Second Edition ClearCorrect Exhibit 1067, Page 1 of 415
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`Optical Properties of Solids
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`Mark Fox
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`OXFORD MASTER SERIES IN CONDENSED MATTER PHYSICS
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`OXFORD MASTER SERIES IN PHYSICS
`
`The Oxford Master Series is designed for final year undergraduate and beginning graduate students in physics and
`related disciplines. It has been driven by a perceived gap in the literature today. While basic undergraduate physics
`texts often show little or no connection with the huge explosion of research over the last two decades, more advanced
`and specialized texts tend to be rather daunting for students. In this series, all topics and their consequences are
`treated at a simple level, while pointers to recent developments are provided at various stages. The emphasis is on
`clear physical principles like symmetry, quantum mechanics, and electromagnetism which underlie the whole of
`physics. At the same time, the subjects are related to real measurements and to the experimental techniques and
`devices currently used by physicists in academe and industry. Books in this series are written as course books, and
`include ample tutorial material, examples, illustrations, revision points, and problem sets. They can likewise be used
`as preparation for students starting a doctorate in physics and related fields, or for recent graduates starting research
`in one of these fields in industry.
`
`CONDENSED MATTER PHYSICS
`
`1. M.T. Dove: Structure and dynamics: an atomic view of materials
`2. J. Singleton: Band theory and electronic properties of solids
`3. A.M. Fox: Optical properties of solids, second edition
`4. S.J. Blundell: Magnetism in condensed matter
`5. J.F. Annett: Superconductivity, superfluids, and condensates
`6. R.A.L. Jones: Soft condensed matter
`17. S. Tautz: Surfaces of condensed matter
`18. H. Bruus: Theoretical microfluidics
`19. C.L. Dennis, J.F. Gregg: The art of spintronics: an introduction
`
`ATOMIC, OPTICAL, AND LASER PHYSICS
`
`7. C.J. Foot: Atomic physics
`8. G.A. Brooker: Modern classical optics
`9. S.M. Hooker, C.E. Webb: Laser physics
`15. A.M. Fox: Quantum optics: an introduction
`16. S.M. Barnett: Quantum information
`
`PARTICLE PHYSICS, ASTROPHYSICS, AND COSMOLOGY
`
`10. D.H. Perkins: Particle astrophysics, second edition
`11. Ta-Pei Cheng: Relativity, gravitation and cosmology, second edition
`
`STATISTICAL, COMPUTATIONAL, AND THEORETICAL PHYSICS
`
`12. M. Maggiore: A modern introduction to quantum field theory
`13. W. Krauth: Statistical mechanics: algorithms and computations
`14. J.P. Sethna: Statistical mechanics: entropy, order parameters, and complexity
`20. S.N. Dorogovtsev: Lectures on complex networks
`
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`Optical Properties of Solids
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`Second Edition
`
`MARK FOX
`
`Department of Physics and Astronomy
`University of Sheffield
`
`1
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`3 G
`
`reat Clarendon Street, Oxford ox2 6DP
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`Optical Properties of Solids
`
`Second Edition
`
`Mark Fox
`Department of Physics and Astronomy
`University of Sheffield
`
`February 26, 2010
`
`CLARENDON PRESS . OXFORD
`2010
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`Preface
`
`Nine years have passed since the first edition of Optical properties of
`solids was published, and in these years I have received many helpful
`comments and suggestions about how to improve the text. By and large,
`the comments from students have been concerned with sections that need
`further clarification, while those from colleagues have been about adding
`new topics. This second edition gives me the opportunity to make both
`types of improvements.
`Science move on, and, even in the relatively short time since the first
`edition was published, some completely new subjects have arisen, while
`others have grown in importance. There are also other topics that should
`have been included in the first edition, but were omitted. It is not pos-
`sible to cover everything in a book of this length, and in the end I have
`settled on the following list of new topics for the second edition:
`
`Electro-optics and magneto-optics New sections on induced bire-
`fringence, optical chirality, and electro-optics have been added,
`namely Sections 2.5.2, 2.6, and 11.3.4.
`Spintronics Three new sections have been added—Sections 3.3.7, 5.3.4,
`and 6.4.5—to cover the physics of optical spin injection in semi-
`conductors.
`Cathodoluminescence This topic is covered in Section 5.4.4.
`Quantum dots Section 6.8 has been substantially expanded to reflect
`the prominence of quantum dots in current semiconductor research
`and device development.
`Plasmonics The discussion of bulk plasmons in Section 7.5 has been
`improved, and a new subsection on surface plasmons has been
`added.
`Negative refraction Section 7.6 gives a brief discussion of this phe-
`nomenon.
`Carbon nanostructures Graphene, nanotubes, and bucky balls are
`discussed in Section 8.5.
`Diamond NV centres Section 9.2.2 has been added to reflect the
`growing interest in diamond NV centres for quantum information
`processing.
`Solid-state lighting A discussion of white light LEDs has been added
`to Section 9.5.
`
`This choice undoubtedly reflects my personal opinions on the present
`state of the subject, but it also based on the suggestions that I have
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`vi Preface
`
`received from colleagues. With some ingenuity, it has been possible to
`work all of this new material into the chapter structure of the first edition
`outlined in Fig. 1. Note, however, that the title of Chapter 6 has been
`changed from ‘Quantum wells’ to ‘Quantum confinement’ to reflect the
`greater emphasis on quantum dots.
`In addition to these new topics, I have made improvements through-
`out the whole text, and have tried to correct any errors or misleading
`remarks that were present in the first edition. All of the chapters have
`been updated, with new examples and exercises added where appropri-
`ate. In some cases new data have been included. The most significant
`improvements have been made to the sections on the Kramers–Kronig re-
`lationships (2.3), birefringence (2.5.1), and the quantum-confined Stark
`effect (6.5). It is inevitable that some errors will still persist in this sec-
`ond edition, and new ones occur. A web page with the errata will be
`posted as these errors are discovered.
`
`M.F.
`Sheffield
`January 2010
`
`Preface to the First Edition
`
`This book is about the way light interacts with solids. The beautiful
`colours of gemstones have been valued in all societies, and metals have
`been used for making mirrors for thousands of years. However, the scien-
`tific explanations for these phenomena have only been given in relatively
`recent times. Nowadays, we build on this understanding and make use
`of rubies and sapphires in high power solid-state lasers. Meanwhile, the
`arrival of inorganic and organic semiconductors has created the modern
`opto-electronics industry. The onward march of science and technology
`therefore keeps this perennial subject alive and active.
`The book is designed for final year undergraduates and first year grad-
`uate students in physics. At the same time, I hope that some of the
`topics will be of interest to students and researchers of other disciplines
`such as engineering or materials science. It evolved from a final year
`undergraduate course in condensed matter physics given as part of the
`Master of Physics degree at Oxford University. In preparing the course
`I became aware that the discussion of optical phenomena in most of the
`general solid-state physics texts was relatively brief. My aim in writing
`was therefore to supplement the standard texts and to introduce new
`subjects that have come to the fore in the last 10–20 years.
`Practically all textbooks on this subject are built around a number
`of core topics such as interband transitions, excitons, free electron re-
`flectivity, and phonon polaritons. This book is no exception. These core
`topics form the backbone for our understanding of the optical physics,
`and pave the way for the introduction of more modern topics. Much
`of this core material is well covered in the standard texts, but it can
`still benefit from the inclusion of more recent experimental data. This
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`Preface vii
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`
`INTRODUCTION (Chapters 1 and 2)INTRODUCTION (Chapters 1 and 2)
`
`• Overview of optical properties (1)• Overview of optical properties (1)
`
`• Classical oscillator model (2)• Classical oscillator model (2)
`
`
`LINEAR OPTICSLINEAR OPTICS
`
`Chapters 3-10Chapters 3-10
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`
`
`VibronicVibronicVibronic
`
`
`systemssystemssystems
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`
`
`
`
`Vibrational physicsVibrational physicsVibrational physics
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`
`
`
`
`Electronic physicsElectronic physicsElectronic physics
`
`
`• Interband absorption (3)• Interband absorption (3)
`
`• Excitons (4)• Excitons (4)
`
`• Interband emission (5)• Interband emission (5)
`
`• Quantum-confined structures (6)• Quantum-confined structures (6)
`
`• Free electrons (7)• Free electrons (7)
`
`
`• Molecular materials (8)• Molecular materials (8)
`
`• Luminescent defects• Luminescent defects
`
`and impurities (9)and impurities (9)
`
`
`• Optical physics• Optical physics
`
`of phonons (10)of phonons (10)
`
`
`NONLINEAR OPTICSNONLINEAR OPTICS
`
`Chapter 11Chapter 11
`
`Fig. 1 Scheme of the topics covered in this book. The numbers in brackets refer to chapters.
`
`is made possible through the ever-improving purity of optical materials
`and the now widespread use of laser spectroscopy.
`The overall plan of the subject material is summarized in Fig. 1. The
`flow diagram shows that some of the chapters can be read more or less
`independently of the others, on the assumption that the introductory
`material in Chapters 1 and 2 has been fully assimilated. I say ‘more
`or less’ here because it does not really make sense, for example, to try
`to understand nonlinear optics without a firm grasp of linear optics.
`The rest of the chapters have been arranged into groups, with their
`order following a certain logical progression. For example, knowledge
`of interband absorption is required to understand quantum wells, and
`is also needed to explain certain details in the reflectivity spectra of
`metals. Similarly, molecular materials provide an intuitive introduction
`to the concept of configuration diagrams, which are required for the
`understanding of colour centres and luminescent impurities.
`The inclusion of recent developments in the subject has been one of
`the main priorities motivating this work. The chapters on semiconduc-
`tor quantum wells, molecular materials, and nonlinear optics will not be
`found in most of the standard texts. Other new topics such as the Bose–
`Einstein condensation of excitons are included alongside traditional sub-
`ject material. Furthermore, it is my deliberate intention to illustrate the
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`viii Preface
`
`physics with up-to-date examples of optical technology. This provides
`an interesting modern motivation for traditional topics such as colour
`centres and also helps to emphasize the importance of the solid-state
`devices.
`Throughout the book I have understood the term ‘optical’ in a wider
`sense than its strict meaning referring to the visible spectral region.
`This has allowed me to include discussions of infrared phenomena such
`as those due to phonons and free carriers, and also the properties of
`insulators and metals in the ultraviolet. I have likewise taken the scope
`of the word ‘solid’ beyond the traditional emphasis on crystalline ma-
`terials such as metals, semiconductors, and insulators. This has allowed
`me to include important non-crystalline materials such as glasses and
`polymers.
`The process of relating measured optical phenomena to the electronic
`and vibrational properties of the material under study can proceed in
`two ways. We can work forwards from known electronic or vibrational
`physics to predict the results of optical experiments, or we can work
`backwards from experimental data to the microscopic properties. An
`example of the first approach is to use the free electron theory to ex-
`plain why metals reflect light, while an example of the second is to use
`absorption or emission data to deduce the electron level structure of a
`crystal. Textbooks such as this one inevitably tend to work forwards
`from the microscopic properties to the measured data, even though an
`experimental scientist would probably be working in the other direction.
`The book presupposes that the reader has a working knowledge of
`solid-state physics at the level appropriate to a third-year undergrad-
`uate, such as that found in H.M. Rosenberg’s The solid state (Oxford
`University Press, third edn, 1988). This puts the treatment at about
`the same level as, or at a slightly higher level than, that given in the
`Introduction to solid state physics by Charles Kittel. The book also nec-
`essarily presupposes a reasonable knowledge of electromagnetism and
`quantum theory. Classical and quantum arguments are used interchange-
`ably throughout, and the reader will need to revise their own favourite
`texts on these subjects if any of the material is unfamiliar. Four ap-
`pendices are included to provide a succinct summary of the principal
`results from band theory, electromagnetism, and quantum theory that
`have been presupposed.
`The text has been written in a tutorial style, with worked examples
`in most chapters. A collection of exercises is provided at the end of each
`chapter, with solutions at the end of the book. The exercises follow the
`presentation of the material in the chapter, and the more challenging
`ones are identified with an asterisk. A solutions manual is available on
`request for instructors from the Oxford University Press web page.
`
`M.F.
`Sheffield
`January 2001
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`Preface ix
`
`Acknowledgements
`
`I would like to acknowledge the many people who have helped in var-
`ious ways in the production of both editions of this book. Pride of
`place goes to Sonke Adlung and his staff at Oxford University Press—
`especially Anja Tschoertner, Richard Lawrence, Emma Lonie, and April
`Warman—for bringing the books to fruition, and to Julie Harris for as-
`sistance with the LATEX typesetting. I would also like to offer special
`thanks to Dr Geoff Brooker of Oxford University for critical reading of
`the whole of the first edition and for a major input to the revised section
`on plasmons (Section 7.5) in this present edition.
`Numerous colleagues have helped to clarify my understanding of cer-
`tain specialist topics and have made comments on parts of the text.
`Among these I would like to thank especially: Prof. Arturo Lousa from
`the Universidad de Barcelona, for comments on several chapters and
`permission to use exercises from his course; Prof. David Smith from
`the University of Vermont, for comments on the theory of dispersion;
`Prof. Richard Harley of the University of Southampton and Dr Odilon
`Couto Jr of the University of Sheffield for suggestions about optical spin
`injection; Prof. Jeremy Allam of the University of Surrey, for providing
`material on carbon nanotubes; my former colleagues Dr Simon Martin
`and Dr Paul Lane at the University of Sheffield, for their critical reading
`of the chapter on molecular materials in the first edition; Dr Friedemann
`Reinhard from the Universit¨at Stuttgart, and Victor Acosta and Prof.
`Dmitry Budker from the University of California, for critical reading of
`the section on diamond NV centres; and Dr Oleg Shchekin from Philips
`Lumileds Lighting, for comments on white light LEDs. I am, of course,
`also very grateful to the students who have used the text and offered
`advice on how to improve it.
`The figures are a major part of this book, and I would like to ex-
`press my thanks to the publishers who have permitted the reproduc-
`tion of diagrams in both editions. I would also like to thank a large
`number of colleagues who have provided original or unpublished data.
`In particular, I would like to thank: Dr Steve Collins for Fig. 2.12(b);
`Prof. Robert Taylor for providing unpublished data for use in Figs 5.3,
`6.16, and 6.23; Dr Adam Ashmore for taking the data in Figs 5.6 and
`5.13; Prof. Gero von Plessen and Dr Andrew Tomlinson for the data pre-
`sented in Fig. 4.5; Prof. Mark Hopkinson for Fig. 6.21(a); Prof. Maurice
`Skolnick for Fig. 6.22; Dr Tim Richardson and Mark Sugden for Fig. 7.17;
`Prof. Frank Hegmann and Dr Aaron Slepkov for Fig. 8.11; Prof. David
`Lidzey for Fig. 8.19; Dr Fedor Jelezko, Philipp Neumann, Dr Friedemann
`Reinhard, and Prof. J¨org Wrachtrup for Fig. 9.6; Prof. Dmitry Budker
`and Victor Acosta for help with Fig. 9.7(b); Prof. Richard Warburton
`for Fig. 11.12; and Prof. Steve Blundell for the periodic table and list of
`fundamental constants on the inside covers.
`Finally, I would like to thank the Royal Society for supporting me as a
`University Research Fellow during the writing of most of the first edition,
`and the University of Sheffield for supporting me in the remaining years.
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`Contents
`
`1 Introduction
`1.1 Classification of optical processes
`1.2 Optical coefficients
`1.3 The complex refractive index and dielectric constant
`1.4 Optical materials
`1.4.1 Crystalline insulators and semiconductors
`1.4.2 Glasses
`1.4.3 Metals
`1.4.4 Molecular materials
`1.4.5 Doped glasses and insulators
`1.5 Characteristic optical physics in the solid state
`1.5.1 Crystal symmetry
`1.5.2 Electronic bands
`1.5.3 Vibronic bands
`1.5.4 The density of states
`1.5.5 Delocalized states and collective excitations
`1.6 Microscopic models
`Chapter summary
`Further reading
`Exercises
`
`2 Classical propagation
`2.1 Propagation of light in a dense optical medium
`2.1.1 Atomic oscillators
`2.1.2 Vibrational oscillators
`2.1.3 Free electron oscillators
`2.2 The dipole oscillator model
`2.2.1 The Lorentz oscillator
`2.2.2 Multiple resonances
`2.2.3 Comparison with experimental data
`2.2.4 Local field corrections
`2.3 The Kramers–Kronig relationships
`2.4 Dispersion
`2.5 Optical anisotropy
`2.5.1 Natural anisotropy: birefringence
`2.5.2
`Induced optical anisotropy
`2.6 Optical chirality
`Chapter summary
`Further reading
`
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`xii Contents
`
`Exercises
`
`3 Interband absorption
`3.1
`Interband transitions
`3.2 The transition rate for direct absorption
`3.3 Band edge absorption in direct gap semiconductors
`3.3.1 The atomic physics of the interband transitions
`3.3.2 The band structure of a direct gap III–V semicon-
`ductor
`3.3.3 The joint density of states
`3.3.4 The frequency dependence of the band edge ab-
`sorption
`3.3.5 The Franz–Keldysh effect
`3.3.6 Band edge absorption in a magnetic field
`3.3.7
`Spin injection
`3.4 Band edge absorption in indirect gap semiconductors
`3.5
`Interband absorption above the band edge
`3.6 Measurement of absorption spectra
`3.7 Semiconductor photodetectors
`3.7.1 Photodiodes
`3.7.2 Photoconductive devices
`3.7.3 Photovoltaic devices
`Chapter summary
`Further reading
`Exercises
`
`4 Excitons
`4.1 The concept of excitons
`4.2 Free excitons
`4.2.1 Binding energy and radius
`4.2.2 Exciton absorption
`4.2.3 Experimental data for free excitons in GaAs
`4.3 Free excitons in external fields
`4.3.1 Electric fields
`4.3.2 Magnetic fields
`4.4 Free excitons at high densities
`4.5 Frenkel excitons
`4.5.1 Rare gas crystals
`4.5.2 Alkali halides
`4.5.3 Molecular crystals
`Chapter summary
`Further reading
`Exercises
`
`5 Luminescence
`5.1 Light emission in solids
`5.2
`Interband luminescence
`5.2.1 Direct gap materials
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`Contents xiii
`
`Indirect gap materials
`5.2.2
`5.3 Photoluminescence
`5.3.1 Excitation and relaxation
`5.3.2 Low carrier densities
`5.3.3 Degeneracy
`5.3.4 Optical orientation
`5.3.5 Photoluminescence spectroscopy
`5.4 Electroluminescence
`5.4.1 General principles of electroluminescent devices
`5.4.2 Light-emitting diodes
`5.4.3 Diode lasers
`5.4.4 Cathodoluminescence
`Chapter summary
`Further reading
`Exercises
`
`6 Quantum confinement
`6.1 Quantum-confined structures
`6.2 Growth and structure of quantum wells
`6.3 Electronic levels
`6.3.1
`Separation of the variables
`6.3.2
`Infinite potential wells
`6.3.3 Finite potential wells
`6.4 Quantum well absorption and excitons
`6.4.1
`Selection rules
`6.4.2 Two-dimensional absorption
`6.4.3 Experimental data
`6.4.4 Excitons in quantum wells
`6.4.5
`Spin injection in quantum wells
`6.5 The quantum-confined Stark effect
`6.6 Optical emission
`6.7
`Intersubband transitions
`6.8 Quantum dots
`6.8.1 Quantum dots as artificial atoms
`6.8.2 Colloidal quantum dots
`6.8.3
`Self-assembled epitaxial quantum dots
`Chapter summary
`Further reading
`Exercises
`
`7 Free electrons
`7.1 Plasma reflectivity
`7.2 Free carrier conductivity
`7.3 Metals
`7.3.1 The Drude model
`7.3.2
`Interband transitions in metals
`7.4 Doped semiconductors
`7.4.1 Free carrier reflectivity and absorption
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`xiv Contents
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`Impurity absorption
`7.4.2
`7.5 Plasmons
`7.5.1 Bulk plasmons
`7.5.2
`Surface plasmons
`7.6 Negative refraction
`Chapter summary
`Further reading
`Exercises
`
`8 Molecular materials
`8.1
`Introduction to organic materials
`8.2 Optical spectra of molecules
`8.2.1 Electronic states and transitions
`8.2.2 Vibronic coupling
`8.2.3 Molecular configuration diagrams
`8.2.4 The Franck–Condon principle
`8.2.5 Experimental spectra
`8.3 Conjugated molecules
`8.3.1
`Small conjugated molecules
`8.3.2 Conjugated polymers
`8.4 Organic opto-electronics
`8.5 Carbon nanostructures
`8.5.1
`Introduction
`8.5.2 Graphene
`8.5.3 Carbon nanotubes
`8.5.4 Carbon bucky balls
`Chapter summary
`Further reading
`Exercises
`
`9 Luminescence centres
`9.1 Vibronic absorption and emission
`9.2 Colour centres
`9.2.1 F-centres in alkali halides
`9.2.2 NV centres in diamond
`9.3 Paramagnetic impurities in ionic crystals
`9.3.1 The crystal-field effect and vibronic coupling
`9.3.2 Rare-earth ions
`9.3.3 Transition-metal ions
`9.4 Solid-state lasers and optical amplifiers
`9.5 Phosphors
`Chapter summary
`Further reading
`Exercises
`
`10 Phonons
`10.1 Infrared active phonons
`10.2 Infrared reflectivity and absorption in polar solids
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`259
`261
`264
`266
`267
`268
`
`271
`271
`273
`
`ClearCorrect Exhibit 1067, Page 17 of 415
`
`

`

`Contents xv
`
`10.2.1 The classical oscillator model
`10.2.2 The Lyddane–Sachs–Teller relationship
`10.2.3 Reststrahlen
`10.2.4 Lattice absorption
`10.3 Polaritons
`10.4 Polarons
`10.5 Inelastic light scattering
`10.5.1 General principles of inelastic light scattering
`10.5.2 Raman scattering
`10.5.3 Brillouin scattering
`10.6 Phonon lifetimes
`Chapter summary
`Further reading
`Exercises
`
`273
`276
`277
`278
`281
`282
`285
`286
`287
`289
`290
`292
`292
`293
`
`295
`295
`298
`299
`302
`305
`305
`308
`310
`313
`317
`317
`318
`
`11 Nonlinear optics
`11.1 The nonlinear susceptibility tensor
`11.2 The physical origin of optical nonlinearities
`11.2.1 Non-resonant nonlinearities
`11.2.2 Resonant nonlinearities
`11.3 Second-order nonlinearities
`11.3.1 Nonlinear frequency mixing
`11.3.2 Effect of crystal symmetry
`11.3.3 Phase matching
`11.3.4 Electro-optics
`11.4 Third-order nonlinear effects
`11.4.1 Overview of third-order phenomena
`11.4.2 Frequency tripling
`11.4.3 The optical Kerr effect and the nonlinear refrac-
`318
`tive index
`321
`11.4.4 Stimulated Raman scattering
`321
`11.4.5 Isotropic third-order nonlinear media
`11.4.6 Nonlinear propagation in optical fibres and solitons 322
`11.4.7 Resonant nonlinearities in semiconductors
`324
`Chapter summary
`326
`Further reading
`327
`Exercises
`328
`
`A Electromagnetism in dielectrics
`A.1 Electromagnetic fields and Maxwell’s equations
`A.2 Electromagnetic waves
`Further reading
`
`330
`330
`333
`339
`
`B Quantum theory of radiative absorption and emission 340
`B.1 Einstein coefficients
`340
`B.2 Quantum transition rates
`344
`B.3 Selection rules
`347
`Further reading
`349
`
`ClearCorrect Exhibit 1067, Page 18 of 415
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`

`

`xvi Contents
`
`C Angular momentum in atomic physics
`C.1 Angular momentum in quantum mechanics
`C.2 Notation for atomic angular momentum states
`C.3 Sub-level splitting
`Further reading
`
`D Band theory
`D.1 Metals, semiconductors, and insulators
`D.2 The nearly free electron model
`D.3 Example band structures
`Further reading
`
`E Semiconductor p–i–n diodes
`Further reading
`
`Solutions to exercises
`
`Bibliography
`
`Symbols
`
`Index
`
`350
`350
`351
`352
`353
`
`354
`354
`356
`359
`362
`
`363
`365
`
`366
`
`376
`
`387
`
`389
`
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`

`

`1
`
`1.1 Classification of
`optical processes
`
`1.2 Optical coefficients
`
`1.3 The complex refractive
`index and dielectric
`constant
`
`1.4 Optical materials
`
`1.5 Characteristic optical
`physics in the solid
`state
`
`1.6 Microscopic models
`
`Chapter summary
`
`Further reading
`
`Exercises
`
`1
`
`2
`
`6
`
`9
`
`17
`
`23
`
`24
`
`25
`
`25
`
`Introduction
`
`Light interacts with matter in many different ways. Metals are shiny, but
`glass is transparent. Stained glass and gemstones transmit some colours,
`but absorb others. Other materials such as milk appear white because
`they scatter the incoming light in all directions.
`In the chapters that follow, we shall be looking at a whole host of
`these optical phenomena in a wide range of solid state materials. Before
`we can begin to do this, we must first describe the way in which the
`phenomena are classified, and the coefficients that are used to quantify
`them. We must then introduce the materials that we shall be studying,
`and clarify in general terms how the solid-state is different from the gas
`and liquid phase. This is the subject of the present chapter.
`
`1.1 Classification of optical processes
`
`The wide-ranging optical properties observed in solid-state materials
`can be classified into a small number of general phenomena. The sim-
`plest group, namely reflection, propagation, and transmission, is
`illustrated in Fig. 1.1. This shows a light beam incident on an optical
`medium. Some of the light is reflected from the front surface, while the
`rest enters the medium and propagates through it. If any of this light
`reaches the back surface, it can be reflected again, or it can be trans-
`mitted through to the other side. The amount of light transmitted is
`therefore related to the reflectivity at the front and back surfaces and
`also to the way the light propagates through the medium.
`The phenomena that can occur while light propagates through an
`optical medium are illustrated schematically in Fig. 1.2.
`Refraction causes the light waves to propagate with a smaller ve-
`locity than in free space. This reduction of the velocity leads to the
`bending of light rays at interfaces described by Snell’s law of refraction.
`Refraction, in itself, does not affect the intensity of the light wave as it
`propagates.
`Absorption occurs during the propagation if the frequency of the
`light is resonant with the transition frequencies of the atoms in the
`medium. In this case, the beam will be attenuated as it progresses. The
`transmission of the medium is clearly related to the absorption, because
`only unabsorbed light will be transmitted. Selective absorption is respon-
`sible for the colouration of many optical materials. Rubies, for example,
`are red because they absorb blue and green light, but not red.
`Luminescence is the general name given to the process of sponta-
`
`ClearCorrect Exhibit 1067, Page 20 of 415
`
`

`

`2 Introduction
`
`
`
`incident lightincident light
`
`
`propagation throughpropagation through
`
`the mediumthe medium
`
`
`
`transmitted lighttransmitted light
`
`Fig. 1.1 Reflection, propagation, and
`transmission of a light beam incident
`on an optical medium.
`
`
`
`reflected lightreflected light
`
`
`
`refractionrefraction
`
`
`absorption andabsorption and
`
`luminescenceluminescence
`
`
`
`scatteringscattering
`
`Fig. 1.2 Phenomena that can occur
`as a light beam propagates through
`an optical medium. Refraction causes
`a reduction in the velocity of the
`wave, while absorption causes atten-
`uation. Luminescence can accompany
`absorption if the excited atoms re-
`emit by spontaneous emission. Scatter-
`ing causes a redirection of the light. The
`diminishing width of the arrow for the
`processes of absorption and scattering
`represents the attenuation of the beam.
`
`neous emission of light by excited atoms in a solid-state material. One of
`the ways in which the atoms can be promoted into excited states prior
`to spontaneous emission is by the absorption of light. Luminescence can
`thus accompany the propagation of light in an absorbing medium. The
`light is emitted in all directions, and usually has a different frequency
`to the incoming beam.
`Luminescence does not always have to accompany absorption. It takes
`a characteristic amount of time for the excited atoms to re-emit by spon-
`taneous emission. This means that it might be possible for the excited
`atoms to dissipate the excitation energy as heat before the radiative re-
`emission process occurs. The efficiency of the luminescence process is
`therefore closely tied up with the dynamics of the de-excitation mecha-
`nisms in the atoms.
`Scattering is the phenomenon in which the light changes direction
`and possibly also its frequency after interacting with the medium. The
`total number of photons is unchanged, but the number going in the
`forward direction decreases because light is being re-directed in other
`directions. Scattering therefore has the same attenuating effect as ab-
`sorption. The scattering is said to be elastic if the frequency of the
`scattered light is unchanged, or inelastic if the frequency changes in
`the process. The difference in the photon energy in an inelastic scatter-
`ing process has to be taken from the medium if the frequency increases
`or given to the medium if the frequency decreases.
`A number of other phenomena can occur as the light propagates
`through the medium if the intensity of the beam is very high. These
`are described by nonlinear optics. An example is frequency doubling,
`in which the frequency of part of a beam is doubled by interaction with
`the optical medium. Most nonlinear effects have only been discovered
`through the use of lasers. At this stage, we only mention their existence
`for completeness, and postpone their further discussion to Chapter 11.
`
`1.2 Optical coefficients
`
`The optical phenomena described in the previous section can be quan-
`tified by a number of parameters that determine the properties of the
`
`ClearCorrect Exhibit 1067, Pa