Tài liệu Optical materials

OPTICAL MATERIALS This Page Intentionally Left Blank Optical Materials Joseph H. Simmons University of Florida, Gainesville, Florida and Kelly S. Potter Sandia National Laboratories, Albuquerque, New Mexico ACADEMIC PRESS An Imprint of Elsevier San Diego San Francisco N e w York Boston London Sydney Tokyo This book is printed on acid-free paper. ( ~ Copyright © 2000 by Academic Press All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in Permissions may be sought directly from Elsevier's Science and Technology Rights Department in Oxford, UK. Phone: (44) 1865 843830, Fax: (44) 1865 853333, e-mail: [email protected]. You may also complete your request on-line via the Elsevier homepage: http://www.elsevier, com by selecting "Customer Support" and then "Obtaining Permissions". (Cover image: Diffraction of white light from a thin film etched grating [K.S. Potter, B.G. Potter, Jr. and M.B. Sinclair, Sandia National Laboratories]). ACADEMIC PRESS An Imprint of Elsevier 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA http://www.apnet.corn Academic Press 24-28 Oval Road, London NWl 7DX, UK http://www.hbuk.co.uk/ap/ Library of Congress Catalog Card Number: 99-65137 ISBN-I 3: 978-0-I 2-644140-6 ISBN-10:0-12-644140-5 Printed in the United States of America 05 06 07 08 09 MB 9 8 7 6 5 4 3 2 Dedication With deep appreciation to our spouses, Cate and B. G., for their enduring support and indispensable assistance with this project. This Page Intentionally Left Blank Contents Preface xiii Chapter I Wave propagation Introduction Waves The electromagnetic spectrum Mathematical waves Electromagnetic waves Propagation characteristics Dispersion Kramers-Kronig relations Wave-particle duality Phonons Measurements 1.11.1 Ruled gratings 1.11.2 The grating spectrometer 1.11.3 Fast Fourier transform spectrometers 1.11.4 Microscopes Appendix 1A Solution of the wave equation by transform methods Appendix 1B General solution for propagation vectors Appendix 1C Kramers--Kronig relations 1 1 2 5 12 16 22 25 28 31 32 34 34 37 41 43 45 48 50 Chapter 2 Optical properties of conductors 57 57 61 68 69 71 75 76 78 79 79 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Introduction Atomistic view: Drude model Plasma frequency Band structure in metals 2.4.1 Density of states Coloration in metals Coloration by means of small metal particles Optical properties of superconductors Measurement techniques 2.8.1 Photoacoustic absorption spectroscopy vii viii Contents 2.8.2 Differential reflection spectroscopy Appendix 2A Solution of the Mie theory equations Chapter 3 Optical properties of insulators--Fundamentals 3.1 3.2 Introduction Harmonic oscillator theory 3.2.1 Classical model (Lorentz) 3.2.2 Quantum mechanical treatment 3.3 Selection rules for transitions between atomic levels 3.4 Propagation of light through insulators 3.4.1 Refractive index and dispersion 3.4.1.1 Clausius-Mosotti equation 3.4.1.2 Dispersion 3.4.1.3 Composition dependence and calculations of the refractive index 3.4.1.4 Temperature dependence of the refractive index 3.4.2 Reflection and transmission 3.4.3 Nonspecular reflection 3.4.4 Optical attenuation 3.4.5 Ligand field theory 3.4.6 Optical scattering 3.4.6.1 Rayleigh and Brillouin scattering 3.4.6.2 Mie scattering 3.4.6.3 Brillouin scattering and the Landau-Placzek ratio 3.4.7 Phonons, Raman scattering, and infrared absorption 3.5 Measurement techniques 3.5.1 Measurements of refractive index 3.5.1.1 Abbe refractometer 3.5.1.2 Minimum-deviation prism goniometer 3.5.1.3 Refractometers 3.5.1.4 Ellipsometry 3.5.1.5 Becke line method 3.5.1.6 Femtosecond transit time method 3.5.2 Infrared absorption and Raman scattering measurements Appendix 3A Quantum mechanical treatment of the simple harmonic oscillator 80 81 85 85 89 89 91 95 98 99 99 100 108 108 110 117 119 124 126 127 131 132 132 134 134 134 135 136 137 139 140 141 144 Contents Appendix 3B Appendix 3C ix Calculation of the refractive index of glass Ligand field theory concepts Chapter 4 Optical Properties of I n s u l a t o r s m Some Applications 4.1 Thin films 4.1.1 Mathematical treatment 4.1.2 Fabry-Perot oscillations 4.1.3 Ellipsometry measurement 4.2 Glasses, Crystals, and birefringence 4.3 Photochromic and electrochromic behavior 4.4 Oxides, chalcogenides, and halides 4.5 Optical plastics 4.6 Sources of color 4.6.1 Emission 4.6.2 Absorption 4.6.3 Reflection 4.6.4 Dispersion 4.6.5 Scattering 4.6.6 Interference colors Appendix 4A Alternate calculation of multiple film stacks Chapter 5 Optical Properties of Semiconductors 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Introduction Free-electron gas (Sommerfeld theory) Nearly free-electron model 5.3.1 Bloch theory 5.3.2 Density of states Band structure Impurity states and lattice imperfections 5.5.1 Donor and acceptor bands 5.5.2 Band tails 5.5.3 Excitons 5.5.4 Donor-acceptor pairs 5.5.5 Amorphous semiconductors Carrier densities 5.6.1 Nondegenerate semiconductors 5.6.2 Degenerate semiconductors Absorption and photoluminescence 151 155 159 159 159 165 168 169 172 174 176 178 180 180 182 182 183 184 187 191 191 193 194 195 199 202 210 210 211 212 214 215 215 216 218 220 x Contents 5.7.1 Direct-gap semiconductors 5.7.2 Indirect-gap semiconductors 5.7.3 Heavily doped semiconductors 5.7.4 Transitions between band tails 5.7.5 Exciton absorption 5.7.6 Defect-associated transitions 5.7.7 Luminescence 5.7.8 Nonradiative processes 5.7.9 Polaritons 5.8 Measurements 5.8.1 Polarized light 5.8.2 Absorption 5.8.3 Photoluminescence 5.8.4 Heavily doped semiconductors 5.8.4.1 Acceptor-band absorption and luminescence 5.8.4.2 Donor-band absorption 5.8.5 Differential reflection spectroscopy 5.8.6 Summary of optical methods 5.9 Materials and properties 5.9.1 Fabrication and growth 5.9.2 Color 5.9.3 Properties 5.9.3.1 Bandgap energies 5.9.3.2 Contact potentials 5.10 Quantum well structures, quantum wires, and quantum dots Appendix 5A Derivation of the carrier concentration equation Appendix 5B Derivation of absorption from direct interband transitions Appendix 5C Band structure of semiconductors 265 268 Chapter 6 Optical Gain and Lasers 6.1 Introduction 6.2 Spontaneous emission 6.3 Line shapes 6.3.1 Homogenous line broadening 6.3.2 Inhomogeneous line broadening 6.4 Stimulated emission and absorption 6.5 Absorption and amplification (gain) 6.6 Operational characteristics of lasers 273 273 274 274 275 276 277 279 280 223 225 227 227 229 231 231 233 234 237 237 241 242 245 245 246 246 247 247 247 253 255 255 255 259 264 Contents xi 6.6.1 Three-level, four-level, and n-level lasers 6.6.2 Gain and gain saturation 6.6.3 Hole burning 6.7 Laser cavity characteristics 6.7.1 Fabry-Perot laser cavities 6.7.2 Population inversion in three-level and four-level lasers 6.7.3 Issues of output power coupling in laser cavities 6.7.4 Issues of modelocking in laser cavities 6.7.4.1 Acoustic Bragg diffraction 6.7.4.2 Saturable absorber (bleachable dye) 6.7.4.3 Giant pulse-Q-switch 6.7.5 Laser efficiency 6.8 Examples of laser systems 6.8.1 Ruby lasers 6.8.2 Nd 3+:YAG lasers 6.8.3 Neodynium-glass lasers 6.8.4 Tunable titanium sapphire lasers 6.8.5 Tunable alexandrite lasers 6.8.6 Color center lasers 6.8.7 Fiber lasers and erbium-doped fiber amplifiers 6.8.8 Helium-neon lasers 6.8.9 Argon-ion and krypton-ion lasers 6.8.10 Helium-cadmium lasers 6.8.11 Excimer lasers 6.8.12 Nitrogen gas lasers 6.8.13 Carbon dioxide (CO2) lasers 6.8.14 Copper vapor lasers 6.8.15 Organic dye lasers 6.8.16 Free-electron laser 6.9 Semiconductor lasers 6.9.1 p-n Junctions 6.9.2 Degenerate p-n junction lasers 6.9.3 Heterojunction lasers 288 289 291 293 294 295 296 297 297 298 300 301 305 305 3O6 3O7 309 310 311 312 312 314 315 317 318 318 319 321 Chapter 7 NonLinear Optical Processes in Materials 7.1 Introduction 7.1.1 Linear materials 7.1.2 Nonlinear processes 325 325 326 326 280 281 284 285 285 xii Contents Mathematical treatment 7.2.1 The anharmonic oscillator 7.2.1.1 Optical linearity--Simple harmonic oscillator 7.2.1.2 Second-order optical nonlinearity-Anharmonic oscillator 7.2.2 Third-order optical nonlinearity 7.3 Second-order susceptibility 7.3.1 Materials 7.3.1.1 Perovskites 7.3.1.2 Poled polymers 7.3.1.3 Poled glasses 7.3.1.4 Surfaces 7.3.2 Systems that use the ~(2) behavior of materials 7.3.2.1 Second harmonic generation 7.3.2.2 Optical parametric oscillation 7.4 Third-order susceptibility 7.4.1 Nonlinear index and absorption 7.4.1.1 Transparency region 7.4.1.2 Infrared region 7.4.1.3 Two-photon absorption region 7.4.1.4 Electronic processes in the band-edge region 7.4.1.5 Other sources of nonlinearity 7.4.1.6 Relative values of the various processes 7.4.2 Structural defect-induced processes 7.4.2.1 Photosensitivity 7.4.2.2 Photothermal effects 7.4.3 DC field-induced processes 7.4.3.1 Photorefraction 7.4.3.2 Second harmonic generation in optical fibers 7.4.4 Materials 7.5 Test methods 7.5.1 Degenerate four wave mixing (DFWM) 7.5.2 z-scan measurement 7.5.3 Pump-probe spectroscopy 7.5.4 Third-harmonic generation 7.2 Index 328 330 331 332 337 339 342 342 343 343 344 344 344 345 347 347 347 35O 351 353 357 359 359 359 362 364 365 367 367 370 371 371 373 374 379 Preface Today, the field of optics is expanding at an explosive rate. The advent of optical communications, personal computers, video-on-demand television, and network interconnections across the globe has placed a heavy burden on materials and devices for signal transmission and processing. Clearly, current state-of-the art technology is being driven, in large part, by advances in both the design and the implementation of complex optical systems. Applications, ranging from optical telecommunications (in which gigabits of encoded optical data are transmitted down hair'swidth glass fibers) to orbiting satellite systems, rely heavily on optical materials, optical systems, and lasers. Undoubtedly, the worldwide political and economic changes of the last decade are a harbinger of the increased need for advanced, compact, multifunctional technologies capable of receiving, processing, storing, and transmitting massive amounts of information faster, over longer distances, and more efficiently than ever before as we move toward a truly global economy. The major role of optics in these advances puts the subject of optical materials in the forefront for the beginning of the twenty-first century. Those of us who have been in science over the last several decades have seen the tremendous impact that the development of a suitable material and process can have on a wide range of industries. The demonstration of the ruby laser in 1964, for example, opened the door for progress that has revolutionized the way we live. Everything from bar-code scanners to compact disk technology to telecommunications to new medical procedures rely on the use of a broad variety of laser sources, each with specific wavelength and bandwidth requirements. Optical materials have played an important role in these advances and promise even greater impact in the future. In signal processing and transmission, the benefits of optical over electronic techniques have already changed our lives in a major way by giving us access to the information superhighway. Optical-fiber communications are already just outside our houses and will cross the threshold within the next decade. Again, this advance results from the development of novel optical materials that not only can handle larger signal bandwidth but also can transmit a great number of communication channels over global distances. The linearity of the transmission media xiu xiv Preface allows the superposition of optical signals without mixing, thus making possible the processing of massive amounts of data simultaneously and in parallel. The promise of materials that exhibit a strongly nonlinear response to optical radiation makes possible the development of large optical memories, optical switches, and computational logic operations. Complex logic processes, like image analysis, can be done more quickly and accurately optically than electronically, as can signal-processing operations such as amplification, wavelength-division multiplexing, and switching. An intense research effort is currently under way to integrate multiple optical technologies on-chip. One can easily envision a system in which optical signals are generated by microlasers, modulated by lightsignal modulators, transmitted and shaped by thin-film digital lenses, coupled into optical waveguide channels by nonlinear optical switches, analyzed by optical logic gates that work as part of complex neural network logic systems, and, finally, stored as information in threedimensional holographic data-storage media, all within the space of a computer chip. This book addresses the underlying mechanisms that make optical materials what they are and that determine how they behave. The book strives to group the characteristics of optical materials into classes with similar behavior. We believe that by presenting a broad range of optical materials behavior, we can show the reader what properties are held in common and what properties differ between various classes of materials. In treating each t5^e of material, we pay particular attention to atomic composition and chemical makeup, to electronic states and band structure, and to physical microstructure. We then strive to relate optical behavior and its underljdng processes to the chemical, physical, and microstructural properties of the material so that the reader will gain insight into the kinds of materials engineering and processing conditions that are required to produce a material exhibiting a desired optical property. The book is aimed at the intermediate or advanced reader (or student) and, in order to achieve accurate and quantitative descriptions, presents the principal equations underl3dng the processes of interest. If only a qualitative understanding is sought, however, then it is fully possible to read the entire book and completely ignore the mathematical treatment. To this end, we have filled the text with explanations and discussions of the physical principles associated with the optical behaviors described. Many of the insights presented here have come from the broad range of Preface xv specialized literature cited and from the authors' own extensive research efforts with optical materials and the authors* interactions with students in the laboratory and in the classroom. Each chapter is essentially self-contained, so the book may be used as a text for any level of course on optical materials. In addition, throughout the book we have tried to tie the material to the research arena by including discussions of equipment and experimental techniques relevant to the topics of each chapter. As such, the book may be used as a reference source for the experimentalist or as a guide for the student. Since we have sought to present a complete picture of the behavior of optical materials, an introductory course may wish to leave out some of the later chapters and the chapter appendices. This Page Intentionally Left Blank Chapter 1 Wave Propagation 1.1 Introduction The optical properties of materials arise from the characteristics of their interactions with electromagnetic waves. In particular, the ability of a material to exhibit an induced polarization or magnetization at a selected wavelength, or over a selected wavelength band, provides the potential for it to change the character of light propagating through it. Such changes can take the form of loss or gain of intensity, shifts in wavelength, and narrowing, broadening or filtering of bandwidth, for example. Different classes of materials will, in general, differ in their response to optical radiation. Insulators and conductors, for example, each exhibit a unique response to electric polarization. While insulators exhibit local induced polarization of bound charges, dipoles, etc., conductors exhibit induced currents from the movement of free charges. In some cases, materials will act as insulators at frequencies or temperatures where only local polarization is possible, and they will act as conductors when conditions are suitable for charge transport. Thus, glasses and semiconductors act as insulators at low temperatures and at frequencies below those needed to excite free carriers, and they act as conductors at temperatures and frequencies high enough to excite free carriers and to allow induced electric currents to form. In between these conditions, materials exhibit a variety of changes in local polarization mechanisms, including (1) molecular or dipolar, (2) ionic or atomic, and (3) electronic polarization, and these mark large changes in their optical behavior. This topic is discussed in more detail in Chapter 3. 2 Chapter 1 Wave Propagation This book will cover the behavior of materials as grouped by the classifications of conductor, insulator, semiconductor, nonlinear materials, and so on, in order to identify characteristics common to all members of the same group. This will EQIOW US to identify the unifying themes that run through the behavior of different groups of materials and to relate them to the underlying physics. This first chapter is a terse review of the principles of optics. We emphasize here the principles that will be used throughout the book. The reader who is not familiar with elementary optics is encouraged to support reading of this chapter with books that cover the subject in more detail. Several such books (Born and Wolf, 1980; Hecht, 1990) that use nomenclature similar to that used in this book are listed at the end of the chapter. 1.2 Waves Light propagates by electromagnetic waves. Therefore, there are certain characteristics of waves, and, in particular, electromagnetic waves, that must be reviewed in order to understand the behavior of light and its interaction with matter. In this chapter, we will review the mathematical structure of wave propagation that will be used throughout the book. We are surrounded by many kinds of waves. For example, acoustic waves propagate the sounds we make and hear. Light that we see comes from electromagnetic waves at very high frequencies. Radio and television signals are carried by electromagnetic waves at much lower frequencies, and the microwaves that heat our food are electromagnetic waves at intermediate frequencies. The cell phone of Fig. 1.1 receives and emits both electromagnetic and acoustic waves. The water waves that entertain us at the beach are mechanical-displacement waves. Because of their constant pounding of the shore, causing erosion and tidal flows, the action of these waves has been recognized as an essential ingredient in the development of advanced life forms on Earth. Waves are different in the way they disturb certain properties of the propagating media. For example, acoustic waves correspond to variations in the local pressure or density of the medium and electromagnetic (EM) waves correspond to variations in the electric and magnetic fields. Since EM fields can exist without the presence of matter, light waves propagate 1.2 Waves Electromagnetic Wave Acoustic Wave Figure 1.1: Acoustic and electromagnetic waves from a cell phone. through empty space, whereas acoustic waves require a propagating medium. While all these waves are perceived to behave totally differently, they actually follow the same mathematical formalism. A traveling wave is a disturbance that propagates both in space and in time (Fig. 1.2). Usually, a wave will decay as it propagates, as shown in the figure. By contrast, a standing wave has spatial extent, with an amplitude that oscillates in time but is stationary. As such, standing waves are characterized by fixed nodes that are constant in time. Resonant systems are represented by standing waves (e.g., a vibrating guitar string). If there is loss in the system, the standing wave's amplitude will, in fact, decrease with time, but its spatial form will remain unchanged (Fig. 1.3). Traveling waves can be either longitudinal or transverse. Longitudinal waves oscillate along the direction of propagation (Fig. 1.4); transverse waves (Fig. 1.2) oscillate perpendicular to the propagation direction. Longitudinal and transverse waves can be formed in solids and in viscoelastic media, but liquids and gases can support only longitudinal waves in the bulk. Liquids can support transverse waves only at their surface; it is the manifestation of surface transverse waves in water that