid-state crystal laser, such as Nd:YAG or ruby, the thermally distorted rod may be treated as a lens which diverges the output beam from parallel. An approximate expression can be reconstructed relating the appropriate constants to the output beam divergence, b : b ¼ 2M

Aðn 1Þ r

ð4:18Þ

82

Damage theory

Figure 4.11. (a) Cw laser damage in a germanium window, and (b) cw distortion trace for a copper mirror.

where M is the average number of double transits per photon given by M¼

Sð1 þ RÞ 2ð1 1RSÞ

ð4:19Þ

where S is the resonator loss, R is the output mirror reflectance (this treatment assumes that the fully reflecting mirror is 100% reflecting), A is the

Thermal mechanisms

83

laser beam output aperture (for circular configurations), n is the lasing medium refractive index, and R is the radius of curvature of the thermally distorted laser rod. The equation relating this output beam divergence to the focused spot size when it is passed through a lens, of focal length f , is d ¼ f b :

ð4:20Þ

It must be pointed out that the relevant radius of curvature of the laser rod is that at the time of lasing. This explains why the beam divergence for constant pulse input changes with pulse repetition frequency. A timeresolved interferometric measurement was made in the early 1970s which provided a good correlation between the optical shape of pumped ruby laser rods and the resonator output beam divergence. This series of measurements showed that a typical parallel-ended ruby laser rod was transformed into a convex lens and that the beam divergence correlated with the interferometric fringe count. It must be emphasized that distortion can be magnified if the component mounting conditions are such that the thermal expansion of the component leads to additional stress. A good example of this came in the UK in the mid1990s in the following way. A high-power laser user found that the output characteristics of their laser processing systems were gradually degrading. After investigating the cause they decided that the final output optic was slightly damaged and was scattering the laser beam rather than focusing it on the workpiece. The laser system suppliers quoted a very high price for the supply of replacement windows. Since the users knew the specification of the window and also had a good relationship with one of the numerous laser optical component suppliers, they ordered replacement windows at a considerably reduced price. The components were supplied and fitted and under reduced input powers worked well. However, when the laser input power was increased the beam first gave an inferior output and finally the window cracked. After a period of recrimination and investigation the component supplier finally supplied a replacement window fabricated to the minimum diameter dimensions rather than to something approaching the maximum. Once these components were fitted there was no trouble and the lasers worked to their original specifications. The investigations had shown that the thermal expansion of the output windows had put them at extra pressure in the cooled window housings with a consequent expansion, distortion, loss of beam output power, increased beam divergence and finally catastrophic shattering. A fairly recent series of measurements was made (Greening 1997) in order to see how the strain induced in a ZnSe window affected the LIDT of the material. This was done as a result of several replacement ZnSe windows failing in a CO2 laser. Straightforward laser damage tests indicated that the damage threshold was constant for the material at a value of

84

Damage theory

3000 W mm1 . However, when the windows were inserted in the laser system they damaged at about 133 W mm1 . Renewed laser testing in a mount, which could be adjusted to give a measurable stress, resulted in a range of intermediate damage threshold values. The LIDT measured with a clamping force of 4 N m torque (giving a clamping force of 1 tonne) was 800 W mm1 . This investigation concluded by calculating the theoretical LIDT of the ZnSe material based on the bulk material properties of the material. The theoretical value for catastrophic shattering was calculated to be 53 kW mm1 . The investigators concluded that the polishing process was the cause of a significant amount of strain induced into the component and that if this could be eliminated and the optical component mounted in such a way as not to induce extra strain the window could be used at a significantly higher power than was possible at that time.

4.3

Dielectric processes

Laser-induced damage to transparent, non-absorbing material occurs at electromagnetic field strengths which induce dielectric breakdown of the material. Bulk insulators have d.c. breakdown strengths of about 1 MV cm1 and a.c. breakdown strengths up to 5 MV cm1 (Maisel and Glang 1970, Fradin et al 1973a–c). Electromagnetic strengths of these magnitudes can be induced by high-power-density radiation at optical power densities of the order of 50 to 1000 MW mm2 . The relationship between the a.c. dielectric breakdown strength and the laser-induced damage threshold, LIDT, is given by PD ¼

Ep VB2 VB2 n Ep ¼ ¼ ¼ Z0 Z1 A b2

ð4:21Þ

where PD is the peak power density, Ep is the energy in the laser pulse, is the equivalent pulsewidth, A is an area parameter, and b is the 1=e2 intensity diameter. The equivalent pulsewidth is the full width of a temporally square pulse, the full width at half maximum (FWHM) of a perfectly triangular pulse or some approximation of the two in the case of most practical pulses. The area parameter, A, which links the peak energy density and the total energy in the laser beam, needs to be measured in most practical cases. In the case of a perfectly focused Gaussian beam it becomes b2 , where b is the 1=e2 intensity diameter. The equation for the spatial profile of a perfect Gaussian beam is

x2 I ¼ I0 exp 2 : b

ð4:22Þ


85

Bettis et al (1979) investigated the relationship between the electric field strength for breakdown and the optically induced field for laser-induced damage and came up with significant correlation in the 10–100 ns pulsewidth region. A polarizable species interacts with an oscillating electromagnetic field through its dipole moment and involves an expression in terms of ðn2 1Þ=N (where n is the material refractive index and N is the number density of dipoles). The variation of the dipole moment with the applied electric field, E, is n2 1 : ð4:23Þ N The volume polarizability due to the application of a local electromagnetic field is given by P ¼ Nð!Þ"0 El ð4:24Þ p/E

where "0 is the free-space permittivity and El is the effective local electric field. The local electric field at an atom embedded in an isotropic medium subjected to an external electric field, E, is El ¼ E þ

P n2 þ 2 : ¼E 3"0 3

ð4:25Þ

Combining equations (4.24) and (4.25) results in the Lorentz–Lorentz expression 3ðn2 1Þ ¼ Nð!Þ n2 þ 2

ð4:26Þ

and the induced dipole moment, p, is given by P ð4:27Þ p ¼ qe x ¼ N where qe x is the electronic charge and x is the displacement of the optical electron from its equilibrium position. These equations can be rewritten as E x ¼ ðn2 1Þ3"0 2 l Nqe ð4:28Þ n þ2 which is the relationship between the displacement of the optical electron and the local electric field. The expression may then be rewritten in terms of the applied electric field: Nq x E ¼ 2 e "0 : ð4:29Þ n 1 The critical free-electron number density which has to be created by the optical pulse before solid dielectric breakdown can occur is Ncrit 1018 electrons cm3 :

ð4:30Þ

86

Damage theory

From energy conservation considerations the laser power density (W cm2 ) necessary to create this Ncrit number of free electrons is some fraction of the energy necessary to ionize every atom in the focal volume and thus 18 1=2 N qe 10 Eth ¼ 2 xth ð4:31Þ N n 1 "0 ! ð1:81 1018 Þxth

N 1=2 n2 1

ð4:32Þ

if we assume that the optical electron is free for a displacement that is half the average spacing of the atoms, s , in the solid material. This results in the observation that a close-packed material should be easier to damage than a less dense material. Assuming that s ¼ N 1=3 , 9:05 103 Eth ¼ pffiffiffiffiffi 2 s ðn 1Þ

MV cm1 :

ð4:33Þ

This work (Bettis et al 1979) and the earlier publication (House et al 1975) compared the calculated threshold electric fields with experimentally generated electric breakdown data, corrected for the surface roughness contribution to the field. The work also calculated the corresponding optical power density using the formula Eth ðV cm1 Þ ¼

38:8 1=2 S nþ1

ðS in W cm2 Þ:

ð4:34Þ

These results are summarized in figure 4.12 and are further discussed in chapter 5. It should also be recognized that the dielectric breakdown threshold is inversely proportional to the wavelength. A table showing dielectric breakdown thresholds and the corresponding LIDTs for a variety of materials, as a function of wavelength, is given in appendix 1. Inspection of equation (4.34) shows that the electric field breakdown thresholds scale proportionately to the atomic density/(n2 1). For example, the ratios of these values for KCl and NaCl are 0.288 : 0:362 0:8 :1. It will be found from inspection of the tabulated values in appendix 1 that this theoretical ratio is the same as that obtained from experimental measurement. The same dependence has been observed for other crystals and thin-film materials at other wavelengths (e.g. by Bettis et al (1975) at 1.06 mm and by Newman and Gill (1978) at 266 nm). 4.3.1

Electron avalanche breakdown theories

In the presence of an electric field, V, and electron–phonon collisions, an electron drifts in the direction of the field gaining energy, V 2 , as it goes


87

Figure 4.12. Electric field versus surface roughness; fused silica.

such that d" e2 k V 2 ¼ dt " mð1 þ !2 k2 Þ

ð4:35Þ

where " is the electron energy, ! is the frequency of the electric field, m is the number of laser pulses, and k is the electron relaxation frequency for largeangle scattering. When the electron gains sufficient energy it can excite another conduction electron across the electronic energy gap from the valence band. Repetition of this multiplication process increases the number of electrons until breakdown occurs, when the energy density reaches 1018 cm3 , from an initial value of 108 cm3 for semiconductors and 104 cm3 for insulators.

88

Damage theory

In the case of d.c. voltage breakdown, electron–phonon collisions prevent the electron from accelerating very rapidly to high energies by changing its direction of travel, on average, every k seconds. If the electron were to go without suffering a collision for a time its energy would be increased more effectively—this is termed a lucky event! Small-angle collisions are less effective in inhibiting such a rapid build-up of energy. In the case of an insulator (e.g. NaCl) there is a negligibly small probability of finding an electron in the focal volume, indicating that there is not a sufficient electron density to initiate the avalanche. A new theory was developed by Sparks (1975) which included mechanisms to generate starting electrons and for commencing and sustaining an avalanche. The major new mechanisms at laser frequencies are the photon–electron–phonon process and the interconduction band transition. The theory assumes that the electron density at time zero is zero and that the criterion for damage is that the temperature is raised to the melting point. In the case where an electron interacts with both a phonon and a photon, the electron can absorb the large energy, h!, of the photon, and the large wavevector of the phonon allows wavevectors to be conserved, so that at 10.6 mm the starting electrons are excited from F-centres by multiphoton absorption or tunnel emission. At 1.06 mm the starting electrons are generated by two-photon absorption by the F-centres. At 0.69 mm the starting electrons are generated by five-photon absorption across the gap and at 0.177 mm (Xe) the starting electrons are generated by two-photon absorption across the gap. This explains the wavelength dependence of the multiphoton breakdown process. The theory gives reasonable agreement with the experimentally measured values which are shown in appendix 1. The temporal variation of the LIDT will be outlined in the following sections. At very short pulse lengths the radiation is supplied so quickly that the electrons interact before they have a chance to move out of the focal volume. In this region the process is power dependent, irrespective of the focal volume. As the laser pulse length lengthens, the electronic relaxation time comes into prominence and the power density at which avalanche breakdown occurs drops with increasing focused spot size as there is a tendency for the electrons to move out of the centre of the beam before avalanche breakdown is achieved. 4.3.2

LIDT versus pulse length and beam diameter

There are four different regimes in which dielectric breakdown may occur. 1. At ultra-short pulse durations ( < 1013 s) multiphoton avalanche processes can occur: LIDT / ED b2 1 ¼ W:

ð4:36Þ


89

2. For extremely short pulse durations (t1 < < 1011 s) the ionization rate limits the build-up of the avalanche process: LIDT / ED / expð=t1 Þ b1 :

ð4:37Þ

3. For normal short pulse durations (5t1 < < 5te ), i.e. pulse lengths between about 1011 and 108 s, the ionization rate is proportional to

Figure 4.13. Variation of LIDT with pulse length and spot size. Fused silica, 1.064 mm.

90

Damage theory VB2 and the build-up of electrons is given by N ¼ N0 expðVB2 Þ expðte Þ:

ð4:38Þ

The LIDT, expressed in terms of peak power density, is proportional to 1=2 b1 . However, a more useful unit to use for comparison with measurements made at other spot sizes is that of W cm1 and the relationship is then proportional to 1=2 . 4. For the long-pulse situation, te , electron avalanche cannot occur, the thermal case gradually takes over, and the LIDT becomes proportional to W b1 . Figures 4.13, 4.14 and 4.15 show the variation of the LIDT with pulse length and spot size for high-quality fused silica (Wood 1997, Hopper 1970). These three graphs all contain the same data but are plotted using different abscissas. Inspection of the three graphs indicates the pulse length regions where the damage threshold can be expected to be constant, if quoted in the correct units. Although these graphs are theoretical values they do correlate very well with a range of results, gained using 1.064 mm Nd:YAG laser radiation from a number of different sources (mainly published in the Boulder Damage Symposium proceedings). It is worth remarking that the only area where the lines are not parallel with changing spot size is below ¼ 1010 s. Although it was predicted as early as 1970 that multiphoton ionization would occur in this pulse length region (Bliss 1969), observation of this was not seen until 1994 (Du et al 1994, Stuart

Figure 4.14. LIDT (W cm1 ) versus pulse length and spot size. Fused silica at 1.064 mm.

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91

Figure 4.15. LIDT (W) versus pulse length and spot size. Fused silica at 1.064 mm.

et al 1994). It was perhaps coincidental that these two papers were presented consecutively at that year’s Boulder Damage Symposium and that there was some doubt because of the apparent discrepancy between the two sets of data. The problem was that the first group were, at that time, limited in their energy output, and could consequently only produce the effect with a small spot size, and the second group were only interested in larger spot sizes.

4.4

Testing regimes

There are three testing regimes, which will be fully covered in chapter 8. They are: 1-on-1 testing: Testing using one site with a single laser pulse at a single laser fluence before moving to another site for testing at a different fluence. S-on-1 testing: Testing each site with several laser pulses at the same laser fluence before moving on to another site for testing at a different fluence. This regime also brings in the subject of ‘conditioning’ the surface. ‘Conditioning’ involves irradiating the surface at about 90% of the surface damage level for up to about 50 shots. This process tends to micro-ablate dust particles and coating defects and to diffuse imperfections and defects out of the beam area without causing visible damage. In many, but not all, cases this process raises the LIDT of the surface.

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Damage theory

Figure 4.16. Dependence of LIDT on spot size and prf.

R-on-1 testing: Testing each site at the same laser fluence with a pulse train with a specific pulse repetition frequency (prf). This measurement procedure takes a long time but is representative of the conditions inside a practical laser system. This test is extremely useful in detecting the presence of absorption in coatings. If measurements are made using single shots (i.e. at lower than 1 Hz) and at some faster rate (e.g. 10 Hz) then if there is absorption in the sample the damage measurements made at the higher prf will yield lower values for the LIDT. This methodology can best be appreciated by reference to figure 4.16. The figure illustrates the two cases where the test spot diameter are a factor of 10 different and two series of tests are made on each, one single-shot test and the other series at 10 Hz. It will be noticed that the minimum LIDT for both spot sizes is the same but that the probability of damage, being a function of the defect density, is greater for the large spot size beam and the corresponding LIDTs are less. If the sample has minimal absorption the LIDT curves would be virtually identical for both test repetition rates. If, however, the sample, or coating, contains appreciable absorption the threshold LIDTs will decrease and the slopes of the curves will increase. Each of these testing regimes, although fundamentally in agreement with each other, has its own methodology. It is frequently possible to gain

Testing regimes

93

different knowledge of the components under test from each of the different testing regimes. When a laser beam is passed through even a partially absorbing material the temperature of the material at the centre of the beam will rise slightly (see figures 4.2(a) and (b)). If a second pulse is incident before the heat of the first is conducted out of the beam spot area, the maximum temperature at the end of that pulse will be higher than the maximum temperature at the end of the first pulse (see figure. 4.2(c)). If a high-prf train of pulses, or a cw beam, is passed through the material the temperature of the material on-axis will rise to a maximum (heat being conducted out of the centre of the beam continually) (see figures 4.2(d) and (e)). If the damage mechanism is thermal, i.e. either melting or stress, then the threshold for laser-induced damage will fall as the temperature rises. This has been measured for a number of window materials at 10.6 mm using CO2 lasers (Wood et al 1983, Wood 1986). Figure 4.17 shows the variation of the LIDT with increasing laser pulse repetition frequency for a range of commonly used infrared transmitting window materials. In all cases the LIDTs have been normalized to the single-shot value. For highly transparent materials (large band gap), e.g. NaCl and KCl, there is no drop in the LIDT with increasing prf. Materials with lower band gaps (i.e. that have an appreciable absorption) exhibit a marked decrease in the LIDT with increasing prf. The precise

Figure 4.17. Normalized LIDT values as a function of prf for a selection of substrate materials. 10.6 mm, CO2 laser, 50 ns.

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Damage theory

form of the curves displayed depends on the thermal diffusivity and the area under irradiation. Single-crystal silicon does not have a marked drop and this is assumed to be because of its high absorption coefficient. The smoother drop in the LIDT versus prf curves for germanium and GaAs is assumed to be because these samples were better single crystals than any of the other materials and had a more homogeneous conductivity.

4.5

Time of damage

Monitoring the real-time transmitted or reflected pulse shapes when laserinduced damage is initiated allows significant deductions as to the damage mechanisms involved to be made (Wood et al 1985, Plass and Giesen 1995). Monitoring the changes of these parameters with time, during the duration of the laser pulse, has also been used to monitor the mechanisms themselves (Plass et al 1994). This paper covered an investigation into the change of reflectance of CO2 window and mirror optics as a function of temperature well below the temperatures necessary for laser-induced damage to occur. The use of time of damage measurements may be discussed by reference to figures 4.18(a)–(f). The analysis (Wood et al 1985) was made assuming that the laser temporal pulse shape consisted of a main peak plus a low-level tail. Six traces are shown in this figure. The first trace, (a), represents the reference or incident pulse, PI . The remaining five traces are examples of the possible results of the transmission, PT , through the material. Trace (b) indicates the case where no damage occurs. The transmission follows the incident pulse in every respect except that it is attenuated by the transmission factor (PI =PT ). Trace (c) shows damage at the maximum intensity of the pulse, at time tp . This result could be produced in a material like NaCl, which damages by dielectric breakdown. In this case the incident pulse was at just the correct power level for the material to damage at the peak of the pulse (PC , the LIDT of the material). Trace (d) could be produced for the same sample if the peak incident power was increased over that used to produce trace (c). In this case the same power level, PC ¼ PD , will be reached sooner, at td < tp , where the dielectric breakdown occurs. In the case of a non-absorbing insulating material, dielectric breakdown occurs when the electric field component of the electromagnetic field exceeds the dielectric strength of the material. Such a material would never exhibit real-time damage at a time after the peak of the power pulse. Traces (e) and (f) indicate cases where the real-time damage occurs after the peak of the power pulse. In these cases there must be an energy dependence in the damage mechanism associated with the material. Consider the case of a hypothetical material which has negligible thermal diffusivity, and for which the damage mechanism is dominated by surface melting. If,

Time of damage

95

Figure 4.18. (a)–(f) Schematics of time-resolved damage measurements made by monitoring the transmitted beams.

as in trace (e), a laser pulse of peak power density Pe passes through the sample the surface will heat up during the course of the pulse. Consider that the melting point is reached at time te after the start of the pulse. The amount of energy needed to raise the surface to the melting temperature,

96

Damage theory

Em , may be found by a simple integration of the area under the pulse envelope of P versus t. Since there is zero diffusivity the time of damage is right out in the tail of the pulse. It is theoretically possible, for materials with zero diffusivity, for the time of damage to be right at the end of the pulse. In all real materials some energy is conducted out of the peak and results as shown in trace (f) are far more likely to occur. However in both these cases the two measured energies would be equal, E1 ¼ E2 ¼ Em , since the amount of heat required to raise the surface temperature to the melting point remains constant. The time of damage has been measured for a range of different samples using time-resolved reflection and transmission measurements (Wood et al 1985). The minimum power necessary to cause a difference in the ratio of either the incident and reflected rays (or the transmitted rays) would be termed the LIDT of the material. Figures 4.19(a)–(d) show the results from a series of measurements made on typical 10.6 mm laser mirror and window materials using a CO2 TEA laser with a 50 ns pulse and 1 ms tail. Typically two-thirds of the pulse energy was in the tail. Trace (a) shows

Figure 4.19. (a)–(d) Time of damage measurements made using a TEA CO2 laser.

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97

the time-resolved reflected power from a copper mirror. This trace was gained by applying the minimum energy under which a change in the pulse envelope could be detected. The time of damage can be seen in the tail. Trace (b) shows the difference between the incident and the reflected powers at some energy above the LIDT. In this case the time of damage is near the end of the main spike, eliminating the tail by plasma absorption. Trace (c) shows this measurement under faster detection conditions. The top trace is the normalized incident pulse shape while the lower trace is the reflected pulse shape. Detailed inspection of this trace shows that there was a small initial change of reflectance followed by a sharper drop. This trace indicates that there some of the laser energy was scattered out of the beam at the damage threshold followed by a greater absorption of energy due to plasma absorption. Trace (d) shows the case for germanium output window material. It was found that, although the damage mechanism in Ge is thermal, it was impossible to move the time of damage later than the peak of the TEA laser spike. This is in contrast to the measurements made on OFHC copper where the time of damage could be found consistently in the tail of the pulse. Similar time of damage measurements have been reported (Plass and Giesen 1995).

4.6 4.6.1

Damage morphology Definition of damage

Before going on to look at the detailed morphology of damage to specific materials it is necessary to consider what defines a damaged material and how the incidence of damage is observed in practical measurements. One of the purposes of conducting investigations into the LIDTs of optical and laser component materials is to distinguish between the sites of low- and high-level LIDTs. In order to get the maximum information out of any tests undertaken they should be non-destructive and should be capable of yielding data for chemical analysis. In situ monitoring to gain as much simultaneous information as possible should be considered as there are sometimes different effects competing, especially in multi-shot testing. The most usual definition of the threshold of laser-induced damage is that level of radiation which causes some alteration of the surface (or bulk) of the component under examination. In most cases this results in the identification of microscopic damage pits/areas. Loss of transmission and scattering occurs when the damage point is large enough. Figure 4.20 shows the spatial transmission profile of a laser pulse (a) when no damage occurs and (b) illustrating absorption of the laser energy due to the formation of a plasma. In some cases visible emission happens simultaneously with pit formation but at other times visible emission occurs once or twice and then

98

Damage theory

Figure 4.20. Spatial profile of transmitted laser pulse. (a) No damage, (b) illustrating absorption of energy due to the formation of a plasma.

stops. In this case viewing the surface with a high-power telescope may lead to the conclusion that the laser pulse has burnt something off the surface or laser annealed the surface so that it can then handle beams with higher power density without damaging. Material, impurities, water vapour etc. can be blown off the surface leaving the surface cleaner or smoother than before. Most laser-induced damage measurement set-ups include either a telescope focused on the sample surface for direct visual monitoring or, even better, a telescope and video camera plus monitor. The latter option is the most flexible as it can be run back frame by frame and the temporal profile of the damage examined carefully. When a component is irradiated with infrared radiation, visible emission may be observed even at irradiation levels well below the visible damage threshold level (Nichols et al 1983). Under large-spot irradiation the total emission signal exhibited a strong time dependence. Spatial imaging of the damage site indicated the visible emission to be from distinct point sources. Spatial correlation was found between the microscopic surface defect sites which were visible before damage occurred, the emission points under low-power irradiation and the damage points due to high-power irradiation. Charge emission and photoconductivity experiments have been used to investigate possible precursors to laser-induced damage. Charge emission has been observed at fluences well below the 1-on-1 damage threshold of metal mirrors (Becker et al 1983). However, the charge emission observed from silicon and from Ta2 O5 films on fused silica occurred simultaneously with the laser-induced damage. Understanding the photo-emission yields and the electron energy distributions gives insight into the fundamentals of the laser–solid interactions because the coupling of the electromagnetic radiation to the individual electrons leads to physical property changes (Siekhaus et al 1983). During these studies it was found that definite discontinuities could be observed as

Damage morphology

99

the laser intensity was increased. At low laser intensities, below those observed to cause significant lattice heating, the electron yields are consistent with multi-quantum processes. Discontinuities in the electron yield occurred at higher laser intensities. These were identified as being due to phase transitions. At even higher laser intensities discontinuities in the electron yield were correlated with visible surface damage. Photo-thermal deflection microscopy is an optical diagnostic method which has been developed to obtain spatially resolved absorption data on dielectric coatings. In most experimental systems (Mundy et al 1982, Abate et al 1983) an argon-ion laser has been used as a pump source and an He– Ne laser as the probe. The use of two different wavelength lasers allows high-spatial-resolution, low-level absorption measurements to be made and the data to be plotted in the form of two-dimensional absorption contour maps. The technique, which is now widely used (Edwards et al 1969, Marrs and Porteus 1985, Hummel and Guenther 1995) monitors the realtime temperature changes across a surface when that surface is irradiated. The technique has usually been used to investigate the quality of the dielectric coatings. In this application the technique monitors changes of temperature which result when heat is absorbed at, say, an impurity inclusion. The technique has been shown to be able to identify microscopic areas where the heat is absorbed. Many times, but not always, it has been able to correlate the heat areas identified with specific inclusions and subsequently to low damage threshold points. There are times, however, when positive correlation has not occurred. It is considered that this principally occurs when the heat spots are at dislocation boundaries, and not at specific inclusions. Dislocation boundaries have been observed to move under high-power irradiation. 4.6.2

Damage morphology

By definition, the front surface of a component has the full force of the incident beam on it, so the beam then traverses the bulk of the material and finally exits from the rear surface. The front surface might therefore be expected to be most vulnerable and the rear least vulnerable. In practice the vulnerability depends both on any focusing of the laser beam and on whether the damage mechanism is thermal or dielectric. The front surface value is the most variable as the LIDT is strongly affected by the condition of the surface. This aspect deserves a complete chapter by itself (chapter 5). Thermal damage to the front face of a component may either be in the form of a molten crater, line cracks or catastrophic shattering. If the material melts before it cracks (short-pulse damage to an absorbing material) then it may protect the main bulk of the component due to plasma formation. Thermal damage inside a component is usually catastrophic, unless the damage is initiated by small absorbing inclusions (e.g. Pt speck in laser glass, misoriented crystallites in KDP etc.). Thermal damage is rarely

100

Damage theory

initiated at the rear surface of absorbing material. However, when damage is initiated on the rear surface of a component it is usually far more evident than when it is initiated on the front face. This is because the damage is initiated =2 inside the sample and a hole is usually blasted out of the material. The morphology of dielectric damage to the front surface is usually minimal as any ejected material vaporizes in the form of a plasma and this absorbs the incoming radiation. Damage in the bulk is usually catastrophic and is often in the form of self-focusing trails. Damage to the rear surfaces of materials and components with uncoated surfaces is lower than for the front surfaces because of constructive interference between the incident and reflected beams. The peak power is enhanced (and the LIDT lowered) by the factor F¼

exit surface electric field 4n2 ¼ : entrance surface electric field ðn þ 1Þ2

ð4:39Þ

As the electric field enhancement maximum is =2 forward of the rear surface the plasma formed when the material is ablated is inside the material. In consequence of this, rear surface damage is usually more catastrophic than front surface damage. Another effect, which is much more obvious in 10.6 mm damage testing than in 1.064 mm testing, is that interference phenomena can occur between the front and back faces of thin, parallel window substrates causing the front surface damage pattern to consist of a series of parallel lines whose spacing is a function of the wavelength and the thickness of the substrate. If the damage threshold is dominated by the bulk absorption the damage characteristic curve (peak test fluence versus the probability of damage) is near vertical (see figure 4.21). In most cases, however, the characteristic curve is angled as the damage threshold is usually dominated by the presence of imperfections (digs, scratches etc.). The curves are slightly different with changing spot size. This is because there is a probability that the laser test spot will overlap a defect. The slopes of the characteristic damage curves can, in theory, give information on both the size and density of the coating, or other, defects. Figures 4.22 to 4.26 contain micrographs of laser-induced damage in and on a variety of laser window materials. Figures 4.22(a)–(d) show melted surface damage, at 10.6 mm on (a) Si single crystal at 10.6 mm, (b) Ge single crystal, (c) GaAs polycrystalline and (d) ZnSe CVD polycrystalline. It is possible to differentiate between the appearance of the laser-induced damage to the high-absorption Si and the lower-absorption Ge single-crystal materials. It is also possible to differentiate between the appearance of the damage to nearly-single-crystal GaAs and polycrystalline CVD-grown ZnSe.

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101

Figure 4.21. Probability of damage.

Figures 4.23(a)–(c) show the appearance of melt damage to (a) a Be-Cu mirror, (b) an OFHC Cu mirror and (c) a highly magnified damaged Cu mirror. The purer the copper the more uniform the melt. Figures 4.24 show the appearance of laser-induced damage at 10.6 mm to (a) KCl single crystal and (b) NaCl single crystal. The damage to each surface

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Damage theory

(a)

(b)

(c)

(d)

Figure 4.22. Photographs of thermally initiated damage. (a) Single-crystal Si at 10.6 mm, (b) single-crystal Ge at 10.6 mm, (c) multi-crystalline GaAs at 10.6 mm, (d) polycrystalline CVD-grown ZnSe at 10.6 mm.

is remarkably similar, mainly cracking along the crystal planes. At high level flux the damage is catastrophic. This action is also apparent, to a lesser degree in both CVD ZnSe (c) and (d) and on the surface of GaAs (e). Figures 4.25 and 4.26 show the appearance of 10.6 mm laser-induced damage under cumulative and prf laser operation. Figure 4.25 shows strain-induced cracking occurring to a ZnSe lens under cw operation. Melting has obviously occurred after the cracking was initiated. Figure 4.26 shows the damage (a) to the front surface and (b) to the rear surface of an irradiated GaAs substrate. The time-resolved photography indicated that the cracking occurred before the melting. Investigation of this phenomenon indicated that the damage was initiated by the movement of impurities in the GaAs crystal away from the centre of the laser beam followed by pinning of these materials at defects/grain boundaries. This process lowered the thermal

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103

(a)

(b)

(c)

Figure 4.23. Metal mirror damage, 10.6 mm, (a) Be–Cu mirror, (b) OFHC copper mirror, (c) high-magnification photograph of damaged Cu surface.

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Damage theory

(a)

(b)

(c)

(d)

(e)

Figure 4.24. Pulsed laser damage at 10.6 mm on transparent materials. (a) KCl single crystal, (b) NaCl single crystal, (c) CVD ZnSe, (d) ZnSe, high magnification, (e) GaAs single crystal.

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105

Figure 4.25. Ge lens damaged under constant cw operation, 10.6 mm.

conductivity of the material and first caused stress cracking at the periphery and then melting at the centre. The change of conductivity and sudden lowering of the LIDT has also been observed in CVD-grown diamond. Figure 4.27(a) shows cleavage damage to calcite crystal when irradiated at 1.064 mm. The primary damage was shown to be dielectric breakdown (the very small spot at the centre of the photograph). The shock wave then initiated a shear force that resulted in cleavage of the crystal. Figure 4.27(b) shows the result of 1.064 mm damage to the bulk of a single crystal of KDP. The cracks are along the crystal axis and the damage is usually associated with a burst of 0.53 mm SHG. Figure 4.27(c) shows the catastrophic nature of rear surface damage. This prism was the turning medium in a 1.064 mm driven SHG/dye laser and the standing wave set up between the entrance and exit surfaces resulted in bulk damage inside the rear face of the prism. Damage to the bulk lattice may or may not damage again at the same irradiation level. Figure 4.27(d) shows the result of damage testing a block

106

Damage theory

(a)

(b)

Figure 4.26. (a) GaAs substrate, front surface damaged under multiple pulses from a hybrid TEA, long-pulse laser, 10.6 mm, (b) GaAs substrate, rear surface damaged under multiple pulses from a hybrid TEA, long-pulse laser, 10.6 mm.

of PMMA. The first shot caused microscopic carbonization (as shown in the centre of the photograph). Subsequent shots were much more catastrophic as the carbon particles formed absorbed heavily and resulted in even more carbonization. Figure 4.28 shows the result of raster scan damage testing of an Nd:glass block. The direction of the laser beam was from left to right. The block was

Damage morphology

(a)

107

(b)

(c)

(d)

Figure 4.27. Bulk damage. (a) Calcite crystal, 1.064 mm, (b) KDP crystal, 1.064 mm, (c) rear surface damage; fused silica turning prism, 0.53 mm, (d) bulk carbonization inside a PMMA block, 1.064 mm.

tested (multiple irradiation, moving the beam slowly across the block) for the presence of Pt specks, originating from the melt crucible, with an unfocused beam at an irradiance which caused damage if there was a Pt speck in the beam path but not otherwise. The damage observed to the right (the rear surface of the block) was mainly initiated at or near the rear surface of the

Figure 4.28. Laser-induced damage testing of Nd:glass. Damage inside Nd:glass block, testing for Pt speck, 1.064 mm.

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Figure 4.29. Damage testing for Pt speck in Nd:glass.

block. Subsequent shots added to this damage (at an angle across the block as the laser was rastered across). Some of the damage was however initiated well inside the glass block. This is best illustrated by looking at the traces to the left of the block. The experiment showed that the Pt speck damaged at the lowest threshold. The subsequent damage void in the middle of the block damaged at a slightly higher flux and the main bulk damaged at some considerably higher level. The results from this testing are illustrated in figure 4.29. This figure attempts to correlate the size of the damage ‘void’ inside the block with the irradiation level causing it. This had to be done ‘after the event’ (rather than identifying the position of an individual Pt speck) as the originating speck was roughly 10 times less in diameter than the damage void formed. It was determined that the Pt speck vaporized at energies proportional to the square of the diameter of the speck (Taylor and Wood 1974, Wood et al 1975). The size of the inclusions may vary but

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109

the critical size in the VNIR appears to be in the 0.1–10 mm diameter range. Smaller inclusions rarely absorb enough energy to cause a damaging stress while large inclusions usually inhibit lasing or can store the energy without giving rise to a critical stress.

Chapter 5 Surfaces and sub-surfaces 5.1

Introduction

We assume, until proved otherwise, that the bulk material is homogenous and is not affected by strain (resulting either from the growth/melt process or from thermal heating and/or clamping). The optical performance of such a perfect component would then relate to its ‘form specification’ (shape or angle). However, although we would like the total topography to be perfect, in practice we find that practical surfaces have ‘texture’ (see figure 5.1): Roughness—deviations from the desired form Waviness—deviations from the measured roughness Imperfections—digs, cuts and sleeks The definitions of each of these texture parameters depend on the spatial density and the spatial frequency of the measurement. Most component polishing specifications are written in terms of ‘form specification’ plus ‘cosmetic quality’, i.e. ‘If you can see it, it is not good enough’, irrespective of its effect on the system/application. The material quality is rarely specified except insofar as quality assurance managers rightly suspect strain and bubbles. Very few companies test for strain, and most would not know what to do if they found it. In particular very few companies look at the strain patterns invoked in a material once it is inside a mount and most assume that the mount is a neutral influence on the performance of the optical component. The form specification comes directly from the application, e.g. ‘flat’ or ‘curved to x m radius of curvature’. The waviness specification is usually quoted as a function of the allowable deviation of the surface from the perfect form, e.g. flat to /10 at 0.5 mm. The roughness is usually specified in terms of an r.m.s. roughness across the usable area of the component. Digs, scratches and sleeks are usually specified in terms of allowable number densities of defined dimensions. 110

Introduction

111

Figure 5.1. Surface texture parameters influencing the quality of the optical surface.

Most ordinary optics specifications, quoted in terms of the number of scratches, blemishes etc., are over-stringent and could be reduced by a large factor without affecting the performance of the system in which they are incorporated. Reducing the polishing specification would have a direct effect on the cost of these components. However, as most system designers do not have any idea what the effect of allowing defects into the optical path is, they adopt a sensible safety first attitude and say that any defect/ scatter centre is potentially problematical. Without input from the optical designers they are merely getting rid of a potential problem. This may sound a sensible approach but it can cause problems when the defect/imperfection sizes and numbers do begin to affect the system performance. As we saw in chapter 2 there are a number of system applications where the power level and/or the system sensitivity is so high that the amount of irradiation scattered out of the laser beam path is strictly pertinent to the overall sensitivity or performance of the system. It is therefore sensible that system designers should ask that the system engineers should try to verify the extent that the material quality and the surface finish affects the performance of the system. Material quality—dislocations and voids Machining—polycrystalline layer

112

Surfaces and sub-surfaces Polish—scratches, digs, roughness Absorption—decorated scratches and dislocations Roughness—dielectric enhancement at scratches scatter loss of specular reflectance Conductivity—resistive scratches and dislocations skin depth

5.2

Surfaces

The natural surface finish of most ‘as grown’ materials, with the possible exception of cleaved optical fibres, is not good enough to prevent the surface affecting the performance of the component in an optical system. Most components have to be ‘finished’ by polishing or laser annealing. 5.2.1

Polishing

There are a variety of polishing techniques, all of which are perfectly valid in their own context. It must be realized, however, that the choice of polishing technique is a function of the material to be polished (e.g. hardness, solubility), and the required finish (e.g. polishing specification, system considerations). It is not valid to use a technique irrespective of these considerations. An all-important consideration, in the search for the appropriate surface finish for optical components for use under high power levels, is that the physical dimensions of surface imperfections/scratches must be much less than /10 (where is the wavelength of the irradiation) before the size of the defect ceases to affect the passage of the radiation. This means that the surface polish specification is directly set by the wavelength of the optical source. This has direct implications on the polishing of (for example) CO2 laser components. This is not generally realized and most system designers put visible light tolerances on these components. On the other hand most visible and near-infrared specifications specify the finish in terms of the amount of light scattered out of the beam and fail to realize that one pinpoint of the dimensions of the laser wavelength is precisely the most damaging facet that could be devised. It must also be commented that most specifications are written in terms of scratch width rather than scratch depth or shape. It is obvious when you come to think about the subject that not all scratch shapes are particularly bad but that one with a 458 base angle can never be good. ‘All scratches and defects are bad but some are far worse than others’

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113

A brief summary of the techniques in common use is (i) mechanical polishing with hard materials—diamond paste, aluminium oxide (ii) mechanical polishing with medium hardness materials—jeweller’s rouge (iii) mechanical polishing with soft material—float polishing and superpolishing (iv) mechano-chemical polishing—Syton for Ge and Si: float polishing (v) etching—water for alkali halides, neutral solution for glass (vi) laser annealing or glazing (vii) electron beam or ion-beam etching (viii) diamond turning The following points are merely given as examples in order to generate thoughts in the minds of the readers as to the applicability of the many and varied techniques available in the context of their ‘real’ requirements. If it is considered necessary to investigate the subject further it is worth starting with the SPIE Milestone Series of selected papers in laser-induced damage (Wood 1990) and the many references in the Boulder Damage Symposium Proceedings (e.g. Vora 1981). Some materials are hard, i.e. they can only be polished with another hard material (e.g. diamond or alumina). However, it must be realized that polishing with diamond paste removes material by scratching and that the material loosened from the surface does not always disappear from the scene but can form a polycrystalline layer on the surface of the material. This layer may not itself be easily removable but it may be weak in terms of its laser power/energy handling capability (because of the possibility of lowering the thermal conductivity of the material due to the presence of defects and grain boundaries). The imperfect surface layer may also add scatter or divergence to the transmitted beam. Polishing with hard compounds is therefore usually done by ‘polishing through the grades’. This entails performing a rough polish with a relatively large diameter material (e.g. 10 mm diameter diamond powder). The polishing process is then transferred to a lap with a finer grade of powder (e.g. 3 mm diameter) and so on until the surface is finally finished with a very fine powder (with diameter less than =10 of the wavelength of light to be used). Each lap must be kept completely free from the coarser grades of polishing compound. Stringent precautions must also be taken to clean the surfaces before changing grades so that the coarser grades of polishing material are not just simply transferred to the new polishing pad, thus negating the whole process. Another drawback of ‘scratching’ the surface is that if the polishing material is absorbing at the wavelength of use it may, because it will be incorporated in the sub-surface, give rise to added absorption and act as a centre for catastrophic damage. This has been observed when iron oxide

114

Surfaces and sub-surfaces

(jeweller’s rouge) has been used to polish glass. Diamond paste in combination with Hyprez fluid is commonly used as it does not matter too much if it is left embedded in the substrate. It must, however, be pointed out that ‘soft’ or ‘ductile’ scratches are preferable to brittle fractures, which extend into the surface, act as large-scale defect traps and impair the thermal conductivity of the surface. There are several ways of finishing surfaces that try to remove the final scratches without ruining the surface finish. These are usually termed ‘superpolishing’. In general they work in terms of polishing using a soft material/ polishing pad and although extremely tedious do result in highly perfect surfaces. Scatter values of less than 0.001% have been gained on fused silica (Spectrosil A) substrates using this technique (Wood 1982e). A good review of soft polishing materials and substrate material combinations, which is still relevant today, was published by Vora (1981). Alternative techniques, of use in certain circumstances, are float polishing and chemical etching. Very good results were gained using SiO2 in an acidic solution with tin laps on BK7 glass (Namba and Tsuwa 1980, Namba 1982). Syton (Al2 O3 in dilute acid solution) is commonly used in the semiconductor industry for the polishing of ultra-flat and defect-free silicon surfaces. Syton has also been used to polish germanium. In general the semiconductor industry has tighter specifications than the laser optics community. Laser annealing and laser polishing are good techniques for removing surface imperfections and micro-scratches but do not usually improve the overall flatness of the component. Ruby laser annealing has been used to remelt the surface of single-crystal material (e.g. Ge or Si) to give high LIDT values, while 10.6 mm CO2 treatment of fused silica (Temple et al 1982) and LiNbO3 has been shown to reduce surface features and scatter. It was shown that, when fused silica was laser polished, material modification took place without macroscopic surface removal and that there was less water and fewer hydrocarbons on the surface than previously measured. In the case of LiNbO3 annealing it was shown that the surface scratches and pits were smoothed over and that the magnitude of the scatter at 0.63 mm was decreased. Laser annealing, using cw CO2 radiation, has also been undertaken on the ends of damaged fibre optic cable with success. Laser annealing can be done even on the surface of transmitting materials. Figure 5.2 shows the effect of irradiating a germanium single crystal with 10.6 mm pulsed radiation. It can be seen that the scratches visible on the unannealed crystal have been annealed out by the action of the laser beam. Some success has been achieved by irradiating large Ge blanks with cw 10.6 mm radiation. However, it must be noted that unless the radiation is very uniform, or the scan very fast, unacceptably high levels of strain can be induced with consequent catastrophic shattering. Electron or ion-beam etching and hrf finishing can remove most of the sharp discontinuities which lower the LIDT. In the case of the ion beam

Surfaces

(a)

115

(b)

Figure 5.2. Laser-annealed spots on germanium single crystal.

etching of germanium, the use of a wide beam at a low angle of incidence even allowed removal of material. This experiment was repeated several times on the same surface to see how the depth of removal affected the overall flatness. It was found that the overall flatness was unimpaired even when 10 mm of material had been removed from the surface. The final surface had fewer features than the original Syton-polished surface. An X-ray topograph of the surface half way through the sequence is shown in figure 5.3. This photograph shows a very smooth surface only broken by two deep scratches. These scratches, which originated in the original cutting process, did not disappear until 10 mm of surface had been etched away. The precise degree of improvement in the LIDT which can be gained varies both with the etch depth and with the material (Gibbs and Wood 1976). In ZnSe the damage threshold was decreased on the removal of about 1 mm of material but was subsequently increased when more material was removed. Germanium, gallium arsenide and cadmium telluride all exhibited higher LIDTs with the removal of about 10 mm of material. This was decided to be due to the presence of embedded polishing material and a machinedamaged surface layer (see section 5.3). The diamond turning technique has been developed in order to produce ultra-clean surfaces on a range of materials. Originally it was expected that its use would be confined to ductile materials (mainly metals) which could not be easily polished to the required tolerances. The essence of diamond turning is a diamond tool and an extremely solid, vibration free lathe. In general the substrate is kept still and the tool moved across as fast as possible, skimming a sliver of material each turn. In order to achieve the required finish both the lead screw and the rotation have to be extremely reproducible. The technique has been far more successful than was originally conceived and the range of materials that can be turned is also wider than expected. However, metal mirrors are still the main materials turned. The finish has been shown to

116


(a)

(b)

Figure 5.3. X-ray topograph of ion-beam-etched germanium.

be vitally concerned with the sharpness and angle of the diamond tool. Typical photographs of the surface finish are shown in figure 5.4, where scanning electron micrographs of diamond-turned copper surfaces are shown. The ‘pear-shaped’ marks are typical turning marks and their magnitude is a function of the sharpness and angle of the diamond tool. The best diamond turning results have been achieved using a facility developed at the US Navy’s research facility at China Lake, California, where r.m.s. surface roughnesses as low as 5 A˚ have been measured. The technique has been proved to be useful on single-crystal materials such as germanium and silicon but cannot be used on multi-grain material since the grain boundaries damage catastrophically.

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117

Figure 5.4. Scanning electron micrographs of a diamond-turned copper surface.

5.2.2

Cleaning

It has long been recognized (Porteus et al 1981) that the surfaces of laser windows, mirrors and components need to be scrupulously cleaned and kept free from water, finger grease, organics and dust particles. The less components are handled the less chance there will be that they will become contaminated. If possible, components should be kept in dry clean-air cabinets and only removed from these to be fitted into sealed laser systems. Nevertheless there is bound to be some contamination and a compromise must be reached between handling and cleaning, and thus a potential worsening of the situation, and leaving the contamination with its potential of lowering the LIDT of the component. There is a continuing drive to ascertain the best cleaning procedures for the whole range of optical materials and surfaces used in modern optics (e.g. Whipple 1997, Johnson 2001, Hatcher 2002). The solutions range from washing with isopropyl alcohol or acetone to shampoo or soap and deionized water. Scrubbing with lint-free optical wipes, special swabs and natural sponges or blow drying with high-purity dry gas have all been recommended. Other suggestions have been to apply hydrophilic and oleophilic coatings to stop the surface absorption. The influence of substrate cleaning on the subsequent LIDT of 355 nm high-reflectance coatings showed that it was virtually imperative to clean the substrate rigorously before coating. However, it was also commented that care had to be taken to avoid introducing laser damage initiation points (in the form of fine scratches) into the surface through the use of inappropriate cleaning techniques (Dijon et al 1996). Desorption of water and many organics may be made with a vacuum technique or by washing with a suitable fluid. Although water can be desorbed under even a relatively low vacuum (see for example the results of making absorption measurements in vacuo—section 7.2) it will be absorbed

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again as soon as the sample is opened to humid air or to a reactive gas, for example H2 and O2 , as contained in most gas lasers. Organics can be more permanently cleaned off a surface by washing with a suitable liquid. Many crystal surfaces can be cleaned and dried using common solvents (e.g. isopropyl alcohol) and these surfaces become resistant to the absorption of water vapour for at least 30 min after such treatment. It is very important that, after cleaning with a solvent, the surface should be blown dry using clean, dry gas (e.g. N2 ). This blow-dry prevents evaporation leaving a dirty stain on the component and removes particulate matter, if not off the component, at least to the edge. It is important to keep particulate matter from the surfaces of components and it is recommended that laser testing is done under clean conditions using a flow of clean, dry, inert gas across the test sample to stop dust particles falling on it. In large laser systems this problem becomes extremely serious (and has a direct effect on the engineering design of such lasers as Nova and the NIF facility at Lawrence Livermore (Stowers and Patten 1977, Denton et al 1980). A useful technique for keeping such large surfaces clean (apart from enclosing the whole laser in a class 1000 clean room) is to use electrostatic technology to repulse and/or trap these dust particles (Hoenig 1981). 5.2.3

Surface imperfections

There are a number of terms by which optical designers refer to the imperfections that may occur in or on a surface. These include scratches, digs and sleeks. Scratches have length, depth and widths larger than /10. Digs (nominally circular) have diameters, depth larger than /10. Sleeks are sub-wavelength and/or sub-surface scratches or flaws. They are visible under darkfield transmission tests but not under dark-field scatter/reflection testing. Types of surface damage/imperfection Type

Source

Physical/chemical property

Digs

Left from polishing particle or tool impact

Chips Scratches Sleeks Particles

Stress-induced impact Abrasion from contamination Cleaning, handling, polishing Micropolishing Dust from coating process

Reflectance change Surface scatter Birefringence Surface scatter

Crazing

Coating stress

Low-angle scatter Surface scatter Absorption Surface scatter Low LIDT Change in reflectivity

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119

Types of surface damage/imperfection (continued) Type

Source

Physical/chemical property

Staining

Absorbed chemicals Fungus, mould, insects Optical cement Striae Inhomogeneity Material bubbles and voids Thermal- and laser-induced damage

Absorption

Bulk Fracture

5.2.4

Stress-induced birefringence Catastrophic damage Stress-induced birefringence Large-angle scatter

Measurement of surface roughness

The questions regarding the true specification for a surface should, but often does not, concern any optical designer. The specification for the surface finish of optical components should be in terms of the application which necessarily includes the wavelength, power and beam size of the optical radiation source used in that application. A very useful introduction to the subject has been given by Bennett and Mattson (1999). In order to measure the quality of the surface finish that has been specified and that the component supplier has delivered it is necessary not only to agree on the specification but also to agree on the measurement technique used to ascertain it. There are many applications where the specification is really in terms of the light scattered by the surface at the wavelength of interest. In these applications the total internal scatter (TIS) method is applicable. It needs to be recognized that this approach is perfectly good for many applications (and is why the ASTM specify this as a standard test (ASTM 1995)). However, for most high-power laser applications this approach is totally inadequate as it only gives an average value over the surface to be tested. In the high-power laser scenario the problem is to identify the presence, density and magnitude of the largest surface defects. It must also be realized that specifying r.m.s. roughness is no use at all unless the specification, at the same time, specifies the spatial frequency at which this surface roughness figure is to be measured. The measurement resolution must therefore be specified in both the z and the x–y directions. It should also be noted that, even after using extremely stringent finishing conditions, the surface finish is not necessarily constant over the whole of the surface. This subject has been exercising the minds of optical designers and quality assurance managers over recent years (Langhorn and Howe 1998, Bray 2000, Coursey 2001). It must be realized that surfaces may have the same r.m.s. roughnesses and even the same peak/valley heights but have totally different spatial

120


Figure 5.5. Eight different scans of the surface profile of a scratch on fused silica made using atomic force microscopy (Gomez et al 1998).

frequencies. This is because a ‘dig’ is rarely circular and cone shaped and a ‘scratch’ rarely has constant width, depth or surface roughness associated with it. Figure 5.5 shows a series of eight micrographs measured, using atomic force microscopy, across the same scratch on a piece of fused silica (Gomez et al 1998). Surface profilometry is therefore only reliable, in the present scenario, when the probe size is smaller and narrower than the surface variations. 5.2.5

Surface measurement techniques

Table 5.1 lists the seven main surface measurement techniques that are used to routinely measure the surface finish of optical components. It will be seen that the relationship of the spatial resolution (in the plane of the surface) and the z (or depth) resolution are not necessarily constant. For example optical interference microscopy can measure depth differences down to

121

Surfaces Table 5.1. Surface measurement techniques. Measurement technique

Spatial resolution

z resolution

Optical microscopy Optical interference microscopy Confocal laser microscopy Scanning acoustic microscopy Scanning electron microscopy Atomic force microscopy Scanning tunnel microscopy

1 mm to 10 mm 1 mm to 10 mm 10 mm to 10 mm 10 mm to 10 mm 1 nm to 1 mm 0.5 nm to 0.1 mm 0.1 nm to 0.1 mm

0.1 mm to 10 mm 0.01 nm to 50 mm 1 mm to 1 mm 10 mm to 1 mm 50 nm to 0.1 mm 1 pm to 0.1 mm 1 pm to 0.1 mm

0.01 nm but cannot resolve areas to better than the wavelength of the probe light. A good summary of the relative measurements of these techniques is given by Lange et al (1994) and by Gomez et al (1998). The ultimate sensitivity of all the optical techniques depends upon the reflecting and transmitting properties of the surfaces under investigation. Scanning acoustic and confocal laser microscopy can also be used to probe beneath the surface. R.m.s. roughness,

ðL 1=2 2 Rq ¼ 1 Y ðxÞ dx

ð5:1Þ

0

where x is the distance along the surface under measurement, YðxÞ is the height of the surface from the mean line, and L is the sampling length. The r.m.s. roughness can also be defined from the measurement of total integrated scatter, S (Lorincik et al 1996, Stover 1995): S¼

R0 R ð4Þ2 R0

ð5:2Þ

where is the r.m.s. surface roughness, R0 is the total reflectance, R is the specular reflectance and is the wavelength of light. 4 2 4 2 R ¼ R0 exp ¼ R0 1 :

ð5:3Þ

Although it is universally recognized that stating the r.m.s. roughness is not the correct way to specify a surface for use in a high-power laser situation there is, at present, no systematic effort being expended in changing the method of specification. The problem with the r.m.s. roughness is that it only measures the optical surface’s average variation from the mean surface. Because the r.m.s. roughness looks at only the height and depth of the

122


peaks and valleys, two very different surfaces can have the same r.m.s. value (Coursey 2001). 5.2.6

Surface absorption

Surface absorption can be in the form of an adsorbed layer (e.g. finger grease or water), of particulate matter (dust or debris) or included polishing material (e.g. Al2 O3 on 10.6 mm components, rouge at all wavelengths), of absorption in thin-film dielectric coatings or a polycrystalline layer left after machining. The latter subject will be dealt with more thoroughly in section 5.3. Such layers can sometimes be removed by low-power laser treatment (e.g. ‘conditioning’ or ‘laser annealing’) or can be cleaned off (e.g. an isopropyl alcohol wash of Ge, ZnS and ZnSe substrates leads to lower absorption values (Wood et al 1982d). It was shown that the GeO2 layer which grows on a Ge surface in the presence of air absorbs water (Foley et al 1980). This investigation showed that when a germanium surface was dried, under vacuum in a flow of dry argon, water could be drawn off consistently. The amount of water was calculated to be equivalent to an even layer 130 A˚ thick (0.66% absorption at 10.6 mm). Experiments showed that if the surface was dried under vacuum the water (and therefore the absorption) was replaced almost instantaneously. If the Ge surface was dried using isopropyl alcohol (thus reducing the thickness of the GeO2 layer) the absorption took hours to reappear. The timescale for this was variable and appeared to depend both on the thoroughness of the isopropyl cleaning and the humidity of the ambient atmosphere. The importance of the surface contribution to the total absorption and hence to the LIDT was revealed by a simple experiment undertaken at the GEC Hirst Research Centre (Wood 1986). Two uncoated germanium substrate windows (9 cm1 resistivity) were obtained, cleaned, and tested for their cw laser power-handling capabilities. Both substrates were subjected to 400 W of incident power in a 5 mm beam diameter. The first sample (4 mm thick) cracked after 27.8 s exposure while the second (2 mm thick) cracked after 14.9 s exposure. The samples had been cut from the same boule, had been prepared in as identical a manner as possible and were identical apart from their thicknesses. It was therefore assumed that the absorption which led to the different times of damage must be largely associated with the surfaces, since bulk absorption alone should have produced the same temperature rises and therefore the same time of damage in each case. As a first approximation, assuming that there was no flow of heat during the irradiation time, it is possible to write E ¼ KtðAs þ lÞ

ð5:4Þ

where E is the energy absorbed, K is a constant, As is the surface absorption, is the bulk absorption, l is the thickness of the sample, and t is the irradiation time.

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123

The temperature rise at the centre of the beam axis is given by T /

energy absorbed E / : sample thickness l

ð5:6Þ

The temperature rises can be equated at the point of damage, K 27:8 ðAs þ 0:4Þ K 14:9 ðAs þ 0:2Þ ¼ : 0:4 0:2

ð5:7Þ

As ¼ 2:58:

ð5:8Þ

This gives

The contribution to the absorption from the two surfaces is therefore 2.58 times that of a 1 cm length of bulk crystal. This therefore yields surface absorption 2:58 ¼ ¼ 6:45 total bulk absorption 0:4

ð5:9aÞ

for the 4 mm sample and surface absorption 2:58 ¼ ¼ 12:9 total bulk absorption 0:2

ð5:9bÞ

for the 2 mm sample. Assuming that the bulk absorption coefficient is 0.005 cm1 then the surface absorption would be 1.29%, or 0.645% per surface. This value for the surface absorption of germanium in air is reasonable (see figure 3.1). This demonstrates that the surface absorption may be equal to, and in certain cases greater than, the sample bulk absorption. Newman et al (1979) proved that the presence of water vapour affected the damage thresholds of both NaCl and KCl adversely by a factor of two. The water vapour was shown to be removable by treatment with an HCl acid etch but was reabsorbed within 20 min. Kovalev and Faizullov (1978) also showed that improvements in the LIDT of Ge and NaCl could be gained by chemical etching. Surface absorption is not just confined to water vapour. Sparks (1976) published a record of the spectral positions of the absorption peaks of common contaminants. Figure 5.6 shows a ‘schematic representation’ of the typical spectra seen in most samples in the laboratory atmosphere (Braunstein et al 1980). This work identified over 20 different species which had been removed from ordinary optical surfaces by drying, heating, or washing. In addition to gas and liquid absorption, extra-particulate absorption may arise during cumulative testing or running of a laser system. This is particularly relevant to gas lasers where nearly all gas laser output mirrors have particulate matter embedded in them due to transport in the gas plasma. It

124


Figure 5.6. Schematic representation of the typical spectra seen in most samples in the laboratory atmosphere (Braunstein et al 1980).

has frequently been possible, by careful X-ray testing of the surface of such a window, to analyse the materials used in the construction of the laser tube. Figure 5.7 shows an SEM micrograph of microscopic copper debris which had accumulated on the output mirror of a 10.6 mm CO2 gas laser during operation. The copper was shown to have originated in the fully reflecting copper mirror at the other end of the resonator, about 1 m away from the output window. 5.2.7

Surface damage thresholds

In the light of the discussion of the effect of the surface finish on the optical properties of that surface it is now relevant to discuss the effect of that finish on the LIDT of a material or component. The first effect is that there is an enhancement of the electric field by scratches, digs and voids (Bloembergen 1973, Genin et al 2001). This is illustrated in figure 5.8. It is then relevant to realize that the electric field is affected by the reflection from the surface (Crisp et al 1972). This means that unless a component

Surfaces

125

Figure 5.7. SEM micrograph of copper debris on a germanium window surface (20 000).

is anti-reflection coated the power at the exit face is less than that at the entrance face. The ratio is obviously dependent on the refractive index of the material (Stickley 1973): incident power at the entrance face 4n2 ¼ : incident power at the exit face ðn þ 1Þ2

ð5:10Þ

It also needs to be noted at this stage that the front (incident) face LIDT is apparently lower than the exit face LIDT (when measured in terms of the power incident into the material). However, when damage is initiated the exit

Figure 5.8. Enhancement of the electric field by scratches, digs and voids (Bloembergen 1973).

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Table 5.2. Ratio of entrance and exit powers for a range of material refractive indices. Refractive index, n

1.2

1.5

2.0

3.0

4.0

Ratio

1.19

1.44

1.77

2.25

2.56

face damage is usually more catastrophic than the entrance face damage. This is because the reflected beam interferes with the forward-going beam. In the case of the front (air–material) face, the maximum power density is found at a distance of /2 in front of the front surface. Either air-breakdown occurs at this point, thus shielding the front face, or, if the LIDT of the material is less than the power density for air-breakdown, a plasma is formed from the ablated material and this then absorbs part of the incident radiation. In the case of the rear face of the material (material–air) the maximum power density occurs at /2 in front of the face (i.e. inside the material). If damage appears at this point a cone of material is ejected. The differences in the published laser processing thresholds (see appendices) for the same materials when normalized to the same irradiation length come about mainly because of the differences in the material surface finish. If a material has a rough or scratched finish then the processing threshold will normally be lower than for a polished surface. The highest surface damage thresholds are obtained from samples which have undergone very careful polishing so that scratches and/or digs with dimensions greater than one hundredth of the wavelength of the laser radiation are absent. When this specification is met it is usual to be able to measure values for the surface damage threshold which are of the same order as those measured for the intrinsic bulk damage threshold. The effect of the surface finish on the measured LIDT is typified by the following results which were gained on Schott LG 360 optical glass (Wood et al 1975). A sample of glass was obtained and inspected. The quality was good and there were no visible inclusions (inspected using an He–Ne laser beam under dark-field conditions). The six surfaces of this sample were extremely carefully finished to different tolerances with different grades of diamond powder, cleaned and then damage tested. The results of this series of tests are plotted in figure 5.9. The graph plots the log of the r.m.s. surface finish against the log of the front surface LIDT. Although there are individual deviations from a perfectly straight line, because even the best surface has some deviations (waviness), the broad relationship is clear. The experiment indicated that once the maximum scratch, or dig, dimensions were less than /100 then the surface damage threshold was almost indistinguishable from the bulk damage threshold. Similar results have been gained from lithium niobate and lead lanthanum zirconate titanate (PLZT) electro-optic crystals at 1.06 mm, from single-crystal germanium,

Surfaces

127

Figure 5.9. Variation of the front surface damage threshold with surface finish (Schott LG 360 glass) (Wood et al 1975).

chemical-vapour-deposited (CVD) polycrystalline ZnSe blanks and from copper mirrors at 10.6 mm. In the case of the copper mirrors the relationship depends on the increase of absorptivity with increasing r.m.s. finish (Wood et al 1983) while in the case of dielectric materials the relationship is a function of the scatter and constructive interference. In CVD-grown ZnSe the grain size as well as the surface finish affects the LIDT of the material. This phenomenon can be used to lower the processing threshold by marking the point of initiation with an absorbing material. Once processing has started, the threshold can change rapidly as the reflectivity and absorption of the material changes rapidly once it has started to melt or to damage. Very similar results were gained by House et al (1975) who compared the calculated breakdown threshold fields with the surface roughness, as measured from TIS scans, of a series of fused silica substrates. The substrates were first conventionally polished and measured. They were then overcoated with /2 layers of either SiO2 or MgF2 and remeasured. The results are summarized in figure 4.12. It is interesting to note that the overcoated samples had both lower roughness and lower electric-field breakdown values than the bare surfaces. This was taken to indicate that the major breakdown sites still dominated the damage process but not the TIS values. Comments were made to the effect that, although the decrease in

128


Figure 5.10. Damage probability plot.

surface roughness should increase the LIDT of a material, the larger defects would still dominate. It was also noted that the TIS measurement was concerned more with the overall roughness while the breakdown threshold (or LIDT) was concerned with the dimensions of the largest defect in the focal volume. The LIDTs of a range of metal mirrors have already been shown in figure 4.7 and tables 4.3 and 4.4. The majority of these values have been gained using nearly perfect material blanks. However, all materials can exhibit lower LIDTs if they are tarnished (extra absorption) or are scratched. Figure 4.8 showed the correlation between the absorption and the damage threshold. This was brought about because a number of copper mirrors were finished to slightly different perfection levels. The surfaces with higher r.m.s. roughness exhibited higher absorption and lower LIDTs. As should be expected, from consideration of the effect of scratches etc. on the incident electric field (Bloembergen 1973, Genin et al 2001), practical laser damage thresholds are lower in the presence of scratches than for clear surfaces. However, the effect of a scratch in many practical systems is complicated if the light beam is not uniform. This leads to the production of percentage damage versus incident flux graphs (see figure 5.10). This graph indicates that for any surface there is, above some minimum value, a percentage chance of the material being damaged at any given light flux. This percentage is a function of both the surface roughness and the incident beam shape. On the surface roughness, there is only a certain probability that the most easily damaged scratches lie in the area covered by the laser beam and on the beam shape because, in the case of a focused beam, the maximum flux only occurs over a small area.. In summary the sharpest discontinuity with dimensions in the range 0:1 > d > 10

ð5:11Þ

Surfaces

129

will have the lowest LIDT, and much measurement technology in current usage is not capable of measuring the dimensions of the narrowest of the relevant scratches. The absolute shapes of these plots are, as already emphasized, dependent on the surface quality, the beam shape and the laser-testing wavelength. In practice, most component specifications are written in terms of scratches visible under white light or maybe at 0.5 mm wavelength. As it is costly to make and hard to inspect surfaces with scratches smaller than about 0.2 mm width, these specifications are usually applied to all components. It is now easy to realize that components for use in the far infrared will easily meet the criterion for maximum damage threshold and their percentage damage plots will be approximately vertical. Others, particularly those for use under short-wavelength conditions, will find it harder to meet the most stringent specification and their percentage damage spots will be more sloping (see also figure 4.21). Figure 5.8 indicated that the LIDT associated with surface scratches etc. would be lower than the intrinsic surface LIDT. This may be illustrated by reference to figures 5.11(a) and (b). Figure 5.11(a) shows a photograph of the incidence of laser-induced damage on the surface of a germanium substrate. The laser damage has been initiated on a small scratch on the surface (400 magnification) and an area of the germanium has been ablated. The depth of this ablation was considered to be the depth of the polycrystalline worked surface (see section 5.3). At the centre of the photograph there is a very small melted area residing on the remains of the scratch. Figure 5.11(b) shows a photograph of cumulative damage on an MgF2 anti-reflective coating on an Nd:YAG laser rod. This laser rod had been pulsed for 2 106 shots (at an output level of 100 mJ at 10 Hz in 10 ns pulses of 1.064 mm radiation). There was no appreciable degradation of output of the laser rod although some slight damage was observed to the coating. This damage (see figure 5.11(b)) was in the form of minimal coating damage initiated on a barely visible scratch. As the threshold for damage to both the remainder of the coating and to the crystal surface was well above the maximum fluence generated no further damage resulted. If the surface finishing technology results in linear scratches and if these happen to be aligned orthogonally to the incident laser electric field then the laser-induced damage occurs as a set of parallel lines parallel to the original scratch (see figure 5.12). This phenomenon has been observed and assessed at 10.6 mm (Emmony et al 1973), at 193 and 248 nm (Wiseall and Emmony 1982) and at 0.53, 1.06, 2.7 and 10.6 mm (Soileau and Van Stryland 1982) on a wide range of window and mirror substrates. The ripples are associated with interference of the incident field with the non-radiative field induced by the material defects or scratches. The ripple spacing is =n (where is the laser wavelength and n is the refractive index of the second medium). This

130


(a)

(b)

Figure 5.11. Laser-induced damage to scratches. (a) Pulsed laser-induced damage, 10.6 mm, on a scratch on a germanium substrate. (b) Pulsed laser damage on a scratch on a MgF2 anti-reflective coating on a Nd:YAG laser rod. 2 106 pulses of 100 mJ, 10 ns, 1.064 mm radiation at 10 Hz.

explanation indicates why the ripple spacing is usually greater for rear surface damage than for front surface damage. Particulate material often arrives on the internal mirrors and window surfaces of lasers during cumulative life testing and operation. This is particularly severe in the case of gas lasers where the output windows in particular suffer from a build-up of embedded particulate matter due to transport in the gas plasma. It is possible, by careful analysis of the surface of a gas laser output window or mirror, to analyse the construction of the resonator. For example it is relatively easy, using the SEM technique, to identify the anode and cathode materials, the tube envelope and the window and mirror materials. Figure 5.7 showed an SEM photograph of copper debris (from the fully reflecting mirror) which had accumulated

(a)

(b)

Figure 5.12. Photograph of the linear interference patterns associated with a scratch.

Sub-surface

131

on the dielectric-coated germanium output mirror of a 10.6 mm pulsed CO2 TEA laser.

5.3

Sub-surface

Whenever a blank of material is machined, no matter how uniform or perfect the quality of the basic material, the machining leaves a thin layer of damaged material on the surface. From a number of measurements made in a variety of disciplines it has been estimated that this layer ranges from 50 mm up to 1 mm in thickness. It has further been found that this layer consists of polycrystalline ‘rubble’, full of broken electronic bonds which either link up together forming a weak surface or link up with atmospheric and particulate impurities, which give added absorption. In addition many damaged surfaces contain weak oxygen bonds which in turn absorb water. This phenomenon has been found with both perfect single crystals (e.g. silicon in the microelectronics field and the halides and germanium in the infrared laser field), with polycrystalline material (such as zinc selenide laser and optical windows) and with highly polished/machined metal surfaces and mirrors. Only amorphous materials, such as silica, do not suffer from this effect and even silica can ‘bury’ polishing particles under the surface. The process can best be explained by reference to figures 5.3(a) and (b) (Sharma et al 1977). A well-polished germanium substrate was characterized, laser damaged and photographed. As the thresholds were fairly low it was decided to look at the surface in more detail. A fairly heavy scratch was put on the surface (the scratch and a damage spot were then used as spatial references). The surface was then ion etched and subjected to X-ray topographic investigation. The initial topographs (the X-rays penetrating to a depth of about 0.5 mm) indicated that the sub-surface contained a mass of fine lines and misoriented crystal. A second investigation (penetrating to a depth of about 10 mm) indicated that at this depth the surface contained evidence of crystal defects but no scratches or radically misoriented polycrystalline material. Subsequent X-ray topographic studies on polished germanium have shown that the origin of the polycrystalline layer was the diamond cutting procedure and that the mass of fine lines originated from polish-lapping. If a germanium crystal is finished with an acid etch (e.g. Syton) then the number of fine lines can be minimized, although there is still the necessity of removing an unspecified polycrystalline sub-surface. It has been shown, both in laser testing studies (Wood 1986, 1994) and in laser annealing trials, that impurities and dislocations, both in the bulk and in the surface layer, move across the irradiated area when a material is irradiated. This happens most conspicuously under high-prf or continuous irradiation. It was shown (Wood 1986) that not only do the dislocations

132


(a)

(b)

(c)

Figure 5.13. Laser-induced damage—single-crystal GaAs.

move through the irradiated area but that many migrate to the edge of the irradiated area and coalesce. When sufficient impurities and defects are pinned together at the edge of the irradiated area, the thermal conductivity is modified and the temperature of the central, irradiated region rises. This has been observed in both GaAs at 10.6 mm and in CVD diamond at 1.06 mm. In the case of the GaAs tests, the continued irradiation resulted in catastrophic cracking, in the form of an arc centred around the focused beam spot, followed by melting of the centrally irradiated area (see figure 5.13; Wood 1986). In early damage measurement trials, ordinary copper blanks were polished and damage tested. Ordinary copper blanks contain grain boundaries that can be observed under X-ray analysis. However, it was not realized, until damage threshold measurements were made, that these boundaries also

Sub-surface

133

contained higher levels of absorbing impurities than the grains themselves. Hence when the blanks were damage tested, by making tests across the face of the blank at the same irradiance, the grain boundaries became obvious as they damaged at a consistent and lower damage threshold than the rest of the blank. The main reason why OFHC copper is now used as the substrate for many high-power CO2 laser mirrors is that it does not contain grain boundaries. The highest thresholds for polished copper substrates have been gained from the use of single-crystal copper. The problem remains, however, that copper oxidizes easily and it is therefore expedient to coat it with an oxidation-resistant coating. This is usually gold but evaporated dielectric coatings have also been applied and yield high-damage-threshold surfaces. There are several measurement techniques that have been used with advantage to explore the surface and sub-surface characteristics of laser substrates. The first two are specifically for the investigation of quasisingle-crystal material and the other two are more general. X-ray topography This technique involves looking at the micrograph formed when a surface is irradiated by a focused X-ray beam at a glancing angle. The depth of the surface investigated is a function of the energy of the X-rays involved. If the substrate is a perfect single crystal, the X-ray picture is blank. If the crystal surface contains crystallites or grains the Bragg angle for these will be different for these areas than for the main body of the crystal and the image from these areas will be formed at different angles of incidence. The micrograph from polycrystalline areas will therefore show blank or overdeveloped areas. By varying the incident angle, or by using more energetic beams, the depth of the polycrystalline surface layer can be estimated. It has been shown that it was possible to verify the depth of the polycrystalline surface layer on polished germanium substrates by chemically etching the surface and showing that the underying material was good single-crystal material (Sharma et al 1977). SEM micrographs of polished and etched germanium substrates are shown in figure 5.3. X-ray rocking method This technique is a variant of X-ray topography in that it also involves irradiating the surface of the polished single-crystal material and observing and recording the reflected X-rays. The technique, which was used to investigate the perfection of the polished surface of single-crystal silicon substrates for semiconductor fabrication (Wood 1990b), involves rocking the X-ray beam across the surface of the surface under consideration, as illustrated in figure 5.14. If the surface is completely perfect, the X-rays are reflected at the Bragg angle and a plot of angle versus intensity is very sharp. The

134


Figure 5.14. Schematic diagram of a double-crystal goniometer.

more polycrystalline the surface is, the wider the intensity plot. A study was made which included etching the substrate under investigation and remeasuring the shape of the reflected intensity plot. A summary of these results is shown as figures 5.15(a)–(c). The plots indicate that, for the substrate under consideration, there was at least a 3 mm polycrystalline layer on the polished substrate prior to the etching treatment. It was found that the sawing process, which preceded the polishing process, could leave a damaged layer of up to 50 mm in depth and that conventional etch polishing could remove all of this. The practical difficulty is to decide when the etch polishing procedure is sufficiently complete for the substrates to be sent to the next manufacturing process.

Sub-surface

135

(a)

(b)

Figure 5.15. (a)–(c) Results of X-ray rocking method studies, silicon.

Photo-thermal technique This technique, which has been reported widely in the scientific literature (Abate et al 1983, Marrs and Porteus 1985, Edwards et al 1969, Hummel et al 1995), basically looks at the rise in temperature across a surface when that surface is irradiated. The technique has generally been used to investigate the quality of dielectric coatings. The technique monitors the changes in temperature which result when heat is absorbed at, say, an

136


(c)

Figure 5.15. (Continued)

impurity inclusion. The technique has been shown to be able to identify microscopic areas where the heat is absorbed but it has not always been possible to correlate this with any specific inclusion or to tie up the inclusion with a lowered damage threshold. This is probably due to the fact that some of the heat spots are in fact at dislocation boundaries and not at specific inclusions. Thermal conductivity It is fairly easy to measure the thermal conductivity of a substrate or surface in the presence of pulsed radiation (Guenther and McIver 1988). The presence of dislocations and grain boundaries tends to lower the thermal conductivity but impurities may be more neutral, some lowering and some increasing the conductivity. It has certainly been shown that the higher the perfection of the material and/or coating the more consistent is the conductivity of the bulk material. It has also been shown that laser irradiation of the surface can improve not only the optical quality and smoothness of the surface but can also improve the conductivity and the laser-induced damage threshold. Conversely it has also been shown that high-power laser treatment of a surface or crystal which contains an appreciable number of defects can move those defects to the edge of the irradiated area. When this happens the defects may join up, lower the thermal conductivity and lead to laser-induced damage. This has been observed in both single-crystal GaAs (Wood 1986) and in CVD-grown diamond (Sussman et al 1993).

Chapter 6 Coatings 6.1

Introduction

The surfaces of bare optical materials rarely have the desired reflectance/ transmittance characteristics so they have to be coated. If the surface is left uncoated then it may have a high LIDT but it will also certainly act as an effective loss mechanism, as n1 2 : ð6:1Þ R¼ nþ1 Reflective surfaces inside a laser resonator act both as a transmission loss and as a source of extraneous modes. These considerations are very important for low-gain media and for high-refractive-index substrates. All lasers have some degree of output coupling, the most common being dielectric-coated partial reflectors. The precise reflectance required to produce maximum input/ output pump efficiency is a function of the internal gain and the pump level. A low-gain medium requires a high-value reflector while a high-gain medium requires a relatively low output-coupling coefficient but is more susceptible to feedback and off-axis modes. In general the higher the reflectance the higher the standing wave ratio and, as most damage occurs at either the internal air/coating or the coating substrate interfaces, the lower the LIDT. If care is taken to minimize the standing wave voltage ratio (SWVR) at the interface then the LIDT usually rises. For well-polished substrates and good quality coatings there is a clear relationship between the scatter from the uncoated surface and the coated surface (Wood et al 1982e). This was shown in figure 2.13. This figure indicated that there was a straightforward correlation between the measured scatter, the density of defects, the defect density, the defect dimensions as a ratio of the beam diameter and the reflectance of the surface, both coated and uncoated. This relationship was only found to be true in the case of well-polished, good optical quality substrates, which had intrinsically low scatter values. Coatings can be anti-reflectance coatings to reduce/eliminate the surface loss, anti-reflectance coatings to eliminate constructive interference losses, 137

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Coatings

controlled reflectance/transmittance characteristics, band-pass and rejection filters, or total reflectors. But coatings are bad news in terms of their power/energy handling capacity, as coatings are rarely totally uniform and homogeneous, they often contain ablated material, they have voids, they do not eradicate surface irregularities and flaws, and they multiply surface irregularities and flaws. However, despite these problems, coatings are usually better than no coatings. The problem which is in the forefront of research at the present is to deposit coatings that minimize the above faults and allow the optical component to be used at as high a power/energy flux level as possible. In theory, and increasingly in practice, dielectric coatings can be deposited to any desired average thickness. The main problems are the elimination of particulates and the deposition of spatially uniform layers. Interfaces collect dust and act as a source of voids. X-ray and e-beam analysis of coating interfaces almost invariably show particulates, voids and change of structure. If coatings are ‘conditioned’ some of these voids can be dispersed into the bulk of the coating or benignly ejected from the coating. If coatings are irradiated at too high a level then the particulates and voids can act as centres for thermal mismatch and result in delamination. Deposited material gives rise to refractive index gradients, which in turn act as a lens, focusing the irradiation on the particle. Coatings can yield very high LIDTs but only if the ‘composite surface’ is extremely smooth and the surface is an efficient anti-reflector. High-reflectivity coatings generally have higher LIDTs than antireflectance coatings, because the irradiation is reflected back from the first surface into the atmosphere, and only a small percentage reaches the coating/substrate interface. Most coating deposition techniques replicate the surface, including scratches. They only gradually smooth out scratches and digs at the expense of increasing the number of voids and/or modifying the local refractive index. There are a few techniques, however, which can ‘fill in’ holes and scratches and these have been shown to yield superior damage and reflection characteristics. A coating material usually exhibits absorption of orders of magnitude more in the film than in the bulk (Sparks 1976). This absorption may ‘only’ be of the order of 103 or 104 , and hence have little or no perceptible effect on the R, T and A characteristics of a coating (see section 2.9). However, this is large in terms of the local absorption coefficient and can have an appreciable effect on the thermally dominated LIDT. Contamination of the film occurs during deposition (insufficiently cleaned vacuum chamber, vacuum oil contamination), upon exposure to the atmosphere (water vapour), during use (plasma-borne impurity deposition inside a gas laser), during cleaning (inefficient cleaning/drying procedures) or during storage,

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139

inspection or transit (lint from tissues, plastics from ‘protective’ overlays and finger grease). All these effects have been observed to increase the localized surface absorption and to decrease the LIDT. These issues were extremely common in the early days of laser research. Most of the issues have been, or can be, eliminated by close attention to such detail as using films with a high packing density, vacuum vapour cleaning and ultra-clean deposition, handling and storage procedures. For absorptions of the order of 2 104 , the film and the bulk contributions to the spatially averaged absorbed energy are equal, and thermally induced optical distortion and failure take place. Under cumulative pulsing, time-averaged heating takes place with a consequent lowering of the LIDT. The linear absorption of 1 mm radius inclusions is of the order of 104 and therefore inclusion damage occurs at 10 to 100 J mm2 for nanosecond pulsewidths. Intrinsic (dielectric breakdown) damage occurs at ED 10 J mm2 . A detached film heats up preferentially and experiences thermally induced stresses of the order of 103 psi. The following sections first summarize the various coating technologies, then the measurement of coating parameters and the various types and morphology of damage, and then discuss coating design. All these sections are, of necessity, just summaries of the subject and if readers need to go further they should consult some of the detailed treatises on the subject (MacLeod 2001, Heavens 1955).

6.2

Coating technology

There are a number of coating technologies and an even greater number of proponents of each of these technologies. It must be stressed at the outset that the results gained using each technique are a direct consequence of the quality of the equipment and the expertise of the equipment operator. It has been instructive over the past 40 years to watch the quality of dielectric coatings improve as increasingly sophisticated techniques have been developed. It has also been instructive to look at the published comparisons of these techniques, such as Partlow and Heberlein (1983), Wodarczyk et al (1983), Lewis et al (1993, 1996), and MacLeod (2001). The deposition process and conditions have to be chosen with care so that the design of the deposited coating can be reproduced exactly and the substrate/coating stress/strain can be minimized. For instance, when evaporating ZnS or ZnSe the temperature of the substrate has to be controlled within a fairly tight tolerance. ZnS and ZnSe dissociate on heating and, hopefully, react together again on the substrate. If the substrate temperature is too low (250 8C) then Zn will be predominantly deposited. If either S/Se- or Zn-rich coatings are deposited

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Coatings

then the refractive index of the coating will be lower/higher than if ZnS or ZnSe were deposited uniformly. If the composition varies during the deposition layer it will prove nigh impossible to tune the optical response exactly. The problem is compounded by the fact that deposition increases the temperature of the substrate. These comments do not mean that good quality ZnS or ZnSe cannot be deposited, solely that the technology to manage this requires a far higher degree of control than is expected on a first impression. A similar problem applies to the deposition of the refractory metal oxides. For example TiOx may be deposited with x ranging from 1 to 2, with a consequent change in the refractive index of the material. SiOx and GeOx may also be deposited with a similar range of values of x. If such a variation can be controlled it can be used to advantage (e.g. in the deposition of Rugate structures—see section 6.4). Thermal evaporation This is the oldest and probably still the most used technique. It has been transformed, since the early days, by a great number of people and can be made to yield very good results. However, it is limited as to the number and range of materials which can be deposited by heating material in a high-meltingpoint crucible. Care has to be taken to screen out large lumps of evaporant. Evaporation of the source material is normally from a refractory boat using a movable shutter to control the deposition. It is particularly suitable for large-area deposition. It is most commonly used to deposit /4 layers. Either optical or quartz crystal technology is used to control the thickness of the deposition. Reasonably good columnar structure coatings can be produced by this method (Guenther 1983) although decrepitation commonly occurs, leading to a fairly high incidence of ‘coating defects’ (see figure 6.1(a)). These coating defects are usually the cause of low values of the LIDT. Strain, either between the coating and the substrate or between the alternate layers of a stack, may occur if unmatched materials are used (see figure 6.1(b)). Electron-beam deposition This technique has been widely used to evaporate the highly refractory materials that cannot be deposited using thermal techniques. Again care must be taken to ensure that ‘spitting’ of the source material is negated. Although it is possible to control the deposition with precision and even to co-deposit materials it is usually used to deposit /4 layers. The refractory oxides are usually hard, adherent and amorphous but still contain pinholes (Sites et al 1982). Ion-beam deposition This was developed as an advance on the early e-beam technology although in practice it has much the same advantages and drawbacks. In general the

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141

Figure 6.1. Undamaged coatings. (a) Thermally evaporated dielectric coating. (b) Cracking of strained coating. (c) RF sputtered coating. (d) Gold-plated Cu mirror.

more energetic the deposition process the better the bonding between defects and the surrounding material with a consequent catastrophic ejection when damage does take place. The r.m.s. roughness of the as-deposited films is usually extremely good (Lewis et al 1998). RF sputtering A photograph of an RF-sputtered coating is shown in figure 6.1(c). The uniformity of this coating has been shown to be due to the slow growth nature of this technique and the fact that large particles are just as likely to be pulled off the substrate as to be deposited on it. This technique is particularly useful as a means of coating a substrate with a close-packed pinhole-free sealing layer (Lunt 1983). Chemical vapour deposition Plasma deposition is particularly useful for depositing hard carbon and silicon coatings (Bubenzer and Dischler 1981, Dischler et al 1982). The

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Coatings

refractive indices of these coatings prepared by this method can be tuned over quite a large range by adjusting the hydrogen atmosphere. These coatings are widely used in the semiconductor industry for encapsulation, passivation and diffusion barriers (Partlow and Heberlein 1983) The chemical vapour deposition technique, although proving more difficult to deposit highly uniform large-area coatings, has the advantage that it can be used to deposit very fine-grained coatings (since the deposition is from reacting gases) and can also be used to deposit true ‘Rugate’ structures (Dobrolowski and Lowe 1978, Baumeister 1986, Wood 1992). These coatings, because the deposition design is in the form of the Fourier components of the ideal design, can be deposited to only have reflecting peaks (or anti-reflecting properties) without the commonly experienced side bands observed when strict /4 layer designs are fabricated. Since the design of the coatings can be such that there are no sudden changes in material, or even reflection surfaces, the coatings are fundamentally highly laser damage resistant (Wood et al 1992)). Molecular beam epitaxy This technique, since the deposition is achieved using a molecular beam, can be used to deposit extremely fine-structured coatings (Lewis et al 1998). However, at the present time it can only be used to deposit coatings on relatively small-area substrates. Coatings deposited using this technique offer improvement over amorphous or polycrystalline films because of the absence of grain boundaries, with their associated impurity absorption, and because there is no replication of the substrate surface roughness (Rona and Sullivan 1982, Lewis and Savage 1983, Lewis et al 1989, Kaiser et al 1996). Langmuir–Blodgett films and sol–gel coatings These techniques can be used to deposit very finely controlled layers of material from a solute (Lowdermilk and Mukherjee 1981, Spriggs et al 1996, Belleville and Pegon 1996). Although there can be problems with keeping the surface free from ripples (as the material is either ‘spun’ on to the surface or the surface is ‘dipped’ into the solution) it has been shown to give highly reproducible results. One of the interesting side effects of these deposition techniques is that they have been used to show up the effect of scratches etc. on the surface of the substrate. It has been found that the best course of action is to deposit a first layer, with the same refractive index as the substrate, before going on to form a half-wave design. This process has been shown to raise the LIDT of the coating. The sol–gel coating technique has the potential to enable the fabrication of really large-area coatings of ultra-perfect purity and freedom from coating defects. If, and when, this can be done there is every possibility that they will exhibit very good optical and laser damage properties. The laboratories where these coatings are being prepared (see

Measurements and morphology of coated surfaces

143

above references) all require perfect anti-reflective coating characteristics over large-area components with extremely high LIDTs. Other techniques, such as photochemical deposition (Wodarczyk et al 1983) and chemical etching techniques (Swain et al 1982) also owe their potential usefulness to the slow nature of the process. Plating of metal mirrors (e.g. gold plating of copper mirrors to inhibit tarnishing) is usually much better than evaporating a gold layer or overcoating the surface with a dielectric layer. This is because the evaporated gold layer commonly exhibits more absorption and the dielectric layer more pinholes than the plated surface (see figure 6.1(d)).

6.3

Measurements and morphology of coated surfaces

Both the substrate and the coating influence the optical characteristics of a coated component. Although the characteristics of the bare substrate can be measured, prior to the substrate being coated, and then the characteristics of the coated component remeasured, it is still not easy for the relative influence of the coating and the substrate to be separated. However, if the reflection, transmission, absorption and scatter values of a component are measured, from each side of the component, it is possible to make an approximate calculation of the contributions of the coating. One useful method of measuring the absorption of a material or of differentiating between the absorption introduced by the coating and that of the substrate is by coating a wedge sample and measuring the absorption at different thicknesses of the sample (Temple 1979). This technique is only useful for wedge samples but it has been used to prove the basic absorption coefficients, especially where there has been a suspicion that the surface absorption was not negligible. The LIDTs of even identical coating materials and designs on nominally identical substrates, which have been prepared and cleaned under similar procedures, are affected by the differences in the coating fabrication process. There has been a considerable number of reports over the years (see the Boulder Damage Conference Proceedings) on the LIDTs of a wide range of coating types on a similarly wide range of substrates deposited by a variety of techniques. The reports on this topic are sufficient to fill at least another such book as this. However, in summary there is no substitute for matching each deposition technique with particular substrates and coatings (for example Lewis et al 1996, Kaiser et al 1995). Some of the common problems associated with coated surfaces can be discussed by reference to figure 6.2. The influence of lumps of coating material landing on the substrate during the coating run is illustrated in figures 6.2(a)– (c). When a substrate is coated under most deposition technologies, the coating roughly replicates the bare surface. However, if a lump of material is

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Coatings

Figure 6.2. Coated surface schematics.

deposited, of larger size than normal (a), then when more material, of lesser size, is deposited it replicates the new surface and (b) only gradually evens out again. The resulting structure either replicates itself into (c) a lenslike structure or, if the coating has crystal structure (e.g. as in zinc selenide), forms a cone-shaped inclusion (nodular defect) of different refractive index. Both of these possible structures can result in extra focusing of the transmitted light which in extreme cases results in laser-induced damage (Stolz and Kozlowski 1994). Measurements on nodular defects indicated that there was a definite threshold size (height and diameter) above which the LIDT of the defects dropped markedly (Staggs et al 1992). An investigation into the ageing of coatings (Kennedy et al 1995) has shown that the size of the nodular defects increases with time, and in particular exposure to the atmosphere. This resulted in a reduction of the defect LIDT whilst having little or no effect on the more ‘macroscopic’ absorption and reflectance values. In theory, deposition of material replicates the surface (figure 6.2(e)), but in practice the scratches get filled in with a lower density of material than the average coating (the coating contains more voids than the average)

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(figure 6.2(d)). The local reflection characteristics are modified in this region. The only way to fill in the scratches, and achieve a perfect optical response from a scratched surface, is to deposit a layer of material, of the same refractive index as the surface, which will fill in the scratch and leave a perfectly flat surface. This has been done using the sol–gel technique. A layer of sol–gel, of the same refractive index as the silica surface, was deposited on the surface. Since a sol–gel is basically a liquid it flows over the surface and is microscopically thicker in the scratches. It then proved possible to deposit a sol–gel anti-reflection coating on this ‘new’ surface (see figure 6.2(f)). This coating was shown to have both better scatter and anti-reflection characteristics than normal, but also to have slightly higher damage threshold than substrates which were coated at the same time but did not have the same pre-treatment.

6.4

Coating design

There is a wide range of coating design programmes available and it is not in the scope of this book to discuss the differences in approach between them. It is, however, necessary to have some idea of the basic theory of the various coatings because it is only too easy to assume that all programmers know what the particular application is and to miss the one aspect which affects this application. There are a number of excellent texts which cover the basics of coating fabrication and design (MacLeod 2001, Heavens 1955). Standard dielectric reflectors are fabricated using alternate layers of high-, nh , and low-, nl , refractive-index materials of quarter-wave optical thickness: nd ¼ =4:

ð6:1Þ

The designs work on the basis of coherent interference between the surfaces of these /4 thickness layers (see figures 6.2(g) and (h)). These lead to standing wave voltage ratio (SWVR) maxima at the surfaces of the /4 layers precisely where the coating is physically weakest. This is because the interface between two different materials contains impurities, lattice mismatch and polycrystalline material. This SWVR is a function of the refractive indices of the coating materials and the substrate, the film thickness and the wavelength of the incident laser radiation and varies sinusoidally through the coating (Apfel 1977, Apfel and Enemark 1977, Gill et al 1977). If non-/4 designs are used then it is possible to move the SWVR maxima away from the surfaces and thus raise the LIDT of the coating. Alternatively it is possible to modulate the refractive index variation and thus to eliminate the interfaces. The number of high/low layers can usually be counted from the spectral characteristics of the coating. The design and the resulting optical characteristic are illustrated in figure 6.3(a) and (b). Damage to a multi-layer

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Coatings

(a)

(b)

Figure 6.3. (a) High-reflectance /4 wave coating design and (b) characteristic.

layer coating usually arises at a high-/low-refractive-index interface rather than at the air/coating interface. Since most laser-induced damage is initiated at discontinuities, one way to increase the LIDT is to design coatings which place the electric field maxima inside the coating layers and to minimize the electric field at the interfaces. This may be achieved by either using graded index designs

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Figure 6.4. Normal incidence spectral reflectance of a double-layer dielectric coating as a function of the phase changes of the two layers.

(Moravec and Skogman 1978) or non-/4 designs (Gill et al 1977). In the latter work a substantial increase in the LIDT of a multi-layer dielectric (MLD) stack coating was gained by using non-/4 layer designs and ensuring that the peak electric fields occurred inside the low-index layer, as the high-refractive-index layers are more vulnerable to the SWVR maxima. This point is particularly pertinent in the first few layers of an MLD stack or in a two-layer coating. It is possible to illustrate this point by reference to the phase diagram of a two-layer anti-reflection coating as the reflection characteristics for anti-reflection coatings are usually much sharper than for normal /4 designs and therefore make more demands on the deposition process. Figure 6.4 shows the variation of both the phase and the reflectance of a typical non-=4, two-layer anti-reflection coating design. The thicknesses of the two layers may be chosen such that there is a minimum at the reference wavelength. The position of the minimum in the phase diagram is a function of the refractive indices of the coating materials. Whether or not there can be a minimum for any two particular coating materials depends on the refractive indices, as can

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Coatings

Figure 6.5. Schuster diagram for two-layer anti-reflection coatings on a substrate of refractive index n3 .

be seen by reference to the Schuster (1948) diagram shown in figure 6.5. A two-layer anti-reflection coating with zero reflectivity can only be achieved if the refractive indices at the wavelength of use both fall in the shaded areas of the diagram. In practice, damage usually takes place at either the air/coating interface or the coating/substrate interface and in the absence of coating defects is usually due to absorption or stress. Any mismatch between the thermal coefficients of the substrate and the coating materials may lead to a buildup of stress and film flaking. For this reason pairing of the thin-film materials and the substrate is a very important part of the design. For obvious reasons it is also sensible to deposit the materials at as low a temperature as possible. There are many combinations of materials and substrates which seem perfect until the coated optic is cooled to room temperature. Optical coating designs exist for a wide range of applications. Most commonly deposited coatings are recurrent high-/low-refractive-index, /4 stacks of suitable materials. The optical performance of most designs depends on the uniformity of the deposition process and the constancy of the refractive index of the deposited material throughout the deposited layer. It is possible to design special coatings with non-/4 stacks. These designs are usually made to achieve extra-low reflectance or to try to

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eliminate the coating interfaces. Overcoating existing multi-layer stacks is often practised in order to protect the coating surface. Rugate technology is a very promising and flexible design technique providing the deposition process can give the desired uniformity over the substrate area. Although the following comments are specifically centred

(a)

(b)

Figure 6.6. (a) Quarter-wave sinusoidally modulated high-reflectance coating design. (b) Optical characteristic.

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Coatings

around this technique the same principles apply to other deposition techniques. This technique presupposes that the refractive index of the deposited material can be varied smoothly as the deposition proceeds. If a true Fourier deposition design is deposited then there should be no side bands. As already stated, most high-reflectance coatings are based on the deposition of a series of /4 layers ( being the wavelength at which the coating is designed to have peak reflectance). The design and the theoretical optical characteristic of a simple multi-layer stack are shown in figure 6.3(a) and (b). The precise reflectance and the width of the reflectance peak are a function of the number of the high/low stacks and the difference between the high and low refractive index values. It will be noted that there are reflectance sidebands and that the reflectance at wavelengths off the design wavelength is nowhere zero. If the optical characteristic was extended to shorter wavelengths it would be seen that there was a second reflectance peak occurring at a wavelength of /2. If instead of using discrete layers of different material the refractive index of the deposited material could be varied sinusoidally, as in figure 6.6(a), then roughly the same optical characteristic would be reproduced (figure 6.6(b)). The advantages of this design are that there are no sudden refractive index discontinuities, no sharp SWVR maxima and minima, no surfaces with deposition dust and therefore no internal low-damagethreshold surfaces. The following designs have been fabricated by varying the composition between SiO2 (refractive index of 1.45) and GeO2 (refractive index of 1.7). An extension of this design is that if, instead of depositing a full sinusoidally varying refractive index, the deposition comprised a ‘Fourier’ of the desired optical characteristic then the reflectance characteristics of the coating could be controlled more closely. This is illustrated in figure 6.7(a) and (b). The Fourier analysis of a simple high-reflectance peak comprises a smooth envelope with a varying sinusoidal variation inside this envelope. It will be noted from figure 6.7(b) that the main reflectance peak is sharper and that the side bands are reduced in amplitude but not totally obliterated, as the coating index starts and finishes at values firstly above the substrate index and secondly above the index of air. The problem, if it is seen as a problem, can be at least partially solved by starting the deposition at the substrate refractive index and concluding with a similar reduction (see figure 6.8(a) and (b)). The rise and fall illustrated in figure 6.8(a) was over a matter of 3/4 but the optical characteristics do not vary much if the rise is taken over a slightly greater thickness. It is not recommended, however, that the change in refractive index be much sharper than this value as it can lead to stress mismatch between the film and the substrate. It will be seen that this design modification again leads to a slight narrowing of the reflectance peak and to the near eradication of the side bands (figure 6.8(b)). The reflectance away from the reflectance peak

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(a)

(b)

Figure 6.7. (a) Fourier Rugate high-reflectance coating design. (b) Optical characteristic.

is flat but not zero because the coating/air interface still has a refractive index mismatch. The Rugate design technique is very powerful and can be applied to any desired characteristic. It is possible to design-in regions with near zero reflectance characteristics alongside other regions with controlled reflectance.

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Coatings

(a)

(b)

Figure 6.8 (a) Fourier plus matching layer high-reflectance coating design. (b) Optical characteristic.

The deposition design is, as will be expected, a combination of the simple sinusoidal Rugate designs for each characteristic. An example of the design for a double reflectance peak with minimal side bands at other wavelengths is shown in figure 6.9(a) and (b).

Damage to dielectric coatings

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(a)

(b)

Figure 6.9. (a) Fourier double-reflectance-peak coating design. (b) Optical characteristic.

6.5


Variations in the single-shot LIDT across a typical sample occur because of defects both in the coating and in the substrate. Experiments which involve a large-area irradiation show the least apparent variation and the lowest LIDTs. Experiments performed with small spot sizes show a wide variation

154

Coatings

(see figure 4.24). This is because the combination of a small spot with a Gaussian intensity distribution and a statistical distribution (in terms of both size and dimensions) of coating defects results in a damage characteristic with a wide variation. The advantage of using a small beam spot is that multiple measurements can be made on the same coating and that it leaves areas for other tests if there is a dispute. Tests with large spot sizes are more

(a)

(b)

ðdÞ

(c)

Figure 6.10. (a) Typical ‘onion-ring’ damage to a multi-layer dielectric coating ZnS/ ThF4 /–/–/fused silica, 1.064 mm, magnification 200. (b) ‘Onion-ring’ damage to a threelayer anti-reflection coating on fused silica, 1.064 mm, magnification 400. (c) ‘Onionring’ cumulative damage to a multilayer coating, 1.064 mm, magnification 20. (d) Damage to a single-layer anti-reflection coating, ZnS on Ge, 10.6 mm, magnification 400.


(e)

(f )

(g)

(h)

(i)

( j)

155

Figure 6.10. (e) Damage to a compressive dielectric stack combination, 1.064 mm, magnification 400. (f) Damage to a two-layer hard coating, TiO2 :SiO2 on glass, 1.064 mm, magnification 200. (g) Surface damage to the anti-reflection coating on a laser rod after multiple pulsing. (h) Line of laser-damaged spots showing the variation in the damage spot size at the same irradiance, magnification 100. (i) SEM micrograph of damaged ZnS/ThF4 /Ge window showing decrepitation of the ThF4 layer, 10.64 mm, magnification 2000. (j) SEM micrograph of damage to a Ge/ZnS Ge-coated window, magnification 200.

156

Coatings

(k)

(l)

Figure 6.10. (k) Previous sample tested in EDAX mode scanning for Zn. (l) Previous sample tested in EDAX mode scanning for Ge.

suitable for quality assurance purposes where the requirement is aimed at proving that the coated surface can withstand a particular fluence rather than determining the possibility of the substrate/coating combination. The morphology of coating damage varies widely. A range of the different types of damage is shown in figure 6.10.

Chapter 7 Special topics 7.1

Ambient atmosphere/gases

The ambient atmosphere has an effect on the LIDT mainly because of induced absorption. It must be realized that even ‘cleaning’ can add absorption, as well as reducing it. The effect on the surface depends on the characteristics and properties of the airborne contaminants. There has been a lot a work, not all of it well documented, on the effect of the surface contribution to absorption of a range of common cleaning fluids. It is sufficient to mention just two examples to give an idea of the problem. Nd:YAG laser rods are commonly coated with a /4 layer of MgF2 to provide an anti-reflection layer. Because of the relative refractive indices of the Nd:YAG (1.83) and the MgF2 (1.38) this should result in a lowreflectance surface (since 1:382 ¼ 1:90 and reflection theory says that this combination should yield a reflectance as low as 0.04%). An experiment was carried out to check this value and a reflectance of nearly 1% was measured on a nominally clean anti-reflection-coated rod. The rod was recleaned and the reflectance re-measured, four times in all, before the ‘correct’ reflection value was achieved. A second example, which has been more thoroughly documented, was the measurement of the surface contribution to the absorption for a germanium substrate (Wood et al 1982e). This work reported the results of a series of absorption measurements of germanium, zinc selenide and copper mirrors in air and under evacuated conditions. It was shown that both germanium and zinc selenide absorb water vapour, and then exhibit a higher absorption, whilst the copper mirrors were more stable. The results for germanium were followed up by a more exhaustive study of the absorption as a function of the material resistivity. This study not only showed that the water vapour could be pulled off under vacuum but that it could be absorbed again almost instantaneously if ambient air was reintroduced into the measurement chamber (see figure 7.1). Even under perfect conditions it is necessary to realize that air breakdown can occur. This sometimes shields the crystal surface from the 157

158

Special topics

Figure 7.1. Absorption coefficient of n-type germanium as a function of resistivity under ambient and vacuum conditions.

effects of the focused laser beam (for example, when the beam is focused to a point in front of the component surface) or can help initiate damage to that surface by supplying ionized species. Laser-induced gas breakdown consists of three steps, preionization, ionization growth and absorption. Preionization can be externally supplied (electric field), induced (by heating particulates, dust etc.) or by photo-ionization. Direct photoionization is most probable in the visible/near infrared (Milam 1976) whilst thermal mechanisms are dominant at 10.6 mm. Ionization growth occurs by impact ionization and can proceed only once an initial charge is supplied. The number of initial electrons will grow exponentially at a rate which is linearly dependent on the intensity and the ionization potential and inversely dependent on the pressure and the pulse duration. Absorption occurs when the electron concentration exceeds a critical density of about 1018 cm3 (see section 4.3.1). Linear absorption becomes dominant for long-duration pulses, for continuous wave (cw) beams and for wavelengths near absorption maxima. Air breakdown occurs at electric field strengths of the order of 5 108 V m1 (Maissel and Glang 1970, Fradin and Bass 1973a). This value translates to somewhere between 1 and 104 MW mm2 depending on the wavelength of the irradiation. Figure 7.2 shows a typical curve indicating the relationship between the laser-induced air-breakdown power and the laser wavelength (Woskoboinikow et al 1978, Wood 1986). For moderate pressures the breakdown threshold increases as the pressure decreases (figure 7.3). At low pressures direct photo-ionization (which depends on

Ambient atmosphere/gases

159

Figure 7.2. Variation of laser-induced air breakdown with laser wavelength (Woskoboinikow et al 1978).

the pulse duration) becomes dominant over cascade ionization and the threshold ceases to rise as the pressure is further reduced. This is because the photo-ionization rate is only weakly dependent on pressure. At high pressures the breakdown threshold increases as the mean time between collisions becomes less. The statistical distribution of breakdown times of gas volumes irradiated with square waveform pulses has been shown (Milam et al 1975)

Figure 7.3. Air breakdown, energy density versus pulse width and air pressure (Musal 1980).

160

Special topics

to account for the probability that initial electrons are produced by photoionization. This work indicated that the probability of breakdown increased and the breakdown time decreased with increasing laser input power. The relationship for threshold flux for non-equilibrium electron cascade in air is 6 2 10 fbda ¼ PD ¼ C MW mm2 ð7:1Þ where C 15 for air at N.T.P. and becomes asymptotic when 6 2 10 fbda ¼ P1 J cm2

ð7:2Þ

where P is the ambient air pressure (in atmospheres). This fluence is expressed as an increment because it must be provided after the initial electrons are produced. The threshold flux for non-equilibrium electron cascade in a metal vapour is given by C 102 for a metal vapour and becomes asymptotic when 6 2 10 V fbdv ¼ J cm2 P1 I ð7:3Þ I A where I V=I A 0:5 if rotational and vibrational sinks are not present. A graph of the energy versus spot size for air breakdown under 10.6 mm irradiation is shown in figure 7.4. It will be realized from the discussion in chapter 4 that this effect will be both wavelength and pulselength dependent. Graphs showing the variation of laser-induced air breakdown with laser wavelength (Woskoboinikow et al 1978) and versus pulse width and air pressure (Musal 1980) are shown in figures 7.2 and 7.3 respectively. It must be realized that these values only apply to the conditions applying at the time since the humidity, and other airborne materials, affects the breakdown value. The electron temperature is determined by losses to the translational and electronic excitation modes of the heavy particles. This allows much higher electron temperatures to be reached at much lower incident laser fluxes. The threshold for non-equilibrium electron cascade is therefore lower. This can be seen by reference to figure 7.3, where graphs of gas breakdown fluxes versus pressure are plotted. If an electronegative gas is mixed with the air the LIDT increases for pulselengths longer than 100 ns (Volkin 1981). It has also been shown that in the medium-pressure region the breakdown field for air varies as ED ¼ ðHV 1 þ CÞ 1=4

ð7:4Þ

where H and C are material-dependent constants and V is the focal volume (Van Stryland et al 1980).

Liquids

161

Figure 7.4. Energy versus spot size for air breakdown, 10.6 mm.

A graph of the energy versus spot radius for observed plasma formation is given in figure 7.4. These measurements were made under moderatehumidity conditions. The energy and power densities necessary to cause plasma formation would be higher under lower-humidity conditions. The air breakdown threshold may well be less than the LIDT levels of many dielectrics for pulse durations of less than 10 ns. In addition the air breakdown threshold is still less than the melt threshold for most metals for pulse durations of less than 1 ns (Musal 1980). Air breakdown is therefore the reason why many materials have anomalously high LIDTs at short pulselengths. Air breakdown is commonly observed, at both 1.06 and 10.6 mm, on the surface of irradiated samples without any visible evidence of damage. Repeated irradiation, however, usually leads to electrostatic charges building up on the irradiated surfaces followed by microscopically small visible damage.

7.2

Liquids

The laser-induced breakdown power, PD , for liquids has been shown (Soileau et al 1980) to be proportional to 1=n2 (where n2 is the nonlinear index of refraction). This is because the power-dependent nonlinear susceptibility, 3 , leads to self-focusing and catastrophic beam collapse. The equation for the least power required for catastrophic self-focusing is PD ðminÞ ¼

3:27 c2 : n2 322

ð7:5Þ

162

Special topics

The refractive index of a medium may be expressed as n ¼ n0 þ n2 hEi2 ¼ n0 þ n2 I

ð7:6Þ

where hEi is the time average of the electric field, n0 is the linear index, n2 is the total nonlinear index, and I is the optical beam intensity. The value of n2 is given by n2 ¼ ne2 þ nn2 ¼

12 Re½ð3Þ ð!; !; !; !Þ n0

ð7:7Þ

where ! is the laser angular frequency and Re[ ] is the real part of n2 . Therefore I¼

n0 hEi2 4c

and

¼ ð4:19 103 Þ

n2 n0

ð7:8Þ

where is the power-dependent nonlinear coefficient of the refractive index. It will be noted from equation (7.7) that two major effects account for the third-order nonlinearity in solids and liquids: ne2 , the electronic contribution due to the nonlinear distortion of the electronic clouds around the nucleus, and nn2 , the nuclear contribution due to the nuclei as they attempt to minimize the total matter–field interaction (Brown et al 1979). Both these mechanisms are extremely fast (less than 1012 s). The electronic contribution is given by ne2 ¼

Kðn0 1Þðn20 þ 2Þ2 vd f1:517 þ ½ðn20 þ 2Þðn0 þ 1Þvd =6n0 g1=2

ð7:9Þ

where vd is the Abbe´ value of the Na ‘d’ line and K is a normalization constant. The Abbe´ value is given by vd ¼

nd 1 nf nc

ð7:10Þ

where nd , nf , nc are the linear indices at d ¼ 5876, f ¼ 5861 and c ¼ 6563 A˚ respectively. It is possible to calculate the value of ne2 from equation (7.9) by measuring nd , nf and nc using a refractometer. K may be measured by a least-squares fit to experimental data, although a value of K ¼ 101:5 has been used for benzene (Brown et al 1979) as a general approximation. The nuclear contribution, nn2 , is more difficult to quantify. However, it has been shown (Hellwarth 1977) that it is possible to write 2 3 þ A0 þ B0 n2 ¼ ð7:11Þ n0 4

163

Photodetectors

Table 7.1. Measured (M) and calculated (C) breakdown thresholds and nonlinear refractive indices for liquids.

Liquid Carbon disulphide Nitrobenzene Chlorobenzene Bromobenzene Benzene Toluene -Chloronaphthalene Carbon tetrachloride 1-Bromonaphthalene

PD (kW)

P1 N2 n2 1020 ne2 1020 nn2 1020 D normalized normalized (m2 V2 ) (m2 V2 ) (m2 V2 )

14 M 25 M 35 M 36 M 51 M 54 M 13.4 C

1.0 0.56 0.40 0.39 0.27 0.26 –

1.0 0.52 0.34 0.34 0.20 0.19 0.96 C

1.07 M – – – 0.19 M 0.29 M 1.03 M

0.13 M – – – 0.05 M 0.05 M 0.91 M

0.94 – – – 0.16 0.23 0.13

0.26 C –

0.02 C

0.02 M

0.06 M

0.04 M

–

–

–

0.15 M

–

M

M M M

–

where , A0 and B0 are Born–Oppenheimer coefficients which describe the electronic () and nuclear contributions such that ne2 ¼

3 2n0

and

nn2 ¼

2 4B0 ðA0 þ B0 Þ : n0 3n0

ð7:12Þ

This paper derived values for B0 for a variety of liquids from Raman scattering data. However, it is usually easier to measure the total nonlinear index and subtract the electronic contribution. Shen (1966) measured the critical breakdown power for a series of nonlinear liquids and showed that the P1 D / n2 relationship held (see table 7.1). Soileau et al (1980) built on these results and showed that the relationship held for combinations of miscible liquids as well as for neat liquids.

7.3

Photodetectors

The thermally dominated LIDTs of all materials vary with wavelength because of variations in the absorption spectrum of the materials. For example, there is a factor of three increase in the experimentally measured LIDTs of GaAs between the ruby (0.694 mm) and the CO2 (10.6 mm) laser wavelengths (Smith 1973). This study also showed that p-type material damaged in the bulk at lower irradiance levels than did n-type material, which damaged at the surface. This was consistent with the fact that the p-type material had a considerably higher absorption coefficient than the n-type material. Laser-induced damage to photodetectors is therefore expected to be closely associated with thermal effects. It should, however,

164

Special topics

Figure 7.5. LIDT—photovoltaic effect in CMT (Bartoli et al 1975).

be noted that migration of defects and peak current effects have also been noted. In a typical detection system the photodetector has a considerably higher absorption than its associated lens, window and components. The photodetector LIDTs are therefore low compared with the rest of the system components. There is a well-documented trend in all semiconductor materials (Bartoli et al 1975, 1976) which goes from average energy density at short laser pulse lengths to constant power density at long-pulse and cw regimes (see figure 7.5). This behaviour is associated with thermal conductivity and diffusivity and is in line with the theory presented in chapter 4. Bartoli et al (1975) formulated an expression for this dependence PD ¼ ET

1 ð2Þ1=2 k þ R tan1 ð8k=r2 Þ1=2

ð7:13Þ

where ET is the energy density required to raise the crystal surface to the melting temperature. Assuming that the thermal conduction is negligible this is given by ET ¼ ðTm Ta Þ C =ð1 RÞ

ð7:14Þ

where is the density, C is the specific heat, is the depth of material heated in the absence of thermal conduction, R is the reflectance, k is the thermal conductivity, r is the radius of the laser beam, Tm is the melting

Fibre optics

165

temperature—the nonlinear absorption threshold (see chapter 3), and Ta is the ambient temperature. This analysis differs from that presented in chapter 4 in that although the radiation penetrates a reasonable distance into the crystal (in contrast to the metal mirror situation) the absorbed energy is sharply non-uniform (in contrast to the window substrate case). It has been shown (Guiliani 1973) that pulsed laser damage occurs when intense heating by the laser partially destroys or disrupts the surface of the p–n junction. As damage occurs the dark current rises and the diffusion length drops, along with the photoconductive gain. The dark current rise is associated with the surface recombination effect and the electrical conductivity across the junction increases as the junction is degraded. Laser-induced damage is associated with an increase in the number of surface recombination or defect centres. Damage to the electrodes and contacts (giving rise to an open circuit) can be induced either by direct irradiation or by inducing very high photocurrents. Cw laser-induced damage in semiconductors has been concluded to be dominated by parametric instability (Gulati and Grannemann 1976) in solid-state plasmas. The intense laser beam interacts nonlinearly with the electron plasma, resulting in anomalous absorption and heating of the sample with subsequent lattice damage. This results in an increase in the resistivity along with an decrease in the carrier mobility, carrier concentration and photoconductive gain. There is a small body of evidence to show that the photoconductive gain can increase (due to laser annealing of the photoconducting crystal) at irradiance levels immediately lower than the LIDT. In contrast to this there is also evidence that in all but the highest-quality crystal lattices, impurities, defects etc. are mobile and are swept towards the output surfaces of the photodetector with a consequent degradation of the junction. In the infrared, photodetectors frequently employ semiconducting windows or lenses in front of the detector surface. It has been shown that there is a likelihood of this surface distorting under the high-power irradiation and spreading the beam across the photodetector rather than focusing it on the detection element. This has been shown to be the cause of photodetectors showing anomolously high LIDTs together, when it occurs, with extremely catastrophic damage morphology.

7.4

Fibre optics

There is a growing requirement for high-power laser beams, both pulsed and cw, to be delivered from a laser to a remote workpiece or workstation via a fibre optic cable (figure 7.6). The power and energy handling capabilities of fibre optic cables are affected by both linear and nonlinear effects, any inhomogeneity in the

166

Special topics

Figure 7.6. Fibre-optic schematic.

fibre and, in particular, the surface finish of the input and output faces of the fibre itself. The power handling capacity is almost always limited by the LIDT of the input and output faces. The maximum power/energy that can be transmitted down an optical fibre is dependent upon the launch and output delivery conditions, the input laser beam divergence, the focusing arrangements, the finish of the fibre ends, the position of the focus within the fibre, Rayleigh scattering, Brillouin scattering, Raman scattering, self-focusing, and laser-induced damage of the end faces and the bulk material. In practice it has been found that the best end treatment is diamond cleaving, followed where necessary by either polishing with 0.1 mm diamond powder or 10.6 mm CO2 laser annealing. The fibre end perfection specification is directly related to the peak power density that can be launched into the fibre and also affects the minimum output divergence which can be obtained (Wood 1996b). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin1 ¼ NA ¼ n2 n2c ; ð7:15Þ i.e. is the angle at which total internal reflection occurs (the maximum input divergence which can be maintained inside the fibre). In a straight fibre the input divergence, , may be maintained. In a coiled fibre the numerical aperture (NA) controls the output divergence, i.e. =d < < where =d is the diffraction limit. In a coiled fibre the output energy/power is evenly distributed across the fibre aperture. This results in the fact that if the input end of the fibre does not damage at a particular laser input then the fibre should be able to handle that power without damaging. It can also be used to provide a circular ‘top hat’ uniform energy density profile. The transmission through an optical fibre can be seen to be both a function of the fibre length (Itoh et al 1983) and of the bending of the fibre (Boechat et al 1991). The bending, which results in beam homogenization,

Fibre optics

167

Figure 7.7. Plot of output power density and pulse width as a function of fibre length (Itoh et al 1983).

also affects the pulse width, as does the power transmitted through the fibre (see figure 7.7 and figures 7.8(a)–(c)). It must be remembered that although the process of transmission homogenizes the beam the bulk damage threshold may be lowered due to the following.

(a)

Figure 7.8. (a) Theoretical and practical bend loss as a function of bend radius and core diameter (Boechat et al 1991). HCS fibres with an NA of 0.37, 100% filling, L ¼ 6 m, and core diameters of 200, 400, 600 and 1000 mm.

168

Special topics

(b)

(c)

Figure 7.8. (b) Theoretical and practical bend loss as a function of fibre numerical aperture. Fibre core diameter, 600 mm, fibre length 6 m. HCS fibre, NA ¼ 0:37 and allsilica fibre, NA ¼ 0:22. (c) Theoretical and practical bend loss as a function of launching condition (NA). HCS fibre, core diameter 600 mm, fibre length 6 m. Input numerical apertures of 0.28, 0.32, 0.37.

Enhancement of the power due to reflections from the rear surface of the fibre. This is usually minimized by anti-reflection coatings or index-matching. Raman scattering. Again the threshold is proportional to cross-sectional area and inversely proportional to fibre length and the length is therefore more critical than the diameter (see section 3.2).

Fibre optics

169

Brillouin scattering. The SBS threshold is proportional to the fibre crosssectional area and inversely proportional to the fibre length. This means that this mechanism will be more likely to be present in long runs of fibre rather than by a decrease of the fibre diameter (see section 3.3). Self-focusing. This mechanism is inversely proportional to the secondorder power-dependent refractive index and not to either the cross-sectional area or the fibre length. In practice this effect will either occur in short lengths of fibre or not at all, assuming that the critical interaction length is great enough to be neutralized by the beam homogenization due to fibre bending. The theoretical and measured input surface damage thresholds for silica have already been shown in figures 4.11, 4.12 and 4.13 as a function of the laser spot size and the pulse length. It will be noted that the damage mechanism gradually changes from being power dependent to linear power density dependent as the pulse length increases. However, as most fibre

Figure 7.9. Maximum power handling capacity of glass fibre power versus fibre diameter and pulse length.

170

Special topics

optic applications are cw or high prf (irrespective of the pulse length) the relevant LIDT is constant if expressed in terms of W cm1 . However, as the fibre constrains the radiation into definite spatial cross-sectional areas it is also relevant to plot the graph in terms of power handling capability (W) for ease of reference (figure 7.9). The powers shown in this graph are therefore the maximum powers that can be inserted into the fibre and are therefore the maximum powers that can be transmitted through the different diameter fibres.

7.5

Scaling laws

For any material there will be a variation in the measured value because of physical factors, variability due to statistical factors and differences due to laboratory measurement procedures. Variations in the LIDTs are explained by well-understood physical laws, as listed in table 7.2. It is not too late to reiterate the comment that although there are pulse length regimes where the LIDT may be expressed as a constant if quoted in either J cm2 (constant energy density) or W cm1 (constant linear power density), there are none where the LIDT can be expressed as a constant power density (W cm2 ). This is not well understood by the measurement community because, using a particular laser system, the power density is the easiest parameter to measure. Measurements have therefore been historically quoted in terms of peak power density. This is alright as long as measurements made at the same wavelength and pulse length are scaled to take the differences in pulse length and spot size into account. However, it has become normal to quote just the peak power densities without quoting the other parameters. It is generally agreed that scaling is likely to be flawed if carried out over a wide pulse length range. Table 7.2. LIDT /

Dielectric breakdown

Thermal effect

Pulse length, Wavelength, Spot size, b Ambient temperature, A Laser prf Sample absorptance, A Sample properties Surface finish

1=2 1=2 b2 – – – – f ðn; Þ

f ðÞ b1 M A eK f ðÞ f ð; Þ

Depends on units and changes with pulse length regime (see chapter 2).

Scaling laws

171

The variability of the LIDT of a material or component in a given experimental or practical situation is mainly due to statistical factors. These factors include such things as the sample spatial and temporal variation (i.e. defect density and distribution, or scratch density and geometry), and any laser beam non-uniformity These factors decrease the LIDT below that calculated from knowledge of the physical characteristics of the material and of the laser operating parameters. The variability of the bulk material cannot usually be changed (except in some cases by laser annealing). The surface characteristics of an optical component, on the other hand, can have a marked effect on the LIDT. Much research has been done, and still is being done, on the improvement of the surface quality and finish. It must be remembered that the surface finish specification must, if any credence is to be put on it, be tied to the application, and particularly to the wavelength. Coatings may improve the optical performance of the component or system, but also it must be remembered that although a coating may hide blemishes, scratches and digs, they are only hiding under the surface and will interact with the radiation. In general, any surface feature only degrades the optical performance. Most laser measurements are made using good single-mode laser beams. However, it must be realized that most practical/industrial systems are maximized more for the total energy output than for a single fundamental mode. If the modes are mixed, then the peak power density may be well above the power density measured using a simple 1=e2 measurement and laser-induced damage may occur at seemingly low peak power/energy densities. It is recommended that, particularly when using multi-mode systems, the local peak power/energy density be measured. The differences reported, between similar or identical samples, on the LIDTs measured by different testing laboratories are usually due to differences in procedure in those laboratories. These differences may be summarized as being due to inaccurate measurement of the power/energy, to differences in the ambient atmosphere, to cleaning procedures and to strain due to mounting the component in the sample holder/optical system. It may seem obvious that only if we all use the same standard measurement units can we hope to make repeatable measurements. However, there have been many occasions where measurements made in different laboratories have been found to differ because somewhere in the measurement chain the calibrations and/or the measurements have been different. In the past, there were problems in transferring calibrations from the various National Standards Laboratories to the measurement laboratories. In the 1970s, for instance, although the National Physical Laboratory, Teddington, UK, and the US National Bureau of Standards, Boulder, Colorado, agreed in their measurement of the Joule to within a fraction of a per cent, measurements made on a particular item of equipment were shown to be out by a factor of two between measurements made at two

172

Special topics

laboratories, both of which had calibrations directly traceable to the Standards Laboratories. The problem in this particular case was found to be due to the differences in the measurement procedure and the fact that one of the secondary standards was essentially a power measurement device and the other an energy measurement device. On the other hand, where the calibrations have been cross-checked and found to be consistent, repeatable measurements of the LIDT of a range of components have been made. This stricture applies as much to the calibration of the measurement system as to the measurement applying to the whole beam. For example, many lasers have very wide, low-power, sidelobes. If calculations are made without ascertaining that all the beam is included when the power density is measured, while the energy is measured using an integrating type instrument which does collect and measure all the beam, then the calculation of the peak power density will be wrong. It is particularly necessary for the measurement system to be able to measure both temporal and spatial non-uniformity in the measurement beams. It was observed in chapters 5, 6 and 7 that both the component cleaning procedure and the ambient atmosphere could affect the LIDT of some components. For example, temperature directly affects the measurement of the LIDT of components in regimes where the LIDT is thermally dependent (e.g. metal mirrors). This is why most metal mirrors are heat-sunk and in the case of very high-power lasers, back-cooled. In the case of most transmitting infrared components, the problem of thermal runaway arises at some elevated temperature and this can be directly affected by the ambient temperature. The relative humidity and/or the thermal properties of the ambient atmosphere can also affect the absorption/transmission of the optical components and eventually the LIDT. It must be realized that it may be irrelevant to make R=T=A=S measurements under vacuum conditions if the component is to be used in a system that is exposed to the atmosphere. As an aside, there is a long-standing joke between the measurement laboratories in the USA that halide mirrors are perfectly acceptable on the West coast, but are only fit for flavouring food on the East coast. This is particularly pertinent in the infrared where water vapour absorbs appreciable amounts of radiation. It has been shown that not only do most infrared substrates absorb water vapour, but that this water vapour can be pulled off under vacuum conditions and will gradually be absorbed when the substrate is exposed to water vapour once more. Even cleaning can change the surface state of a substrate. The irradiation history of a surface affects the state of that surface and the subsequent optical properties of that surface e.g. the absorption measured. It has only been relatively recently been demonstrated, although theoretically known for over 30 years, that the component mount directly affects the transmitting properties and eventually the LIDT of an optical component. This is particularly marked in crystalline and polycrystalline components (e.g. germanium, zinc selenide and the halides). The mechanical

Scaling laws

173

strain imparted by the mount can be augmented by the thermal strain induced by the absorbed laser radiation and can reduce the LIDT markedly. Component mounting has been found to be a prime bone of contention between industrial laser users and the component polishers and suppliers. Care must be taken to ensure that mounting the optical component in a high-power beam induces as little stress as possible. As was shown in chapter 4 there are no cases where the LIDT can be quoted as being constant irrespective of material, wavelength, pulse length, or spot size. There are ultra-short-pulse regimes, where multiphoton avalanche is initiated, when the LIDT can be quoted in terms of peak power, W, irrespective of the focused spot size. There are short-pulse regimes, when the LIDT is thermally dominated, where the LIDT, of a particular material at a specified wavelength, can be expressed in terms of a constant energy density, J cm2 . There are regimes (long pulse and cw) where the LIDT can be expressed in terms of a constant linear power density, W cm1 , irrespective of the laser spot size. There are no regimes where the LIDT can be expressed in terms of a constant peak power density, W cm2 , irrespective of the laser spot size.

Figure 7.10. Measured, bulk LIDT: diamond versus wavelength. Scaled and enhanced to 100 mm 1=e spot size.

174 7.5.1

Special topics Variation of damage threshold with wavelength

Davit (1968) derived a set of equations correlating the LIDT with the wavelength of the intermediate excitation absorption and the fluorescent lifetime of this absorption peak. In the region < 5te LIDT / b1 ; 1=2 :

ð7:16Þ

This relationship has been found to hold for both laser glass and diamond windows (Wood 1994) (see figure 7.10).

7.6

Significance of the units of measurement

Because most people make measurements using a constant spot size and at a constant pulse length, many data are expressed in terms of W cm2 . There is therefore a common perception that these values can be taken irrespective of the spot size and pulse length and compared directly. This is not true and care must therefore be taken in comparing values obtained by other workers and the appropriate scaling laws must be applied. It must be realized that unless the correct units of measurement are used then not only will the correct correlations be hidden but there may be a safety or health hazard when measurements and values gained at one spot size are compared with those expected at a different spot size. A simple example of the reason for quoting the LIDTs in the correct units of measurement for the pulse length may be taken from the literature (Greening 1997). This paper reported the results of a series of damage measurements made to check the variation of the LIDT with the damage test spot diameter. These measurements were made using a cw CO2 laser and measuring the power in the beam which initiated damage as a function of the laser spot size. The workers had not realized that for cw beams the power at which damage occurred was not scaleable in terms of power density and were most surprised to find that the only correlation they could find was that of a constant LIDT when expressed in terms of the linear power density (see table 7.3). Table 7.3. CW LIDT for ZnSe, measured using a cw 10.6 mm CO2 laser. Laser power (W)

Spot diameter (mm)

LIDT (W mm1 )

LIDT (kW cm2 )

200 400 828 5000

0.067 0.133 0.276 1.66

3000 3000 3000 3000

5673 2879 1384 231

175

Significance of the units of measurement

Table 7.4. Example 1. Beryllium mirrors have been measured as being able to withstand 56 W of 10.6 mm cw laser power from a 0.33 mm ‘top hat’ CO2 laser. This can be expressed as 1700 W cm1 or as 65 W cm2 . Spot diameter (mm)

Maximum safe power (W) using 1700 W cm1

Maximum safe power (W) using 65 W cm2

Power above LIDT

0.33 0.5 1.0 5.0 10.0

56 85 170 850 1700

56 127 510 12 763 51 050

1 1.5 3 15 30

Examples of how the use of the wrong units can lead to dangerous scenarios are in extrapolating the LIDTs of hazardous materials (e.g. Be, ZnSe, GaAs, ThF4 ) and in the use of laser screens (Wood 1997). Table 7.4 outlines the case where a beryllium mirror was measured as being able to withstand 56 W of CO2 laser power. On questioning the manufacturer it was explained that this had been measured using a 0.33 mm ‘top hat’ beam. Calculation shows that, using this spot size, the LIDT of the beryllium mirror was 65 W cm2 . If this level of irradiation was used to define the ‘safe level’ of irradiation for a beryllium mirror for larger-diameter beams we see, from table 7.4 (column 3), that the levels are reasonable and that present designs of cw CO2 lasers do not reach these power densities at these beam diameters. If, however, the 56 W in a 0.33 mm diameter beam is expressed as 1700 W cm1 we then see that the maximum ‘safe powers’ which could be used with this beryllium mirror are those listed in column 2 of table 7.4. It will be realized by those who know the present capabilities of cw CO2 lasers that these powers are capable of being generated at the appropriate Table 7.5. Example 2. Calculation of the LIDT of a typical laser safety screen, based on a measured value of Y W cw radiation in a 0.33 mm diameter spot. The true LIDT is 30Y W cm1 whereas the commonly quoted value would be 1170Y W cm2 . Maximum safe power Spot (W) using diameter 30Y (mm) (W cm1 )

Safe power (W) using 1799Y Col 3/2 (W cm2 ) threshold

Real safe power density (W cm2 )

Approx. thermal diffusion limit (s)

Real safe energy Safe density energy (J cm2 ) (J)

0.1 0.33 1.0 10 100

0.092Y Y 9.2Y 920Y 92 000Y

3820Y 1170Y 382Y 38Y 3.8Y

104 3:3 104 103 102 101

0.38Y 0.38Y 0.38Y 0.38Y 0.38Y

0.3Y Y 3Y 30Y 300Y

0.3 1 3 30 300

3 105 Y 3:3 104 Y 3 103 Y 3 101 Y 30Y

176

Special topics

diameter outputs. Column 4 shows how much above the real threshold the use of the units of W cm2 instead of W cm1 has led us. Table 7.5 shows how the use of the wrong units allows the experimenter to gain an optimistic idea of the degree of safety given by a typical laser safety screen. Based on a measured value of (say) Y W cw radiation in a 0.33 mm diameter spot the ‘true’ LIDT is 30Y W cm1 whereas the use of power density, W cm2 , gives a value of 1799Y W cm2 .

Chapter 8 Measurement techniques 8.1

Introduction

In the 1970s, when data on the laser-induced damage thresholds (LIDTs) of optical materials were being published for the first time, the range of values measured for even high quality materials varied markedly. A collation of the LIDTs of high quality fused silica (appendix 2; Wood et al 1975) showed that there was a published variation of about 103 . These values were investigated and the conclusion was reached that although all the values were genuine the workers had not given enough data on the parameters used to allow a meaningful comparison to take place. The measurement and reporting of three areas of parameters were concluded to be suspect. The first was the measurement of the pulse energy delivered to the sample under investigation. At that time there was a severe difference between calibration of energy measurement devices across the world. The second area was in the measurement, and particularly the reporting, of the focused beam spatial and temporal beam profiles. The third area was in the measurement and reporting of the component characteristics. Even cross-laboratory comparisons, with two or more laboratories making measurements on the same samples, have yielded differences outside the expected error limits. When these differences have been investigated it has usually been found that differences in the measurement procedure have proved critically important (Guenther 1984a–c). The lessons of measurement history are therefore that only if all the relevant parameters are known and controlled, and the same measurement procedures undertaken, can the measurements be relied upon. It is necessary therefore for research workers, the component suppliers and the customers to agree not only on the specification of the components but also on the methods of measurement in order to enable the quality of the components to be ascertained. Even then it is necessary for the two measurement systems to gain data using the agreed procedure and to agree before the measurement systems can be used to settle disputes etc. There are numerous occasions where component suppliers and their customers disagree about the quality of the components supplied. This is 177

178

Measurement techniques

usually because the specification is flawed and/or incorrect for the application. Most specifications are written in terms of parameters that can be measured. However, this does not mean that all of the parameters are necessary or that all of the necessary parameters are specified. Many laser applications depend on a high degree of definition of the laser parameters and as the subject matures the precise parameters of importance are gradually being recognized. It is also vitally necessary for common terminology to be used, for standard techniques to be used and for standard procedures to be followed. When this has been done, very good agreement has been gained between measurements made on identical materials in a variety of different laboratories. The writing and proving of standards can be a lengthy process. Each industrialized country has set up standards institutes (ASTM, BSI, DIN, UNM, etc.) to help the process along and international cooperation has been encouraged by such organizations as ISO, IEEC and CEN. These international bodies have split the responsibility for the range of standards on particular subjects between them so as not to duplicate effort. The field of optics and optical instruments, and in particular lasers and laser-related equipment, has been allocated to ISO/TC 172. This committee comprises technical experts from each country in membership with ISO. In general the individual countries usually have a shadow committee of experts in the field as well as a designated expert to each ISO working group. When published the standards can be bought from any of the aforementioned institutes. ISO/TC 172 have drafted a number of International Standards that define the recommended measurement procedures for a range of relevant parameters. Many of these standards have recently been completed or are in the last stages of being drafted. The following sections include summaries of the standards relevant to the specification of laser-related optical components and to the measurement procedures related to the parameters critical to the power handling capacity of optical components.

8.2

Measurement of power, power density, energy and energy density

Before it is possible to measure and to quote values for the LIDTs of optical materials it is necessary to ensure that the laser-based measurement will be able to measure traceable and reproducible values. In order to do this it is necessary to: 1. Specify the conditions of measurement so that they can be reproduced elsewhere. This includes information on the sample source, dimensions and any pertinent material parameters, handling, cleaning and mounting procedures.


179

2. Careful and unambiguous measurement of the LIDT by characterizing the laser pulse. This includes: measuring the energy in the laser pulse; measurement of the peak power in the laser pulse; statement of the focusing conditions; measurement of the laser spot size; measurement of the laser beam spatial profile variation at the sample; the temporal characteristics of the pulse; any cumulative and/or pulse repetition frequency parameters. 3. Apply, and state, an agreed definition of laser-induced damage. Monitor the moment and appearance of laser-induced damage. This may include: monitoring the presence of plasma spark formation; visible microscopic damage; variation in the transmittance of the sample; change of sensitivity of an active detector device. 4. Assess the cause of damage so that the values measured can be quoted in the correct units of measurement. This will ensure that cross comparisons can be made with other workers. In order to measure the LIDT of a material or component it is necessary to measure the minimum irradiance under which the material damages. This may be (see chapter 4) dependent upon the peak energy density Hmax expressed in J cm2 , the instantaneous power P expressed in W, or the linear power density F expressed in W cm1 , depending on the irradiation time. It was shown in chapter 4 that there are no pulse length regimes over which the irradiance should be quoted in terms of the peak power density Emax expressed in W cm2 , irrespective of the pulse length . However, since the peak power density is the most easily measured parameter the majority of measurements have been made in these units. The problem comes in transferring the measurements made in these units to the appropriate units. If all the measurements apply only to the system used in taking the measurements (i.e. same wavelength, pulse length and focusing conditions) there is no problem in using peak power density. The main value in using the peak power density values is that they can yield accurate comparative values without having to measure the other laser parameters. This may be enough in a practical situation, for example, if an engineer wants to know whether a ZnS window can be substituted for a ZnSe window in a particular CO2 laser system. However, problems come when people try to scale their results to other spot size and pulse length systems to predict what the LIDTs of materials would be under different spatial and temporal regimes. In the case of a square pulse (or chopped cw beam) the length of the pulse, , can easily be measured using a fast detector/oscilloscope combination. In the case of a typical triangular Q-switched pulse is the full-width half-maximum (FWHM) width of the pulse. In the case of a more complicated mode structure an effective pulse width, eff , may be defined as H eff ¼ max ð8:1Þ Emax

180


where Hmax is the maximum energy density in the laser spot, J cm2 , Emax is the maximum power density in the laser spot, W cm2 , and Hmax ¼

Q ATeff

ð8:2Þ

where Q is the energy in the pulse and ATeff is the effective area of the spot. In order to complete the calculations it is therefore necessary to measure the area of the laser spot. In the general case the relationship is ATeff ¼

Q d 2 ¼ eff Hmax 4

ð8:3Þ

where deff is the effective diameter of the laser spot. The most difficult part of this analysis is the definition of the effective area of the laser spot. In the case of a circular (diameter d100 ) square topped ‘top-hat’ pulse shape the area is simply given by 2 d100 : 4 In the case of a perfect Gaussian pulse shape x2 I ¼ I0 exp 2 b

AT ¼

AT ¼ 18 b2

ð8:4Þ

ð8:5Þ ð8:6Þ

where b is the beam diameter when I ¼ I0 e2 or AT ¼ !2

ð8:7Þ

where ! is the beam radius when and

I ¼ I0 e1

ð8:8Þ

pffiffiffi b ¼ 2 2 !:

ð8:9Þ

In order to make accurate measurements it is necessary to have the use of a well-characterized laser and to ensure that there are traceable calibration standards so that cross comparisons can be made with other workers. A lot of time and energy has been put into characterizing laser beams which are neither Gaussian nor square topped (for example see the proceedings of the International Workshops on Laser Beam and Optics Characterization—SPIE). Whilst these are incontrovertibly practically experienced beams, the use of such beams is discouraged for characterizing components. This is because any asymmetry in the beam shape makes the measurement of the spatial and temporal profile problematical and sharply varying along the transmission axis. If the beam is single-mode Gaussian or square topped the peak power density and the spatial characteristics can easily be measured at


181

any point along the transmission axis and, as long as the focusing conditions are not too sharp, there is a certain amount of distance along the transmission axis where the beam waist will be parallel and the beam parameters constant. If this can be achieved then one of the largest problems, that of being absolutely sure that the component under measurement is under known test conditions, is solved. As will be recognized from the above definitions the most difficult part of the measurement analysis is the definition of the effective diameter, deff , for laser beams with non-symmetrically circular beams. Although most of the measurements of the laser-induced damage have been made either with square topped or Gaussian pulse shapes the subject of beam asymmetry has long exercised the minds of the laser measurement community (Hall and Stewart 1985, Sasnett and Johnston 1991, Sona 1993, Jones and Scott 1993, Greening 1994). Two descriptive parameters used to characterize a laser beam are the diameter, deff , and the divergence angle, . These parameters have been used to define an analytical expression that relates the beam parameter product, 1=K, and the propagation factor, M 2 . 1 deff ¼ ¼ M2: K 4

ð8:10Þ

The parameters deff and contain 86% of the total beam power emitted at a wavelength . The beam parameter, K, is a number between 0 and 1 and represents the quotient between the beam parameter product for the fundamental Gaussian mode (TEM00 ) and the actual mode of the laser beam under examination. Conversely 1 < M 2 < 1 and M 2 ¼ 1 represents the conditions for a TEM00 mode. Using these definitions the beam diameter can be defined as the full width at the 1=e2 intensity points (near Gaussian beams) or the diameter of a circle enclosing 86% of the power (cylindrical beams) or four times the square root of the second moment of the distribution. The second moment definition is based on statistics and beam propagation theory and is applicable to both Gaussian and non-Gaussian beams. Using the definition of the second moment of the energy density distribution function, Hðx; y; zÞ at location z, ð 1 ð 2 r2 Hðr; ’Þr dr d’ 0 0 2 ðzÞ ¼ ð 1 ð 2 ð8:11Þ Hðr; ’Þr dr d’ 0

0

and the definition of the beam diameter, pffiffiffi d ðzÞ ¼ 2 2 ðzÞ:

ð8:12Þ

182


The effective area can be expressed in the form: (a) For a flat topped ‘top-hat’ beam: 2 ATeff ¼ 14 d100 ¼ 14 d2 ¼ 22

ð8:13Þ

where d100 ¼ d . (b) For a Gaussian beam: ATeff ¼ 18 b2 ¼ 18 D2 ¼ 2

ð8:14Þ

where b ¼ 1=e2 diameter and ¼ d or ATeff ¼ !2 ¼ 14 d2 ¼ 22 pffiffiffi where 2! ¼ d and b ¼ 2 2 !. 8.2.1

ð8:15Þ

Beam divergence and spot size

The relevant ISO standards for this topic are: Optics and optical instruments—Lasers and laser-related equipment— Test methods for laser beam parameters. Beam widths, divergence angle and beam propagation ratios ISO 11146: 1999. ISO 11146-1. Part 1: Stigmatic and simple astigmatic beams. ISO 11146-2. Part 2: General astigmatic beams. ISO/TR 11146-3. Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods. One of the most relevant, but also the hardest to quantify, laser parameters is the spatial profile. While there are some laser beams that are single-mode Gaussian the majority of working laser beams are of less quality and either have ‘skirts’ or side-modes or are ‘multi-mode’. The energy distribution across a good single-mode beam can be accurately quantified in terms of simple geometric parameters such as the 1=e2 beam diameter at the focus of a lens or the laser beam divergence. For most laser beams, however, these parameters are a function of the distance of the measurement plane from the laser output window. One problem that has occurred in practice is that although the intensity of the laser radiation may be low in the skirts of a laser beam the integrated energy may amount to a reasonable fraction of the whole. Any radially symmetric laser beam requires three parameters for full characterization: 1. location of the beam waist, z0 , 2. waist diameter, d0 , 3. far-field divergence angle, .


183

Table 8.1. Correlation factor between alternative measurement methods. Alternative method

ci

Variable aperture Moving knife slit Moving slit

1.14 0.81 0.95

To a first approximation the beam propagates as 2 þ ðz z0 Þ2 2 ; d2 ðzÞ ¼ d0

ð8:16Þ

provided that the second moments of the power (energy) density distribution function are used for the definition of beam widths and divergences. The beam propagation factor, K, or a times-diffraction-limit factor, M 2 , can be derived: K¼

1 4 1 4 1 ¼ 0 ¼ 2 d0 2 nd0 M

ð8:17Þ

where K is the beam propagation factor, M 2 is the times-diffraction-limit factor, 0 is the wavelength in vacuum, is the wavelength in the medium, n is the medium refractive index, is the divergence angle and d0 is the waist diameter. The standard specifies a method for measuring the beam widths, divergence angles and beam propagation factors of laser beams. Three alternative measurement methods are recognized (see table 8.1), but care must be taken in comparing them as the beam propagation factors are not identical and must be corrected to achieve agreement. 1 1 pffiffiffiffiffiffi ¼ M ¼ ci ðMi 1Þ þ 1 ¼ ci pffiffiffiffiffiffi 1 þ 1 ð8:18Þ Ki K where Ki is the beam propagation factor according to method i, Mi is the square root of the times-diffraction-limit parameter and ci is the correlation factor between the alternative method and the standard method. These values have been verified for radially symmetric beams. Substantial agreement has been attained on the principles and practice of measuring the beam widths, beam divergence angles and the beam propagation factor for ‘real’ laser beams. Round-robin measurements have been made during the EU–CHOCLAB programme and good agreement has been reached for good and moderately good beams. However, there is a problem with specifying these parameters when unstable resonator beams and beams which show strong diffraction effects are considered. A summary of some of the alternative methods which have been used for these measurements is given in the following sections.

184 8.2.1.1

Measurement techniques Avizonis’ method

This method, which has been included only for historical reasons, was based on the premise that photographic film exposes uniformly at constant energy density. It was devised by Avizonis et al (1967) for the measurement of the divergence of ruby (Cr3þ :Al2 O3 ) single-shot laser systems. Since the ruby laser output is very temperature sensitive the early laser systems were usually single-shot devices and there could be no reliance on the shot-toshot repeatability of the output beam divergence. A procedure was adopted which allowed a series of photographic exposures with known decreasing intensity to be made on the same plate for a single laser pulse. A schematic diagram of the experimental apparatus is shown in figure 8.1(a). The apparatus consists of a thick beam-splitting plate of known reflectivity at an angle to the input laser beam that is focused on to a film plane set at an angle. The angles of the glass beam splitting plate and the film plane are chosen to compensate for the extra beam path length covered by the multi-reflected beams (as shown in the figure). The laser pulse is fired and a succession of exposures of known decreasing intensity is made on the plate. The diameters of the optically saturated spots then correspond to levels of relative energy density in the focused beam, inversely proportional to the intensity of the exposures. A photograph of the optically saturated spot is shown in figure 8.1(b). A correction has to be made for the elongation of the spots due to the angle of the photographic plate to the beam. Avizonis’ original analysis assumed that the focused laser beam has a Gaussian distribution. The analysis is virtually the same as for the aperture method and is shown in the next section. The method can be used for any distribution although much more detailed analysis is then required. This method has been used by the author to measure the beam divergence of a ruby laser, 0.694 mm, but was found to be less useful for 1.064 mm radiation of the Nd:YAG laser, because the sensitivity and linearity of the exposure curve was not suitable in the infrared.

8.2.1.2

Aperture method

As long as the beam shape is regular and reproducible enough for the user to assume that it will be virtually the same from shot to shot it is possible to use multi-pulse measurements. The method measures the amount of energy, ET , passing through a series of different diameter apertures set at the focus of a lens. A special meter capable of accepting a beam up to at least plus or minus 458 from the normal over an area of 70 mm diameter without change of sensitivity was developed at the GEC Hirst Research Centre for use with this method (see figure 8.2). The large aperture was found to be invaluable in measuring the fraction of the pulse energy which lies in the skirts of typical laser beams.


185

Figure 8.1. (a) Schematic of Avizonis’ method of measurement of beam width In ðmaxÞ ¼ I0 ð1 RÞ2 R2ðn 1Þ . þ ¼ 908 for all path lengths from point P to the film plane. (b) Photograph of optically saturated spot.

The energy transmitted through an aperture of radius r is given by ðr EðrÞ ¼ 2 ED ðrÞ dr ð8:19Þ r¼0

where ED ðrÞ is the energy density and ð E ¼ EðrÞ dr or 2

ED ðrÞ ¼

1 dE : 2r dr

ð8:20Þ

186


Figure 8.2. GEC F series laser energy meter.

The quantity dE=dr may be taken from the graph of E against r and ED ðrÞ may be calculated. The peak energy density must then be deduced by extrapolating EðrÞ against various functions of r (r, r1=2 , r1=3 , etc.) and noting the peak value. Figure 8.3 shows a typical graph of ln½ðE0 ET Þ=E0 versus d 2 . The peak power density of the laser beam may be calculated from this graph by measuring the value of rðbÞ at ðE0 ET Þ=E0 ¼ 0:13 and substituting in the equation P¼

EðrÞpeak 2E ¼ 20 : b

Figure 8.3. Graph of normalized attenuation versus (diameter)2 of aperture.

ð8:21Þ

Measurement of power, power density, energy and energy density 8.2.1.3

187

Knife-edge method

This method, which employs a knife-edge traversed across the laser beam, is principally applicable to the measurement of Gaussian profiles. It can be used for both cw and pulsed laser beams. The Gaussian beam intensity is given by 2 x I ¼ I0 exp 2 ð8:22Þ b where b is the 1=e2 intensity radius. Equation (8.20) has a similar form to the well-tabulated normal frequency function: 2 t =2 ’ðtÞ ¼ exp pffiffiffiffiffiffi : ð8:23Þ 2 This function has been integrated and the values of ’ðxÞ tabulated between various limits (Lindley and Miller 1966, Abramowitz and Stegun 1970) (see figure 8.4(a)). ðx ’ðtÞ dt: ð8:24Þ ’ðxÞ ¼ 1

(a)

(b)

Figure 8.4. (a) Fraction of Gaussian beam transmitted past an edge. (b) Fraction of Gaussian beam transmitted through a centred slit.

188


The fraction transmitted, ET =E ¼ TðxÞ, is equal to ’ð2x=bÞ and for, say, 10% transmission is given by TðxÞ ¼ 0:1;

’ð2x=bÞ ¼ 0:1;

2’=b ¼ 1:28

from figure 8.4(a) when x ¼ 0:64b. Similarly, for 90% transmission, TðxÞ ¼ 0:9;

x ¼ 0:64b:

Therefore for a 10–90% movement of the knife-edge, the distance traversed is equal to 1:28b and hence b can be determined across any plane of the laser beam. Figure 8.4(a) shows the fraction of the Gaussian beam transmitted past a knife-edge. A resolution of 10 mm in moving the knife-edge is easily achievable using a micrometer. If tighter resolution is required it is recommended that a differential transformer probe is used. In this case the resolution can be improved to better than 0.1 mm. One major advantage of this method is that, as it is recommended that both measurements are made by moving the edge in the same direction, no centring of the knife-edge relative to the slit is necessary. In order to eliminate the possibility of damage being done to the knife-edge it is recommended that the knife-edge is gold plated. 8.2.1.4

Slit method

The knife-edge method may be extended by placing two symmetrically placed slits, one either side of the beam centre. It will be seen from the analysis given in the previous section that the transmission through the slits is given by T ¼ 2’ð2x=bÞ 1

ð8:25Þ

where the slits are placed at x and þx. Figure 8.4(b) gives the relationship between the normalized slit width and the transmitted power. If the slit is not placed symmetrically across the beam, the transmission can be obtained from T ¼ ’ð2x1 =bÞ þ ’ð2x2 =bÞ 1

ð8:26Þ

where the edges are now placed at x1 and x2 . In practice, in monitoring a repetitively pulsed laser beam, the measurement is made by measuring the maximum energy passing through a slit of given width and then changing the width and repeating the measurement. 8.2.1.5

Saito’s method

A sophisticated combination of the two methods has been demonstrated by Saito et al (1982). This method consisted of firing the laser at a linear array of circular holes, placed in front of the lens focusing the laser radiation for small spot damage testing. This technique produces a set of different intensity


(a)

189

(b)

Figure 8.5. Spatial profile of laser pulse.

spots, the 1=e2 size of each being negligibly larger than that due to the lens alone. If a photographic plate or a photodiode array is placed at the focus of the lens then the power and energy density can be monitored and calculated as outlined in the previous sections. 8.2.1.6

Linear arrays

An extension of Saito’s method is to make the measurement using a linear array of photodiodes, or similar detectors, and to integrate the energy received at each detector. An oscilloscope trace of such a beam scan, made using a single pulse, is shown in figure 8.5. In order to gain the desired accuracy it is necessary to use at least 20 detectors in line and to transfer the outputs to an accurate monitor/measurement facility. This technique is usually used for large beams as the mark/space ratio of small high-definition arrays may lead to errors. The main advantage of this technique is that the whole measurement can be made on a single pulse. Similarly the calibration (plus any compensation for non-uniform sensitivity across the array) can also be made semi-automatically by monitoring the outputs in a uniform (scatter) field. There are a number of commercial beam profile monitors on the market. In general the only problem with this technique is that not all diode arrays are linear at high power input. This is relatively easily sorted out by measuring the transmittance of a filter under increasingly higher system inputs or by monitoring the shape of the oscilloscope trace using a series of filters of increasingly higher transmittance. If the diodes are nonlinear the beam profile will become increasingly flatter topped. 8.2.1.7

Discussion

Avizonis’ single-pulse photographic method is quick and easy to use once the equipment is set up and has the advantage over all the other methods in that

190


is possible to measure the beam divergence at any azimuthal angle across the beam in a single shot. Photographic methods are therefore useful in showing up irregularities in the beam structure. The method finds its best application in the measurement of pulsed laser radiation in the visible (e.g. ruby or frequency-doubled YAG) because of the poor sensitivity of photographic emulsions in the ultraviolet and the infrared. The multi-shot methods require very little setting up and are easily set up in situ. They have the advantage of measuring the percentage of the beam energy within any given beam divergence. Care must be taken to avoid damage to the slits or edges and to replace them whenever necessary. The laser-induced damage that occurs at the high energy/power densities at the focus of a focused laser spot can be a problem. This can sometimes be overcome by the use of calibrated neutral density filters/attenuators but sometimes requires beam splitting to bring the measured beam down to a safe level. One problem of beam splitting is that it can introduce errors due to polarization effects. The slit method is probably the hardest technique to use but it can be used at high peak powers and for cw irradiance. In practice the focused laser beam from many Q-switched lasers has been found to follow a Gaussian profile down to a radius containing over 95% of the beam energy. It has been shown, using such a near-perfect beam, that most of the techniques can be made to give very similar readings. In the case of multi-mode beams, which are not recommended for high accuracy measurements, it is recommended that the beam propagation factor be measured instead of the beam diameter. 8.2.2

Laser temporal profile

The temporal profile is probably one of the easiest laser parameters to measure although it is also one of the most problematical when it comes to apply. In principle the detector should be fast enough to follow the beam temporal profile and should also operate on the linear section of the detector characteristic. In practice most detectors have a linear characteristic from the detection threshold up to some value at which saturation of the output occurs. Each detector its own range of measurement wavelengths over which it exhibits a linear input/output characteristic. Some detection systems exhibit saturation of the output although the integrated outputs are linear. In this case it is possible to monitor energy but not power above the nonlinear threshold point. As long as the sensitivity of the measuring diode does not change over the power range received, the profile of the pulse can be monitored and/or measured accurately. It is important to ascertain what the linear range of any detector used for a particular application is. Photographs of the oscilloscope traces from a number of pulsed lasers were shown in chapter 4 (see figures 4.1(a)–(h)). These indicate that many, but not all, laser pulses are not symmetrical. These photographs also indicate


191

the necessity of checking that the speed of the detector is fast enough to monitor any laser structure. The main problem with non-triangular pulses, multi-mode pulses and those with tails is that the power, power density, energy and energy density are not easily calculated from a simple measurement of the pulse energy and the FWHM pulse width. 8.2.3

Power, power density/energy and energy density measurement

The relevant ISO Standards are: Optics and optical instruments—Lasers and laser-related equipment— Test methods for laser beam parameters. Power (energy) density distribution. ISO 13694: 2000. Optics and optical instruments—Lasers and laser-related equipment— Test methods for laser beam parameters. Power, energy and temporal characteristics. ISO 11554: 1998. There is a problem with measuring the power/energy density distribution in beams and at the focus of a lens for beams that are not circular, single mode and/or uniform. In particular, pulses that have energy outside the simple main pulse profile regularly cause problems with scaling measurements between measurements made with more perfect pulse shapes. Even measurements made with the same laser system can yield different ratios between materials with different physical and chemical characteristics from those measurements made on the same samples using a simpler beam characteristic. With non-Gaussian beams it is not enough to measure the ratio of the energy inside the 1=e-intensity points and it may even not be enough to measure at the 1=e2 diameter points. In many ‘real’ lasers the fraction of energy outside these points can be large. An M 2 measurement has been proposed which addresses this problem. There has been a longstanding problem with laser energy and power measurement. This was largely solved in the 1980s, but there are still instruments which measure incorrectly (usually measure high). This has been found to be mainly due to nonlinearity in the detector characteristic with increasing power density. The GEC F-, G- and H-series of laser energy meters were developed in the 1970s–1990s as secondary transfer standards and the GEC Hirst Research Centre operated a laser energy meter calibration facility during that period with direct traceability to the National Physical Laboratory, Teddington. These instruments were used worldwide to standardize calibration measurements.

192


Some recent round-robin tests have been made as part of the EU– CHOCLAB programme using a 1 kW CO2 laser. Two instruments showed 95% or R; T < 5%) than those of intermediate values. The calibration standards are a problem at all levels as the value used affects the accuracy if not the sensitivity of the measurement. One useful calibration standard, which can be used across the VNIR, is the reflectance of a pellicle of crystal quartz. This has a 3.7% reflectance per surface, which is constant right across the VNIR. Problems can arise if the wavelength to be monitored/measured is near the band edge of the detector. Most detectors exhibit good temperature stability in the mid-point of their detection range but can then exhibit a large temperature variation at the band edges. For example, silicon photodiodes have excellent stability over a range in the visible (e.g. at 0.6328 mm for He–Ne laser radiation, or at 0.694 mm for ruby laser radiation). However, the sensitivity drops either side of the red (e.g. usually 5% less at 0.532 mm for SHG of Nd:YAG and 10% less at 1.064 mm for Nd:YAG). As the whole sensitivity curve moves with temperature, only the wavelengths at the peak of the sensitivity curve do not change detection sensitivity. At 1.064 mm it is common (but not invariant) for the sensitivity to change by several per cent per 8C. For this reason it is sensible to check the temperature sensitivity of any photodiodes and/or to apply some degree of temperature stabilization or temperature compensation. Another major problem, which must be surmounted before reproducible measurements can be made, is that when coherent radiation is used, constructive and destructive interference effects occur. These effects are especially serious when measuring the characteristics of parallel components. It should be noted that the interference pattern changes with changing viewing angle. It is possible to make an accurate measurement of the wedge

198


angle of an optical flat by this method. This is one of the major reasons for anti-reflection coating most of the ‘non-useful’ surfaces in laser-based optical systems. It is particularly important that any beam splitter used in a measurement rig is anti-reflection coated or is a pellicle. A third design consideration in any measurement system is the diameter of the probe beam. In some cases this consideration clashes with the necessity of minimizing the angle of the focused cone of radiation. All components contain small defects (coatings, pinholes, scratches digs, etc.) and the wider the beam the more defects covered by the beam and therefore the more average a result. In practice variations in reflectance and transmittance across a surface in the region of 0.1 to 0.5% can be measured with spot sizes below 0.5 mm diameter. It is highly unusual for variations to be measured when the probe diameter is greater than 5 mm. 8.4.2

Measurement of absorption

Optics and optical instruments—Lasers and laser-related equipment— Test method for absorptance of optical laser components. ISO 11551: 1997. This standard is available for dissemination and use. Good agreement has been gained at a range of measurement laboratories, particularly for 10.6 mm, CO2 laser components (Ristau et al 1995). This paper summarizes the results of an absorption round-robin (seven different laboratories taking part). There was general agreement between the measurements made at the seven laboratories although it was perhaps significant that the bar charts of the absorption measurements for each sample, when plotted against time, but also in fact plotted against laboratory, all looked remarkably similar. There was also a proven increase of absorption of the components over the measurement period. There is a range of common problems that occur when workers at different laboratories or component suppliers and users try to compare measurements. The ambient atmosphere (temperature, humidity and barometric pressure) affects the absorption measured. It has also been shown that the irradiation time relative to the thermal conductivity of the component material can affect the values measured. It is also known that cleaning procedures can alter the surface absorption. This is, however, not always desirable as it has been shown that some of the reduction of absorption is only temporary and rises over a period of time when the component is exposed to an ambient atmosphere. Measurements made under vacuum and under normal, clean air conditions can be surprisingly different. Any measurement system must include: a laser source which in principle should be well characterized with good stability both in terms of power and pulse length; a calibrated reference or reference sample and a linear detection system.

Measurement of optical characteristics

199

There are several different philosophies of measurement. All the methods irradiate the sample whose absorptance is to be measured and measure the temperature rise. The first approach is to measure the absolute power/ energy input and to then calculate the absolute value of the absorptance. The second approach is to make two measurements, using the same irradiating pulse, to provide a comparative measurement between the sample under examination and a standard sample. The ‘standard’ approach is arguably the more absolute (but can yield wrong values if there are cooling currents, draughts etc.) whilst the other methods are comparative (and thus only as good as the calibration standards) but take any deviations in the pulse temporal characteristics into account. Whichever method is used, care must be taken to eliminate the effects of reflected and scattered radiation. The types of measurement divide into: 1. Pulsed ‘standard’ method 2. Pulsed comparative method 3. Pulsed comparative method 4. Pulsed gradient ‘standard’ method

Short pulse, relatively high irradiation levels Short pulse, relatively high irradiation levels Best when the procedure uses adiabatic calorimetry inside a vacuum apparatus. Should only be used when higher power lasers are unavailable.

5. CW method

The mathematics of the different measurement methods will be described in turn. Pulse methods 1 and 2 These are valid when the test laser has sufficient power to rapidly heat the sample to an easily measured temperature Determine an irradiation time, tB . This must be chosen correctly to ensure that the cooling process does not affect the results, that the sample has time to absorb enough energy to reach a temperature high enough to achieve the accuracy of measurement required, that the peak temperature reached during measurement does not damage the sample under test. 1. Pulsed ‘standard’ method Using the agreed procedure, record the temperature of the component versus time (see figure 8.9). Determine T from the graph. Extrapolate backwards to the temperature at time tB =2. Compute the absorptance using the formula: X mI CI T ¼ ð8:28Þ PtB I

200


Figure 8.9. Temperature versus time plot: pulse method.

where mI and CI are the masses and specific heats, respectively, of the test sample, holder etc. and P is either the cw laser power or the average power for a continuously pumped laser. 2. Comparative pulsed method Using the same basic procedure as for method 1, record the temperatures of both the measurement and the reference samples (see figures 8.10, 8.11 and 8.12). It should be noted that in order to carry this out on a practical basis the sample needs to be held in some sort of holder, which has to be in close thermal contact with the sample whose absorption is required. The thermal probe (thermistor or thermocouple) is fixed to the holder (metal to

Figure 8.10. Schematic of absorption measurement apparatus.


201

Figure 8.11. Schematic of thermistor absorption bridge.

keep the thermal memory correct). The fraction of the beam reaching each component has to be measured accurately. In the case of the measurements made at the GEC Hirst Research Centre (Foley et al 1980, Wood et al 1982a) the beam was deflected on to the sample via the reference standard (a copper mirror). The absorption of this standard mirror was measured before and after each measurement against a Nextel black-painted thin metal cone with the same thermal mass. 3M Nextel velvet-black paint has been shown to have 96% absorption on a flat surface and when painted on to a hollow cone has an absorption value of approximately 100%. It is sensible, in

Figure 8.12. Temperature versus time plot: comparative pulse method.

202


order to simplify the calculation, to provide the system with four identical component mounts (mass mh and specific heat Ch ). The same laser pulse is used to irradiate both the reference and the sample for a timed interval, . The temperature rise, T, is related to the total sample absorption, P, by T ¼

P ms Cs þ mh Ch

ð8:29Þ

where P is the incident power, m is the mass, C is the specific heat and subscripts s and h refer to the sample and holder respectively. The absorption of heat by the sample under measurement (under irradiation conditions, P1 , 1 ) can be written as s ¼

T1 ðms Cs þ mh Ch Þ P1 1

ð8:30Þ

and the absorption of heat by the reference standard (under irradiation conditions, P2 , 2 ) is: ref ¼

T2 ðmr Cr þ mh Ch Þ P2 2

ð8:31Þ

where mr and Cr are the mass and specific heat respectively of the standard absorber. An expression for s may now be obtained: s ¼

ms Cs þ mh Ch T1 P2 2 : mr Cr þ mh Ch T2 P1 1

ð8:32Þ

In the HRC measurement procedure, since the reference absorber acts both as a reference and as a beam deflector, both the sample and the reference are irradiated with the same beam power for an identical length of time (thus eradicating any errors due to laser output variations). That is, P1 ¼ ð1 RÞP2 , where R is the reflectivity of the standard mirror, and 1 ¼ 2 , thus leading to the equation s ¼

ms Cs þ mh Ch T1 1 : mr Cr þ mh Ch T2 1 R r

ð8:33Þ

The temperatures T1 and T2 are monitored in terms of voltages developed across thermistors embedded in the sample and reference holders. These outputs may be plotted directly using an x–y plotter (see figure 8.10). The cooling curve needs to be back-extrapolated until a time half way through the pulse for greatest accuracy. The temperature excursions T1 and T2 should be kept well below 0.1 8C to avoid the necessity of making cooling corrections. Differences in the thermistor sensitivities, and hence the exact temperatures reached, are negated by making a second set of measurements, replacing the sample by a standard 100% absorbing


203

sample. This leads to another equation: 100% A ¼

mc Cc þ mh Ch T3 1 : mr Cr þ mh Ch T4 1 R ref

ð8:34Þ

This leads to the final equation: s ¼

ms Cs þ mh Ch T1 T4 100%: mc Cc þ mc Cc T2 T3

ð8:35Þ

As most of the quantities appearing on the right-hand side of equation (8.33) are relative and the masses of the holders and the samples under investigation can be measured accurately, the sample absorption is measured relative to the reference absorption. If the sample and reference holders are identical and have a large thermal mass then any deviation of the specific heat of the sample from the theoretical value does not bear much influence on the final result. The limitations of both the pulsed methods 1 and 2 are that in order to negate any inaccuracy arising from differences in the thermal conductivities of the sample and the reference and calibration samples the probe pulse lengths must be short. This is no problem if really short pulses are used (e.g. Q-switched pulses). However, since the technique has been shown to be useful using interrupted cw laser beams, care must be taken to check the time scale over which the absorption measured is constant. Experience has shown that pulse lengths as long as 10–15 s can be used to measure the absorption. If samples with low absorption levels are under observation relatively high (5 W) of cw probe laser radiation must be used. 3. Pulsed adiabatic calorimetric method It is possible, using adiabatic calorimetry in a vacuum cell, to virtually eliminate convection and radiation. This therefore has the advantage of allowing the use of very low levels of cw radiation (0.1 W) and of being virtually independent of the pulse length. Adiabatic calorimetry also allows the possibility of calibrating the calorimeter by joule heating (Decker and Temple 1977). The sample is held in a light clamping ring, which is in direct thermal contact with a precision resistor, Rp , through which a measured current is passed. The electrical power, necessary to heat the sample up to the same temperature as was reached on irradiation by a laser pulse, can therefore be measured absolutely. A major advantage of this method is that it is not necessary to know the sample mass, specific heat or thermal diffusivity in order to make an accurate measurement of the absorption coefficient. The relationship between the amounts of energy deposited and the temperature rise is given by QL Qcal ¼ TL Tcal

ð8:36Þ

204


where QL is the energy deposited by the laser (power PL in time tL giving a temperature rise of TL ) and is given by the expression QL ¼ APL tL . Qcal is the electrical energy deposited in the sample (power Pcal ¼ V 2 =R for time tcal , giving a temperature rise of Tcal ) and is given by the expression: Qcal ¼ Pcal tcal ¼

V 2 tcal : R

ð8:37Þ

Equations (8.36) and (8.37) can be combined to give a further expression relating the absorption to physically and electrically measured parameters: A¼

QL TL tcal V 2 =R ¼ : PL tL Tcal tL PL

ð8:38Þ

It will be seen from this equation that the major source of systematic error is associated with the calibration of the external power meter. 4. Standard gradient method This method should only be used if the laser available does not have sufficient power to rapidly elevate the temperature of the sample. The inaccuracies involved in determining the gradient, because the time–temperature function is not linear, make the results of limited use. Using the agreed procedure, determine the temperature–time graph (see figure 8.13) as follows. Determine the slope, ðdT=dtÞh , at time t1 at approximately 80% of the total irradiation time tB . Note the temperature T12 at the time t1 . Determine the slope, ðdT=dtÞc , at time t2 , when the temperature has dropped to T12 . Compute the absorptance using the formula X mI cI dT dT ¼ þ : ð8:39Þ dt h dt c P I

Figure 8.13. Temperature versus time plot: gradient method.


205

5. Quasi-cw method It is possible to use a quasi-cw method that takes into account the heat losses from the sample (Hass et al 1974). To a first approximation the rate of heating of a sample under laser irradiation is given by lPT ¼ ms Cp

dT 2n dt n2 þ 1

ð8:40Þ

where l is the sample thickness, is the absorption coefficient, PT is the transmitted power, Ms is the mass of the sample, Cp is the heat capacity, n is the index of refraction and the term 2n=ðn2 þ 1Þ accounts for reflection losses. In order to achieve greater accuracy it is desirable to employ a heat loss correction. In addition, the use of an appropriate correction can greatly facilitate analysis as it negates the necessity to wait until the sample is in thermal equilibrium with its surroundings. The heat-loss corrections can be evaluated from inspection of the temperature–time curves in the following way. In figure 8.14 the sample is initially above the temperature of the surrounds and ms Cp

dT þ pðT1 T0 Þ ¼ 0: dt

ð8:41Þ

On heating by the laser beam the sample temperature increases with time such that ms Cp

dT2 þ pðT2 T0 Þ ¼ lPT ð1 þ n2 Þ: dt

ð8:42Þ

On turning the laser beam off the samples resumes cooling and ms Cp

dT3 þ pðT3 T0 Þ ¼ 0 dt

where p is a heat loss parameter and T0 is the ambient temperature.

Figure 8.14. Analysis of cw calorimetric data.

ð8:43Þ

206


In order to evaluate the absorption coefficient, , accurately the slopes of the linear portions of the graph (see figure 8.14) as well as the temperature differences, T2 T1 and T3 T1 must be measured accurately. Combining equations (8.39), (8.40) and (8.41): dT2 dT1 dT3 dT1 T2 T1 1 þ n2 ms Cp ¼ lPT : ð8:44Þ dt dt dt dt T3 T1 2n The main advantage of this approach is that the length of irradiation does not enter the equation. It is, however, necessary to measure the temperatures accurately. All five methods of making absorption measurements are capable of giving accurate and reproducible results as long as they are carried out properly. The main disadvantage of the pulsed techniques is that it yields spurious results if the irradiation time is long. This is especially true if the thermal conductivities and thermal masses of the reference and the sample are not approximately equal. In practice, irradiation times of under 20 s yield the best results. If extremely low absorption is required to be measured then the laser power (nominally in the range of 1–5 W) may have to be increased and this may give rise to heating of the reference sample. The main advantage of the pulsed measurement techniques, 1 and 2, is that they are fairly quick to conduct and that the measurement does not need anything more than shielding against draughts. The disadvantage of the cw technique is that it takes a longer time to make a single reading and that it necessitates the use of vacuum cells to inhibit losses by convection. Comparisons of the results gained using the different techniques have shown up interesting phenomena (Foley et al 1980). In this series of experiments measurements were made in several laboratories both in the UK and in the USA. A number of Cu, ZnSe and Ge substrates (originating from a number of sources) were exchanged, tested for their absorption at 10.6mm and the results compared. The measurements made on all the Cu substrates were reproducible both in absolute terms and in order of relative value. The measurements of the absorption of the germanium substrates did not agree so well and those made on the zinc selenide substrates were hardly recognizable. After some long and hard heart searching it was shown that the differences were due to the presence of water vapour on the surface of the substrates. The measurements made on the samples without any treatment were all shown to be high. Those that had been cleaned by washing in isopropyl alcohol were shown to be variable (depending on the dryness of the atmosphere and the time taken between the cleaning and the measurement). The measurements made under vacuum were always lowest but could yield anomalously high results if the temperature of the substrate rose above about 30 8C. Another series of measurements showed that water vapour could be pulled off and absorbed almost instantaneously by evacuating the


207

sample chamber. However if, the samples had been cleaned with isopropyl alcohol the absorption dropped and only gradually rose again when exposed to the atmosphere. A third set of experiments indicated that the typical water absorption on the surface of a germanium single crystal at N.T.P. was of the order of 0.13% per surface. This was calculated to be equivalent to 130 A˚ of water on the surface. It was shown that the absorption was in a layer of oxide that formed on the surface and that this could be dried but not eliminated by evacuating the sample chamber. However, when the sample was cleaned with isopropyl alcohol the layer of oxide was virtually removed and took about a week to grow again. It is possible, by making absorption measurements on different thickness samples, to make reasonable estimates of both the bulk and the surface absorption. Temple and Arndt (1983) went so far as to fabricate Brewsterangled wedges in order to eliminate internal reflections and thus make even more accurate calculations of both of these quantities. It should be noted that all absorption measurement procedures should only be made at relatively low power levels in order to eliminate the effect of heating the substrate and bringing nonlinear absorption into play. Bass et al (1981) made absorption measurements using pulsed radiation. As expected, this led to the measurement of a nonlinear absorption with increasing power and energy densities and also to a reversible saturable absorption in KCl. This latter was thought to be due to impurity absorption rather than to an intrinsic process. 8.4.3

Measurement of scatter

Optics and optical instruments—Lasers and laser-related equipment— Test method for radiation scattered by optical components. ISO 13696: 2001. It is possible to undertake total light scattering (TLS) measurements either on small areas of a surface or over some larger area. These measurements relate to the surface roughness of the component, are non-contact, and can be very sensitive. Measurement of the TLS of a surface provides quantitative information on the surface quality (Bennett and Mattsson 1993, Stover 1990, Duparre 1995). It is possible to ‘fingerprint’ surfaces using this measurement to identify areas where the scatter is greater than average. It has still to be proven that these high scatter points also coincide with low laser-induced damage threshold points. In order to measure the total amount of radiation scattered it is necessary to collect the radiation scattered at the surfaces and from the bulk of the sample under investigation. In order to do this it necessary to use an integrating sphere. There are two different types of sphere which can be used. The first is the Ulbricht sphere (see figure 8.15). This sphere is typically

208


Figure 8.15. Scatter measurement: Ulbricht sphere.

coated (for radiation in the VNIR) with barium sulphate powder and can be used to measure scatter over all 4 radians (Guenther et al 1984, Kienzle et al 1994). It is therefore better for the measurement of total scatter. The measurements can be made as a function of the beam position across the sample. It is possible by changing the placement of the sample to distinguish between forward scatter and backscatter. The other sphere in common use is the Coblenz sphere (see figure 8.16). This sphere is hemispherical with the sample holder and the detector placed uniformly off-centre on the base of the hemisphere (Mattson 1986, Duparre and Gliech 1997, Ronnow and Veszelei 1994). This method is much more sensitive as the sphere has a highly reflective surface. As the Coblenz

Figure 8.16. Scatter measurement: Coblenz sphere.

Surface measurement and specification

209

sphere is a half sphere, it is usually used to measure the backscatter from the sample under investigation. A series of round-robin tests have been made both in Europe and in the USA (Kadkhoda et al 1997, Duparre et al 1997, Duparre and Gliech 1997). Good agreement has been reached once a number of common errors/technical problems have been eliminated. It has been shown that it is possible to make scans across a sample and to correlate the scatter peaks with coating inclusions, scratches etc. The main problems that exist concentrate round the elimination of extraneous beams while allowing the apparatus to measure all the scattered light. It is relatively easy to measure the scatter from areas but the problem becomes quickly more problematical as the area of the measurement increases. As all scatter measurements concentrate around the measurement of the variation across a sample surface in the scatter values of low levels of scattered light it becomes important to make the measurements in a light-tight enclosure with plenty of absorbing area so that the reflected beams do not confuse the measurement. In general the simpler the measurement arrangement the easier it is to cut out spurious light beams.

8.5

Surface measurement and specification Optics and optical instruments—Lasers and laser-related equipment— Test methods for surface imperfections of optical elements. ISO 14997. Optics and optical instruments—Preparation of drawings for optical elements and systems. ISO 10110-1: 1996. Part 1: General. ISO 10110-2: 1996. Part 2: Material imperfections—Stress birefringence. ISO 10110-3: 1996. Part 3: Material imperfections—Bubbles and inclusions. ISO 10110-4: 1997. Part 4: Material imperfections—Inhomogeneity and striae. ISO 10110-5: 1996. Part 5: Surface form tolerances. ISO 10110-5: 1996/Cor 1: 1996. Part 5: Surface form tolerances. Technical corrigendum 1. ISO 10110-6: 1996. Part 6: Centring tolerances. ISO 10110-6: 1996/Cor 1: 1999. Part 6: Centring tolerances. Technical corrigendum. ISO 10110-7: 1996. Part 7: Surface imperfection tolerances.. ISO 10110-8: 1997. Part 8: Surface texture. ISO 10110-9: 1996. Part 9: Surface treatment and coating. ISO 10110-10: 1996. Part 10: Table representing data of a lens element.

210


Table 8.2. Acceptable severity thresholds for scratches and roughness.

Description

British grade or LEW

American MIL value

German width (mm)

French grade

Surface roughness, r.m.s. (nm)

1. Camera lens 1.1. Front c 1.2. Inside f 1.3. Near focus f

A C A

20 60 20

0.63 4.00 0.63

T2 T4 T2

2 2 2

2. Projection lens 2.1. Front c 2.2. Inside f

A C

20 60

0.63 4.00

T2 T4

2 2

3. Process lens 3.1. Front c 3.2. Inside f

A C

20 60

0.63 4.00

T2 T4

2 2

4. Copier lens 4.1. Front c 4.2. Inside f

C C

60 60

4.00 4.00

T4 T4

2 2

5. A-focal systems 5.1. Objective c 5.2. Prism f

A B

20 40

0.63 1.60

T2 T3

2 2

10

0.25

T1

1

40

1.60

T3

2

6. Microscope OG f 7. Eye lens c

195

11–45 11–86 10–27 14–180 15–170 50–185 22–>45 5–12 5–15 21–52 20–>180 10–20 21–>180

From Wood et al (1975).

218

Appendix 4

(a) Summary of LIDT measurements made at 10.6 m m at the GEC Hirst Research Centre on infrared window substrates and coatings (pulsewidth, ¼ 100 ns) LIDT (MW mm2 ) Substrate Ge ZnSe ZnS GaAs CdTe Si NaCl KCl Diamond Synthetic diamond As2 S3 KRS-5

Minimum 0.6 0.8 2 1.1 1.1 0.4 – 10 22 – – –

LIDT (MW mm2 )

Maximum Substrate

Coating

Minimum

Maximum

11 15 9 8 2.9 13 43 50 14 12 7 2.5 7

polished

2.5

9.5

polished polished

– 2.8

2.8 6.2

Diamond-turned. From Wood (1986).

Cu Cu Cu Cu Si Ag Zerodur

SiO2 ThF4 ev Au pl Au Ni/Au Ag Si Ag

6.2 0.7 1.3 3.6 2 1.5 1.5 4.2

>11.5 >11.0 2.1 9.8 2.1 5.9 5.6 8.4

Appendix 5

Summary of LIDTs of infrared transmitting materials

Material Germanium (Ge)

LIDT (MW mmÿ2 ) 30

4.1

Pulsewidth, (ns) 1.4

Wavelength (mm) 10.6

77

50

10.6

1.7

13

75

10.6

11.4

103

90

10.6

100 100 150

10.6 10.6 10.6

44 6–19 6 25 Zinc selenide 11 (ZnSe) 15

Zinc sulphide (ZnS)

Sodium chloride (NaCl)

LIDT (J cmÿ2 )

Pulsewidth, (ns)

Wavelength, Reference (mm)

0.2 10

100 100

10.6 0.69

Kruer et al (1977) Kruer et al (1977)

100 50 20 12.5

10.6 10.6 1.06 1.06

Wood (1986) Sussman et al (1993) Kondyrev et al (1992) Sussman et al (1993) Hayden and Liberman (1976) Jacobs and Teegarden (1976) Gibson and Wilson (1984) Gibson and Wilson (1984) Leung et al (1975) Wood (1986) Kovalev and Faizullov (1978)

700–>1200 29–93 12 31 1.5

1.4

10.6

1.5

1

10.6

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