Table Of Content42
Springer Series in Solid-State Sciences
Edited by Hans-Joachim Queisser
Springer Series in Solid-State Sciences
Editors: M. Cardona P. Fulde H.-J. Queisser
Volume 40 Semiconductor Physics - An Introduction By K Seeger
Volume 41 The LMTO Method Muffin-Tin Orbitals and Electronic Structure
By H.L. Skriver
Volume 42 Crystal Optics with Spatial Dispersion, and Excitons
By V. M. Agranovich and V. L. Ginzburg
Volume 43 Resonant Nonlinear Interactions of Light with Matter
By V.S. Butylkin, AE. Kaplan, Yu.G. Khronopulo, and E.I. Yakubovich
Volume 44 Elastic Media with Microstmcture 11 Three-Dimensional Models
By I.A. Kunin
Volume 45 Electronic Properties of Doped Semiconductors
By B.1. Shklovskii and AL. Efros
Volume 46 Topological Disorder in Condensed Matter
Editors: F. Yonezawa and T. Ninomiya
Volume 47 Statics and Dynamics of Nonlinear Systems
Editors: G. Benedek, H. Bilz, and R Zeyher
Volume 48 Magnetic Phase Transitions
Editors: M. Ausloos and R 1. Elliott
Volume 49 Organic Molecular Aggregates, Electronic Excitation
and Interaction Processes
Editors: P. Reineker, H. Haken, and H. C. Wolf
Volume 50 Multiple Diffraction of X-Rays in Crystals
By Shih-Lin Chang
Volume 51 Phonon Scattering in Condensed Matter
Editor: W Eisenmenger, K Laßmann, and S. Döttinger
Volume 52 Magnetic Superconductors and Their Related Problems
Editors: T. Matsubara and A Kotani
Volumes 1-39 are listed on the back inside cover
V. M. Agranovich V. L. Ginzburg
Crystal Optics
with Spatial Dispersion,
and Excitons
Second Corrected and Updated Edition
With 46 Figures
Springer-Verlag Berlin Heidelberg GmbH 1984
ProfessorDr.VladimirM.Agranovich
AcademyofSeiencesoftheUSSR,InstituteofSpectroscopy,Troitsk,
Moscow,r-n,142092,USSR
ProfessorDr.Vitaly Ginzburg
P.N.LebedevPhysicalInstitute,AcademyofSeiencesoftheUSSR
Moscow,USSR
SeriesEditors:
Professor Dr.ManuelCardona
Professor Dr.PeterFulde
Professor Dr.Hans-Joachim Queisser
Max-Planck-InstitutfürFestkörperforschung,Heisenbergstrasse1
D-7000Stuttgart80,Fed.Rep.ofGermany
Titleofthe1.EnglishEdition:
SpatialDispersioninCrystalOpticsandtheTheory01Excitons
© byInterscience,London,NewYork,Sidney1966
Titleofthe2ndcorrectedandenlargedoriginalRussianedition:
Kristallooptikasuchetomprostranstvennoidispersiiiteoriya eksitonov
© by"Nauka"PublishingHouseMoscow1979
ISBN 978-3-662-02408-9 ISBN 978-3-662-02406-5 (eBook)
DOI 10.1007/978-3-662-02406-5
Library ofCongress Cataloging in Publication Data.Agranovich, V.M.(Vladimir Moiseevich), 1929-.
Crystal optics with spatial dispersion, and excitons. (Springer series in solid-state sciences ; v.42).
Translationof:Kristallooptikasuchetomprostranstvennoidispersii iteoriieksitonov,1.Crystaloptics.
2.Exciton theory,LGinzburg,V.L.(VitaliiLazarevich),1916-.II.Title.lll.Series.
QD94LA4131983 548'.9 83-16717
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©bySpringer-VerlagBerlinHeidelberg1984
OriginallypublishedbySpringer-VerlagBerlinHeidelbergNewYorkin 1984.
Softcoverreprintofthehardcover2ndedition1984
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Preface
Spatial dispersion, namely, the dependence of the dielectric-constant tensor
on the wave vector (i.e., on the wavelength) at a fixed frequency, is receiving
increased attention in electrodynamics and condensed-matter optics, partic
ularly in crystal optics.
In contrast to frequency dispersion, namely, the frequency dependence of
the dielectric constant, spatial dispersion is of interest in optics mainly when it
leads to qualitatively new phenomena. One such phenomenon has been weH
known for many years; it is the natural optical activity (gyrotropy). But there
are other interesting effects due to spatial dispersion, namely, new normal
waves near absorption lines, optical anisotropy of cubic crystals, and many
others.
Crystal optics that takes spatial dispersion into account includes classical
crystal optics with frequency dispersion only, as a special case. In our opinion,
this fact alone justifies efforts to develop crystal optics with spatial dispersion
taken into account, although admittedly its influence is smaH in some cases
and it is observable only under rather special conditions.
Furthermore, spatial dispersion in crystal optics deserves attention from
another point as well, namely, the investigation of excitons that can be excited
by light. We contend that crystal optics with spatial dispersion and the theory
of excitons are fields that overlap to a great extent, and that it is sometimes
quite impossible to separate them. It is our aim to show the true interplay be
tween these interrelations and to combine the macroscopic and microscopic
approaches to crystal optics with spatial dispersion and exciton theory.
The book covers a wide range of the crystal-optics and condensed-matter elec
trodynamics problems. The selection reflects, to some extent, the authors, scien
tific interests. Thus, this monograph should not be considered a review of an the
available literature. It was our aim to dea1 with a broad range of problems by ap
plying the above-mentioned approach, as in our previous publications.
To our knowledge, no other books have been devoted to spatial dispersion
in crystal optics. The lack of such a treatment becomes evident in almost any
textbook on crystal optics. These books usually lag behind the current liter
ature. Many experimental and theoretical problems of linear and nonlinear
optics await solution. Their investigation can be accelerated by a sufficiently
comprehensive and detailed presentation of the state-of-the art.
VI Preface
We know that most readers of such monographs are interested only in
specific problems; others find it difficult to read chapters with cumbersome
calculations, etc. Therefare, we made no attempt to avoid certain repetitions
and elementary explanations. Experience shows that it is not the best practice
to save space in such a text by not repeating fundamentals, even several times.
In oUf opinion, on the other hand, it proves more expedient in becoming ac
quainted with details and subtleties of special problems in scientific journals
and papers.
The first English edition of this book was published in 1966 (first and sec
ond Russian editions - in 1965 and 1979). In addition to the quite numerous
changes and additions of new material, many sections have been substantially
altered or even rewritten. We are here referring to the treatments of boundary
conditions, surface-polariton spectroscopy, Raman scattering of light by
polaritons, the calculation of the dielectric-constant tensor by the local-field
method, and experimental investigations of the effects due to spatial disper
sion. These are all problems that have attracted much attention in recent
years, and have been extensively discussed in the literature.
This is also true of nonlinear effects in crystal optics. But we do not deal
with nonlinear crystal optics per se in the present book, except for a discussion
of certain closely allied processes, such as light and x-ray scattering in crystals,
the influence of external electric and magnetic fields on optical processes, and
boundary conditions. In the preface to the original Russian edition, we stres
sed the fact that we had not made any attempt to completely cover the subject,
and had especially not reviewed all the existing literature. Today, when the
volume of available data has increased considerably, the aforesaid is all the
more true. Nevertheless, we are confident that we have elucidated all the most
impartant problems of linear crystal optics with spatial dispersion. This, we
feel, justifies the publication of this new revised and supplemented edition.
In conclusion, the authors wish to thank T. A. Leskova, A. G. Malshu
kov, A. G. Molchanov and V. I. Yudson far their assistance in preparing the
manuscript.
The authors also sincerely thank the translator N. Weinstein for a number
of useful suggestions that have undoubtedly improved the presentation of the
subject. No less gratitude is due to Dr. H. Lotsch for his extensive help in the
editing of our book.
Moscow, December 1983 V. M. Agranovich and V. L. Ginzburg
Contents
1. Introduction ............................................... 1
1.1 Basie Problems of Crystal Opties .......................... 1
1.2 Excitons and Polaritons .................................. 10
2. The Complex Dielectric-Constant Tensor 8iiw,k) and
NormalWavesinaMedium .................................. 18
2.1 The Tensor Gij(w, k) and Hs Properties ..................... 18
2.1.1 The Eleetromagnetie Field Equations and the Introduetion
oftheTensorGij(w,k) .............................. 18
2.1.2 General Properties of the Tensor Gij( W, k) ............. 27
2.1.3 The Approximation of Classieal Crystal Opties.
The Tensor Gij( W, k) in an Isotropie Medium ........... 37
2.2 Normal Eleetromagnetie Waves in a Medium. . . . . . . . . . . . . . . . 42
2.2.1 Wave Equation and Dispersion Equation .............. 42
2.2.2 Transverse and Longitudinal Waves, "Fietitious"
Longitudinal Waves and "Polarization Waves". _
Real, Coulomb and Meehanieal Excitons .............. 47
a) Coulomb Exeitons: Longitudinal and "Fietitious"
Longitudinal Waves ............................. 51
b) Coulomb Excitons: "Polarization Waves" .......... 54
2.2.3 Multiple Roots of the Dispersion Equation . . . . . . . . . . . . . 57
2.2.4 Separating the Transverse FieldEol and the Tensor Gol,ij •• 62
2.2.5 The Dispersion Relations for a Complex Refraetive Index.
Inequalities for the Region of Transpareney . . . . . . . . . . . . 66
2.3 Energy Relations and Other Equations for Waves in
an Anisotropie Medium .................................. 72
2.3.1 The Law of Energy Conservation in the Eleetrodynamies
of Media Displaying Spatial Dispersion ............... 72
2.3.2 Quadratie Funetions ofthe Normal Wave Amplitudes ... 81
a) The Conservation of Energy for a Field . . . . . . . . . . . . . 83
b) The Veetor of Group Velocity . . . . . . . . . . . . . . . . . . . . . 84
e) The Conservation of Momentum for a Field . . . . . . . . . 93
d) Some Applieations of the Poynting Tqeorem ........ 94
e) The Boundary Conditions for a Gyrotropic Medium . . 95
VIII Contents
f) The Boundary Conditions for the Optically Nonlinear
Medium with the Center of Inversion. . . . . . . . . . . . . . . 97
g) Spatial Dispersion and Orthogonality of Normal
Waves ........... ..... .... . .... ... ..... ..... ... 99
h) The Reciprocity Theorem ........................ 100
2.3.3 Certain Theorems for Ray and Wave Propagation in
a Medium ........................................ 103
3. TheTensofGij(w,k)inCrystals ............................... 108
3.1 The Tensor eij(W, k) for Crystals .......................... 108
3.1.1 Introduetion of the Tensor eij(W, k) .................. 108
3.1.2 Weak Spatial Dispersion............ ........ ........ 117
3.2 The Tensor eij( w, k) for Crystals of Various Classes .......... 122
3.2.1 Gyrotropic Crystals ................................ 122
3.2.2 Nongyrotropic Crystals '" . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4. Spatial Dispersion in Crystal Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.1 Gyrotropic Crystals ..................................... 136
4.1.1 Normal Waves in Gyrotropic Crystals . .. . . . . . . . .. . . .. . 137
4.1.2 A New Wave Near the Absorption Lines in a Gyrotropic
Medium.. .. ................ ..... .... . ... ..... .... 145
4.2 Nongyrotropie Crystals .................................. 149
4.2.1 Normal Waves .................................... 149
4.2.2 Isotropie Medium and New Waves Near Dipole
Absorption Lines .................................. 150
a)Group-VelocityVeetor ........................... 165
4.3 Cubic Nongyrotropic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
4.3.1 Optieal Anisotropy: Dipole Transitions ............... 167
4.3.2 Optical Anisotropy: Quadrupole Transitions .. . . . . . . . . . 171
4.3.3 Classifieation of the States of 'Meehanical' Excitons with
k = 0 and Seleetion Rules for Quadrupole Transitions ... 174
4.3.4 New Waves Near Quadrupole Absorption Lines.
Longitudinal Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
4.4 Influenee of Meehanical Stresses and External Eleetrie and
Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
4.4.1 Anisotropy of the Optical Properties and Seleetion Rules
in the Presenee of External Influenees ........ . . . . . . . . . 188
4.4.2 The Explieit Dependenee of the Tensor eij(W, k) on the
Strength of Weak External Fields . . . . . . . . . . . . . . . . . . . . . 192
a) The Magnetic-Field Inversion Effeet .. . . . . . . . . . . . . . . 196
4.4.3 Influenee of Magnetie and Eleetrie Fields on Cadmium
Sulfide (CdS) Crystals .............................. 198
a) Quadratie Magneto-Stark Effeet ................... 202
4.5 Boundary Conditions in the Case of Spatial Dispersion
Near aSeparate Resonanee (Absorption Line) ............... 205
Contents IX
4.5.1 The Tensor tij( w, k) Near an Isolated Resonance ....... 208
4.5.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 211
a) Dielectrie Tensor for Isotropie Nongyrotropie Media. 216
4.5.3 Boundary Conditions .............................. 218
a) The Transition ("Dead") Layer Problem. . . . . . . . . . . . 224
b) ABC for Molecular Crystals and the Surface Current
Appearance .................................... 228
4.5.4 Reflected and Refracted Waves Near Dipole and
Quadrupole Transition Frequencies in a Nongyrotropic
Crystal ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 233
a) The Law of Energy Conservation ..... . . . . . . . . . . . .. 236
4.5.5 Reflected and Refracted Waves Near a Dipole Transition
Frequency in a Gyrotropie Crystal .. . . . . . . . . . . . . . . . . .. 238
4.5.6 The Influence of a Nonhomogeneous Subsurface Layer
on Light Reflection Near Exciton-Absorption Bands .... 242
4.5.7 Transmission of Light Through a Plane-Parallel Plate
(Nongyrotropic Medium) ........................... 244
4.5.8 Transmission of Light Through a Plane-Parallel Plate
(Gyrotropie Medium) .............................. 248
a) The Integral Absorption ......................... 247
4.6 Experimental Investigations of Spatial Dispersion in Crystals .. 253
4.6.1 Gyrotropie Crystals ................................ 253
4.6.2 Nongyrotropic Crystals ... . . . . . . . . . . . . . . . . . . . . . . . . .. 257
5. Surface Excitons and Polaritons .............................. 271
5.1 Polaritons at the Interface of Isotropie Media ............... 271
5.1.1 Dispersion of Surface Waves for Lossless Media. . . . . . .. 274
5.1.2 General Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 274
5.1.3 Surface Polaritons for Layered Structures ............. 275
a) The Brewster Waves .... . . . . . . . . . . . . . . . . . . . . . . . .. 278
b) Propagation of Surface Waves with Damping ....... 279
c) Reflection, Diffraction and Refraction of Surface
Waves at Surface Boundaries ..................... 280
5.2 Spectra of Surface Polaritons in Anisotropie Crystals ......... 283
5.3 Transition-Layer Effects in Surface Polariton Spectra ........ 289
5.3.1 Transition Layers with High Electrie Conductivity ...... 290
5.3.2 Transition Layers in the Presence of a Resonance with
the Surface Polariton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 294
a) The Effective Boundary Conditions . . . . . . . . . . . . . . .. 294
b) Polariton Spectrum Splitting for TH Surface Waves .. 295
c) TE Surface Waves in the Transition Layers' Resonance
Region.. ... ......... ..... .... ........ ......... 298
5.3.3 Effect of Surface Roughness (lrregularities) on the Path
Length of Surface Polaritons ........................ 301
