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首页负折射率与负指数材料的物理原理
"《物理学中的负折射与负指数材料》是一本深入探讨介电常数和磁导率均为负数的特殊材料的专业书籍,它隶属于Springer材料科学系列。这一系列旨在覆盖材料物理的全方位内容,包括基本原理、物理性质、材料理论和设计,反映出当前对材料结构和性能控制的前沿研究。对于超材料和左手材料的爱好者而言,这本书尤其重要,因为它揭示了这些新型材料的独特性。 负折射率是本书的核心主题之一,它打破了传统的光传播规律,即光在某些负指数材料中传播时,其折射角反而成为负值。这种现象不仅在理论上引人入胜,而且对于光通信、光学器件和隐身技术等领域具有潜在的应用前景。双负材料(同时具备负电导率和负磁导率)的研究在此书中得到了详尽的阐述,它们能够引导电磁波以不同于传统介质的方式行进,展现出前所未有的光学性能。 此外,书中还涵盖了其他相关的材料科学话题,如波散射、局域化和介观现象的介绍,磁学中磁场对材料影响的基础和应用,金属材料内部摩擦的研究,固体体动力学的时间依赖性性质,以及锡焊接技术中的材料选择、性质和可靠性分析。最后,展望未来的材料科学,书中的理论、实验和建模部分探讨了如何设计和制造满足现代科技需求的新材料。 《物理学中的负折射与负指数材料》是一本综合性的参考资料,不仅提供了深入理解这些新颖材料的平台,还为科研人员、工程师以及材料科学的研究生提供了宝贵的工具,以推动科技进步和创新。"
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XVI List of Contributors
Yuri S. Kivshar
Nonlinear Physics Centre and Center
for Ultra-High Bandwidth Devices
for Optical Systems (CUDOS)
Research School of Physical Sciences
and Engineering
Australian National University
Canberra, ACT 0200, Australia
ysk@internode.on.net
Clifford M. Krowne
Microwave Technology Branch
Electronics Science and Technology
Division
Naval Research Laboratory
Washington, DC 20375-5347
krowne@webbsight.nrl.navy.mil
Jensen Li
Physics Department
Hong Kong University of Science
and Technology
Clear Water Bay, Hong Kong, China
Zhi-Yuan Li
Institute of Physics
Chinese Academy of Sciences
Beijing 100080
Zifang Lin
Bartol Research Institute
and Department of Physics
and Astronomy
University of Delaware
Newark, DE 19711, USA
Z.Y. Liu
Physics Department
Wuhan University
Wuhan, China
Peter F. Loschialpo
Naval Research Laboratory
Washington, DC 20375
Wentao Lu
Department of Physics
and Electronic Materials
Research Institute
Northeastern University
Boston, MA 02115, USA
w.lu@neu.edu
Angelo Mascarenhas
Materials Science Center
National Renewable Energy
Laboratory (NREL)
1617 Cole Blvd.
Golden, CO 80401, USA
Ekmel Ozbay
Nanotechnology Research Center
Department of Physics
and Department of Electrical
and Electronics Engineering
Bilkent University
Bilkent, 06800 Ankara, Turkey
ozbay@bilkent.edu.tr
Gonca Ozkan
Nanotechnology Research Center
Bilkent University
Bilkent 06800, Ankara, Turkey
Claudio G. Parazzoli
Boeing Phantom Works
Seattle, WA 98124
Frederic Rachford
Material Science and Technology
Division
Naval Research Laboratory
Washington, DC 20375
rachford@anvil.nrl.navy.mil
Ilya V. Shadrivov
Nonlinear Physics Centre
Research School of Physical Sciences
and Engineering
Australian National University
Canberra ACT 0200, Australia
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List of Contributors XVII
Ping Sheng
Physics Department
Hong Kong University of Science
and Technology
Clear Water Bay, Hong Kong, China
Douglas L. Smith
Naval Research Laboratory
Washington, DC 20375
Srinivas Sridhar
Vice Provost for Research
Director, Electronic Materials
Research Institute
Arts and Sciences Distinguished
Professor of Physics
Northeastern University
360 Huntington Avenue,
Boston, MA 02115, USA
ssridhar@neu.edu
Minas H. Tanielian
Boeing Phantom Works
Seattle, WA 98124
P. Vo do
Department of Physics
and Electronic Materials
Research Institute
Northeastern University
Boston, MA 02115, USA
Yiquan Wang
Institute of Physics
Chinese Academy of Sciences
Beijing 100080
Dao-Zhong Zhang
Institute of Physics
Chinese Academy of Sciences
Beijing 100080
Xiangdong Zhang
Beijing Normal University
Beijing 100875, China
zhangxd@bnu.edu.cn
Yong Zhang
Materials Science Center
National Renewable Energy
Laboratory (NREL)
1617 Cole Blvd.
Golden, CO 80401
Yong
Zhang@nrel.gov
Lei Zhou
Bartol Research Institute
and Department of Physics
and Astronomy
University of Delaware
Newark, DE 19711, USA
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1
Negative Refraction of Electromagnetic
and Electronic Waves in Uniform Media
Y. Zhang and A. Mascarenhas
Summary. We discuss various schemes that have been used to realize negative
refraction and zero reflection, and the underlying physics that dictates each scheme.
The requirements for achieving both negative refraction and zero reflection are
explicitly given for different arrangements of the material interface and different
structures of the electric permittivity tensor ε. We point out that having a left-
handed medium is neither necessary nor sufficient for achieving negative refraction.
The fundamental limitations are discussed for using these schemes to construct a
perfect lens or “superlens,” which is the primary context of the current interest in
this field. The ability of an ideal “superlens” beyond diffraction-limit “focusing” is
contrasted with that of a conventional lens or an immersion lens.
1.1 Introduction
1.1.1 Negative Refraction
Recently, negative refraction has attracted a great deal of attention, largely
due to the realization that this phenomenon could lead to the development
of a perfect lens (or superlens) [1]. A perfect lens is supposed to be able to
focus all Fourier components (i.e., the propagating and evanescent modes)
of a two-dimensional (2D) image without missing any details or losing any
energy. Although such a lens has yet to be shown possible either physically
and practically, the interest has generated considerable research in electromag-
netism and various interdisciplinary areas in terms of fundamental physics and
material sciences [2–4]. Negative refraction, as a physical phenomenon, may
have much broader implications than making a perfect lens. Negative refrac-
tion achieved using different approaches may involve very different physics
and may find unique applications in different technology areas. This chapter
intends to offer some general discussion that distinguishes the underlying
physics of various approaches, bridges the physics of different disciplines
(e.g., electromagnetism and electronic properties of the material), and pro-
vides some detailed discussions for one particular approach, that is, negative
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2 Y. Zhang and A. Mascarenhas
refraction involving uniform media with conventional dielectric properties. By
uniform medium we mean that other than the microscopic variation on the
atomic or molecular scale the material is spatially homogeneous.
The concept of negative refraction was discussed as far back as 1904 by
Schuster in his book An Introduction to the Theory of Optics [5]. He indicated
that negative dispersion of the refractive index, n, with respect to the wave-
length of light, λ, i.e., dn/dλ<0, could lead to negative refraction when light
enters such a material (from vacuum), and the group velocity, v
g
,isinthe
opposite direction to the wave (or phase) velocity, v
p
. Although materials with
dn/dλ<0 were known to exist even then (e.g., sodium vapor), Schuster stated
that “in all optical media where the direction of the dispersion is reversed,
there is a very powerful absorption, so that only thicknesses of the absorb-
ing medium can be used which are smaller than a wavelength of light. Under
these circumstances it is doubtful how far the above results have any applica-
tion.” With the advances in material sciences, researchers are now much more
optimistic 100 years later. Much of the intense effort in demonstrating a “poor
man’s” superlens is directed toward trying to overcome Schuster’s pessimistic
view by using the spectral region normally having strong absorption and/or
thin-film materials with film thicknesses in the order of (or even a fraction of)
the wavelength of light [2]. However, with regard to the physics of refraction,
for a “lens” of such thickness, one may not be well justified in viewing the
transmission as refraction, because of various complications (e.g., the ambi-
guity in defining the layer parameters [6] and the optical tunnel effect [7]).
The group velocity of a wave, v
g
(ω, k)=dω/dk, is often used to describe
the direction and the speed of its energy propagation. For an electromagnetic
wave, strictly speaking, the energy propagation is determined by the Poynting
vector S. In certain extreme situations, the directions of v
g
and S could even
be reversed [8]. However, for a quasimonochromatic wave packet in a medium
without external sources and with minimal distortion and absorption, the
direction of S does coincide with that of v
g
[9]. For simplicity, we will focus
on the simpler case, where the angle between v
g
and wave vector k is of
significance in distinguishing two types of media: when the angle is acute or
k · v
g
> 0, it is said to be a right-handed medium (RHM); when the angle is
obtuse or k ·v
g
< 0, it is said to be a left-handed medium (LHM) [10]. If one
prefers to define the direction of the energy flow to be positive, an LHM can
be referred to as a material with a negative wave velocity, as Schuster did in
his book. A wave with k ·v
g
< 0 is also referred to as a backward wave (with
negative group velocity), in that the direction of the energy flow is opposite
to that of the wave determined by k [11, 12]. Lamb was perhaps the first to
suggest a one-dimensional mechanical device that could support a wave with
a negative wave velocity [13], as mentioned in Schuster book [5]. Examples of
experimental demonstrations of backward waves can be found in other review
papers [4, 14]. Unusual physical phenomena are expected to emerge either in
an individual LHM (e.g., a reversal of the group velocity and a reversal of
Doppler shift) or jointly with an RHM (e.g., negative refraction that occurs
![](https://csdnimg.cn/release/download_crawler_static/10935175/bg14.jpg)
1 Negative Refraction of Electromagnetic and Electronic Waves 3
at the interface of an LHM and RHM) [10]. The effect that has received most
attention lately is the negative refraction at the interface of an RHM and
LHM, which relies on the property k · v
g
< 0intheLHM.
There are a number of ways to realize negative refraction [4]. Most ways
rely on the above-mentioned LH behavior, i.e., k · v
g
< 0, although LH
behavior is by no means necessary or even sufficient to have negative
refraction. Actually, LH behavior can be readily found for various types
of wave phenomena in crystals. Examples may include the negative disper-
sion of frequency ω(k) for phonons and of energy E(k) for electrons; however,
they are inappropriate to be considered as uniform media and thus to discuss
refraction in the genuine sense, because the wave propagation in such media is
diffractive in nature. For a simple electromagnetic wave, it is not trivial to find
a crystal that exhibits LH behavior. By “simple electromagnetic wave,” we
refer to the electromagnetic wave in the transparent spectral region away from
the resonant frequency of any elementary excitation in the crystal. In this
case, the light–matter interaction is mainly manifested as a simple dielectric
function ε(ω), as in the situation often discussed in crystal optics [15], where
ε(ω) is independent of k.
1.1.2 Negative Refraction with Spatial Dispersion
The first scheme to be discussed for achieving negative refraction relies on
the k dependence of ε to produce the LH behavior. The dependence of ε(k)
or n(λ) is generally referred to as spatial dispersion [16, 17], meaning that
the dielectric parameter varies spatially. Thus, this scheme may be called
the spatial-dispersion scheme. The negative refraction originally discussed by
Schuster in 1904 could be considered belonging to this scheme, although the
concept of spatial dispersion was only introduced later [17] and discussed in
greater detail in a book by Agranovich and Ginzburg, Spatial Dispersion in
Crystal Optics and the Theory of Excitons [9]. If one defines v
p
= ω/k = c/n,
and assumes n>0, then according to Schuster, v
g
is related to v
p
by [5]
v
g
= v
p
− λ
dv
p
dλ
, (1.1)
and the condition for having a negative wave velocity is given as λ dv
p
/dλ>
v
p
, which is equivalent to dn/dλ<−n/λ < 0. Negative group velocity and
negative refraction were specifically associated with spatial dispersion by
Ginzburg and Agranovich [9, 17]. Recently, a generalized version of this con-
dition has been given by Agranovich et al. [18]. In their three-fields (E, D, B)
approach, with a generalized permittivity tensor ˜ε(ω, k) (see the chapter
of Agranovich and Gartstein for more details), the time-averaged Poynting
vector in an isotropic medium is given as
S =
c
8π
Re(E
∗
xB) −
ω
16π
∇
k
˜ε(ω,k)E
∗
E, (1.2)
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