Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces

717 Pages·1982·70.55 MB·English

by  V.M. AGRANOVICH and D.L. MILLS (Eds.)

MODER N PROBLEM S IN
CONDENSE D MATTE R SCIENCE S
Series editors
V.M. AGRANOVIC H
Moscow, USSR
A.A. MARADUDI N
Irvine, California, USA
Advisory editorial board
F. Abeles, Paris, France
N. Bloembergen, Cambridge, MA, USA
E. Burstein, Philadelphia, PA, USA
I.L. Fabelinskii, Moscow, USSR
M.D. Galanin, Moscow, USSR
V.L. Ginzburg, Moscow, USSR
H. Haken, Stuttgart, W. Germany
R.M. Hochstrasser, Philadelphia, PA, USA
LP. Ipatova, Leningrad, USSR
A.A. Kaplyanskii, Leningrad, USSR
L.V. Keldysh, Moscow, USSR
R. Kubo, Tokyo, Japan
I.M. Lifshitz, Moscow, USSR
R. Loudon, Colchester, UK
A.M. Prokhorov, Moscow, USSR
K.K. Rebane, Tallinn, USSR
NORTH-HOLLAND PUBLISHING COMPANY
AMSTERDAM · NEW YORK · OXFOR D
SURFAC E POLARITON S
Electromagneti c Waves at Surface s
and Interface s
Volume editors
V. M. AGRANOVIC H
Moscow, USSR
D. L. MILL S
Irvine California, USA
1982
NORTH-HOLLAND PUBLISHING COMPANY
AMSTERDAM NEW YORK · OXFORD
© North-Hollan d Publishing Company, 1982
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,
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ISBN 0444 86165 3
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Librar y of Congress Cataloging in Publication Data
Main entry under title:
Surface polaritons.
(Modern problems in condensed matter sciences)
Includes bibliographie s and indexes.
1. Polaritons. I. Agranovich, V. M. (Vladimir
Moiseevich), 1929- . II. Mills, D. L.
III. Series.
QC174. 8. P6S93 530.Ã41 81-224%
ISBN 0-444-86165-3 (Elsevier AACR2
North-Holland )
PRINTED IN THE NETHERLAND S
iv
Other Volumes in this Series:
EXCITONS
E.I. Rashba and M.D. Sturge, editors
ELECTRONIC EXCITATION ENERGY TRANSFER IN CONDENSED
MATTER
V.M. Agranovich and M.D. Galanin
SPECTROSCOPY AND EXCITATION DYNAMIC S IN CONDENSED
MOLECULAR SYSTEMS
V.M. Agranovich and R.M. Hochstrasser, editors
Oh, how many of them there
are in the fields!
But each flowers in its
own way —
In this is the highest achievement
of a flower!
Matsuo Basho
1644-1694
PREFAC E TO THE SERIE S
"Surf ace Polaritons" is the first volume in a series of contributed volumes and
monographs on condensed matter science that the North-Holland Publishing
Company is now beginning to publish. This vast area of physics is developing
rapidly at the present time, and the numerous fundamental results in it define
to a significant degree the face of contemporary science. This being so, it is
clear that the most important results and directions for future developments
can only be covered by an international group of authors working in
cooperation.
Both Soviet and Western scholars are taking part in the series, and each
contributed volume has, correspondingly, two editors. Furthermore, it is
intended that the volumes in the series will be published subsequently in
Russian by the publishing house "Nauka".
The idea for the series and for its present structure was born during
discussions that took place in the USSR and the USA between the President
of North-Holland Publishing Company, Drs. W.H. Wimmers, and the General
Editors.
The establishment of this series of books, which should become a
distinguished encyclopedia of condensed matter science, is not the only
important outcome of these discussions. A significant development is also the
emergence of a rather interesting and fruitful form of collaboration among
scholars from different countries. We are deeply convinced that such
international collaboration in the spheres of science and art, as well as other
socially useful spheres of human activity, will assist in the establishment of a
climate of confidence and peace.
The General Editors of the Series,
V.M. Agranovich A.A. Maradudin
vi
PREFAC E
The purpose of this volume is to present a sequence of articles which
describe the basic properties of surface polaritons, methods of generating
these waves in the laboratory at frequencies of interest to condensed
matter physicists, and then the physics that may be learned from them. In
our view, the collection provides an excellent summary of the activity that
resulted from the recent interest in these modes in the solid state physics
community.
A surface polariton is simply an electromagnetic wave that propagates
along the surface of a medium, or along the interface between two media.
The strength of the electromagnetic fields associated with the wave decay
in strength exponentially as one moves away from the interface into either
medium, but they vary in a wavelike fashion as one moves parallel to it.
Despite the exotic name, upon which we comment in more detail below, if
both media may be described in a continuum approximation by a dielectric
tensor and a magnetic permeability tensor (both are frequency dependent
and complex, in general), then these waves emerge as solutions of Max-
well's equations applied to the pair of media. The chapters in this volume
explore a large number of realizable configurations that support pro-
pagation of these modes.
Despite the fact that the basic properties of surface polaritons may be
obtained directly from Maxwell's equations, most physicists are not famil-
iar with them. This is curious, because they have been studied actively
since the turn of the present century, when Sommerfeld and his students
discussed them within a certain context (Joos 1934). Interest in the waves
has arisen from time to time in many subfields of physics and engineering,
where in each instance they have attracted the attention of specialists in
the area, but not of the general physics community. Largely because of the
recent burst of activity in condensed matter physics, and especially in
physics of surfaces, we now appreciate the ubiquitous nature of surface
polaritons. We hope this volume will show the condensed matter physics
community how surface polaritons may be used to probe the near vicinity
of the crystal surface or of an interface under a variety of circumstances,
in other words, how they may be used to facilitate the development of the
spectroscopy of surfaces.
The interaction of electromagnetic waves with an interface between two
vii
viii Preface
media is discussed in nearly all textbooks on electromagnetic theory when
a derivation is given of Fresnel formulae for the amplitude of waves
reflected from or transmitted through an interface. Yet surface polaritons
are almost never treated (Portis 1978), even though they emerge as solu-
tions of Maxwell's equations applied to the same geometry. The reason for
this may possibly be appreciated by considering a plane interface between
an isotropic dielectric with dielectric constant €, and vacuum. As the reader
will appreciate upon examining the discussion in several of the chapters
(see, for example, the opening chapter by D. N. Mirlin) for the surface
polariton to exist, the requirement is that €, assumed real here for sim-
plicity, be a negative number. More specifically, the inequality e ^ -1 must
be satisfied for this particular example. Most textbooks on electromagnetic
theory assume, either implicitly or explicitly, that the dielectric constant of
matter is always positive when the interaction of electromagnetic waves
with dielectrics is examined.
The static dielectric constant of any insulating solid is, ignoring spatial
dispersion (i.e. for wave vectors k = 0, see Agranovich and Ginzburg 1981)
required to be positive, from stability considerations in thermodynamics
applied to nonconducting media (Callen 1960). No such constraint applies
to the finite frequency dielectric function e(d) that enters the theory of
electromagnetic wave propagation. In fact, as the sequence of chapters in
this volume illustrate very nicely, in a wide class of solid systems one may
have negative values for e(O) over substantial ranges of frequency. Con-
sider, for example, the nearly free electron picture of simple metals. Then
if Ù is the electron plasma frequency, we have €(Ù)=1-Ùñ/Ù 2 (with
ñ
scattering of the electrons ignored), so that the inequality €(Ù)^- 1 holds
for all frequencies below Ù /\/2. For aluminum, Ù /\/2 is 10.6 eV, so on
ñ ñ
the surface of aluminum, surface polaritons may propagate at all frequen-
cies from the microwave through the visible and well into the ultraviolet.
Similar statements apply to a variety of the simple metals. This example
shows that surface polaritons are not strange solutions of Maxwell's
equations encountered under exotic conditions, but in fact they are rather
commonplace.
As several chapters explain, a photon which strikes a perfectly plane,
smooth interface between a dielectric and vacuum fails to "see" or interact
with surface polaritons on the interface. But if a suitable prism is placed
nearby, if roughness is present or a grating is ruled on the surface, one may
easily "drive" the surface polariton by linear coupling to the incoming
photon. A variety of other methods of excitation are also discussed in the
chapters, including the use of nonlinear interactions which allow the
generation of surface polaritons on perfectly smooth surfaces or interfaces.
In an isotropic dielectric, we have D = Å + 4ðÑ = â(Ù)Å. For the dielec-
tric constant to be negative, the external electric field Å must excite a
Preface ix
polarization density Ñ 180° out of phase with the exciting field E. If the
medium has any sharp absorption line at frequency Ù , the excitation of
0
the medium at a frequency just above Ù will result in a negative con-
0
tribution to Ñ that can be very large, if the absorption line is sharp. That
this is so, quite generally is insured by the Kramers-Kronig relations. In
more elementary language, if a very lightly damped harmonic oscillator is
driven just above its resonance frequency, then the response not only has
large amplitude, but is 180° out of phase with the driving field. The induced
polarization is thus directed anti-parallel to the electric field that excites it.
Hence, the condition for surface polariton propagation is realized at the
smooth planar interface between vacuum and an isotropic dielectric almost
always just above an absorption line, in spectral regions where narrow
lines exist. Thus, just above the reststrahl frequency of simple ionic crystals,
we encounter the "surface phonon polaritons" discussed by D. N. Mirlin
and others. "Surface exciton polaritons" are formed just above sharp
exciton absorption lines, as discussed by J. Lagois and B. Fischer. The
additional modifier refers to the elementary excitation in the crystal whose
contribution to the dipole moment density Ñ drives the dielectric constant
negative.
We are now in a position to understand why the surface waves are
referred to commonly as surface polaritons, in the condensed matter
physics literature. Near sharp absorption bands such as those just des-
cribed, å(Ù) is a strong function of frequency both above and below Ù .
0
When å(Ù) is positive, just below Ù and sufficiently far above it, Max-
0
well's equations admit plane wave solutions in the bulk of the material. In
the frequency regime where €(Ù ) displays such sharp resonant structure
near an absorption line, one may describe the electromagnetic wave as a
coupled mode which is an admixture of the electromagnetic field and the
elementary excitation in the medium that produces the resonance in â(Ù )
(Mills and Burstein 1974). Such electromagnetic waves, when described
within this picture, are commonly called polaritons in the literature of
condensed matter physics. Hence, the surface electromagnetic waves of
interest to the authors in the present volume are frequently referred to as
surface polaritons.
As remarked earlier, surface electromagnetic waves have been studied in
various subfields of physics, and within each, a specialized terminology for
them has evolved. This is true within condensed matter physics, as well as
within physics and engineering as a whole. This generated a problem for
the editors of the present volume, in that the set of authors has been drawn
from a broad spectrum of areas in condensed matter physics. Not all
authors used the same terminology, and after initial correspondence and
conversation, it became clear that some felt the particular choice made by
them had historical precedence over other possibilities. The arguments in
÷ Preface
each case seem sensible, but it proved difficult to obtain agreement on the
terminology among the diverse array of authors who have contributed to
the volume. Thus, A. A. Maradudin prefers to use distinctly different
language to discuss waves for which the retardation terms in Maxwell's
equations enter in an essential fashion, and those for which these may be
ignored and an electrostatic description is sufficient. He uses the term
surface polariton to describe surface electromagnetic waves of the first
class, and with the metal/vacuum interface in mind, the solutions found in
the electrostatic limit are described as surface plasmons. In fact, for a
smooth surface, the dispersion relation of the surface electromagnetic
wave is continuous, with retardation important when the frequency Ù of
the wave and its wave vector parallel to the surface Q\\ satisfy Ù = cQ\\ and
9
the electrostatic limit appropriate when Q\\ is so large that cQ\\ > Ù. Here c
is the velocity of light in vacuum. Thus, the terminology used by A. A.
Maradudin, not at all uncommon in the theoretical literature, uses different
terms to denote quasi-particles obtained in different approximations. In the
chapter by V. M. Agranovich, we see the term "Coulomb wave" used to
denote modes that were found when retardation is disregarded. H. Raether,
along with J. Sipe and G. Stegeman use the term surface plasmon to refer
to the surface electromagnetic wave on metals for all values of Ù and Qj,
including the region where retardation is important. Thus, these authors
use the term surface plasmon in the same manner as we employ surface
polariton in the present discussion.
We hope the lack of a uniform terminology will not render the volume
confusing to the reader not familiar with the field; it should be clear that
the same reader will encounter a similar array of terms if he or she consults
the general literature, so it may be that by comparing the material in the
various chapters within one set of covers, the reader can become acquain-
ted with the range of descriptive terminology used in the field.
The present volume confines its attention to the elucidation of the basic
properties of surface polaritons, the methods of generating them in the
laboratory, their use as probes of the surface or interface environment and
finally to the nonlinear interactions in which they participate. These topics
are covered in depth, and we are particularly pleased to see that a large
volume of actual experimental data is reproduced in the figures and tables.
Space limitations then require us to omit material on more specialized or
less developed topics. There is no discussion of the properties of surface
polaritons on magnetic crystals; one of the editors will prepare a chapter
which includes discussion of such modes for another volume in the present
series (Agranovich and Loudon).
Surface spectroscopy and, in particular, spectroscopy of surface polari-
tons continues its rapid development. In this connection, we shall mention
new results that were obtained after this volume had been prepared for
Preface xi
publication. These concern nonlinear surface polaritons (NSP) and waves
of self-induced transparency (SIT) on surfaces.
Previously, when we discussed surface polaritons, surface plasmons,
etc., we were concerned with solutions of linear Maxwell equations. As is
known, nonlinearity appears in these equations when in the relation D = eE
the dependence of e on the strength of the electric field is taken into
account, and not only its dependence on the frequency and wave vector
(the latter corresponds to the taking of spatial dispersion into account, see
Agranovich and Ginzburg (1981)). In the simplest case, i.e., in taking the
dependence of e on only the magnitude of \E\ into consideration, e =
€(Ù) + OL\E\2. If a >0, this nonlinearity leads to self-focusing and to other
nonlinear effects.
In the papers (Tomlinson 1980, Agranovich et al. 1980, Maradudin 1981)
it was established that this same nonlinearity leads to the occurrence of
NSP, that those waves can exist in spectral regions in which no linear
waves are formed, and that the frequency of these waves depends on the
strength of the electric field at the surface. In particular, it was shown by
Tomlinson (1980) and Maradudin (1981) that at the interface between linear
and nonlinear isotropic media NSP exist only in s-polarization. If, however,
the nonlinear medium is optically anisotropic (uniaxial), then, as shown by
Agranovich et al. (1980), NSP are formed in p-polarization as well (recall
that at the interface of the linear media SP are formed only in p-
polarization). The frequency of NSP in p-polarization depends on the wave
vector so that it is precisely in this case that NSP have nonzero group
velocity Üù/dk. This feature of NSP in p-polarization is important because
the waves being discussed can exist, in particular, in the transparency
spectral region, according to theory. In virtue of the fact that da>/dk7*0,
these waves may have considerable lengths of propagation, even along
dielectric surfaces on which linear SP are usually quite rapidly damped. In
connection with the aforesaid, the search for methods of exciting and
detecting NSP would be of especial interest, as would be an analysis of the
feasibility of employing NSP for developing new optical methods of
investigating surfaces and thin films.
An entirely different type of nonlinear surface waves occurs in the
propagation of ultrashort pulses of intensive and resonant radiation along a
surface coated with a thin film of a resonant substance. In this case, as
shown by Agranovich et al (1981a), surface "27r" pulses of self-induced
transparency are found to be stable. The investigation of this problem is
only in an early stage (a similar effect in waveguides is discussed in the
paper by Agranovich et al. (1981b)) and only the simplest situations have
been studied. In particular, there is no rigorous answer to the question of
whether stable surface "27r" pulses exist or not under conditions when the
whole mass of the dielectric is resonant, rather than a thin film on a