left-handed media制成棱镜：入射光与出射光平行。与相对论无关。
left-handed media制成棱镜：入射光与出射光平行。与相对论无关。
以下是我写的和我摘录的有关left-handed media的材料。left-handed media是1999年－2002年的新的热门研究方向。
刘武青先生不要骂我有用英文了。刘先生如果能在中文刊物找到有关left-handed media的文章，那么我将很惊奇。
The demonstration by Smith {\it et al.} of a periodic material
having a frequency band where the effective permittivity
($\varepsilon$) and the effective permeability ($\mu$) are
simultaneously negative has focused attention on the earlier
theoretical analysis by Veselago. Veselago termed a homogeneous
materials with simultaneously negative $\varepsilon$ and $\mu$
left handed because in such a material the Poynting vector and the
wave vector would be antiparallel. He further suggested that
left-handed materials would exhibit a negative index of
refraction. An isotropic two-dimensional extension of the
left-handed material developed by Smith {\it et al.} has recently
been used to confirm that a structured left-handed material does
indeed have a negative index of refraction. All potential methods
of construction of left-handed materials are now of intense
interest, and in this letter we investigate the properties of a
layered material, consisting of alternating layers in which
$\varepsilon <0$ ( but $\mu >0$ ) and layers in which $\mu <0$ (
$\varepsilon >0$ ). In practice one or both layers might be a
metamaterial, but we shall suppose that they are homogeneous
materials with true $\varepsilon$ and $\mu$. \cite {Fredkin}
In ``left-handed'' medium, most phenomena as the Doppler effect,
Cherenkov radiation and even Snell's law are inverted. The concept
of negative $\mu _{eff}(\omega )$ is of particular interest, not
only because this is a regime not observed (rarely met) in
ordinary (regular, conventional, usual) materials, but also
because such a medium can be combined with a negative $\varepsilon
_{eff}(\omega )$ to form a ``left-handed'' material (i. e., ${\bf
{E}}\times {\bf {H}}$ lies along the direction of $-{\bf {k}}$ for
propagating plane waves ). In 1968, Veselago theoretically
investigated the electrodynamic consequences of a medium having
both $\varepsilon$ and $\mu$ negative and concluded that such a
medium would have dramatically different propagation
characteristics stemming from the sign change of the group
velocity, including reversal of both the Doppler shift and
Cherenkov radiation, anomalous refraction and even reversals of
radiation pressure to radiation tension. However, these effects
could not be experimentally verified since, as Veselago pointed
out, substances with $\mu <0$ were not available. Negative $\mu
_{eff}(\omega )$ has been shown to be possible when a polariton
resonance exists in the permeability, such as in the
antiferromagnets MnF$_{2}$ and FeF$_{2}$, or certain insulating
ferromagnets. However, a negative permeability with low losses
coexisting with a negative $\varepsilon $ has not been
demonstrated. \cite{Smith}
The electrodynamic properties of a microsphere made of
hypothetical material with a simultaneously negative permittivity
and permeability ( a ``left-handed'' (LH) sphere ) are considered.
It is shown that three types of resonance modes can be excited in
such a sphere: the whispering gallery modes, the plasmon
oscillations and the new LH surface modes, which have an anomalous
behavior of the resonant curves. The analytical solution of the
dispersion equation is found. It is demonstrated that the electric
(E1) and magnetic (M1) dipole decay rates of an atom placed near
such left-handed sphere suffer a substantial enhancement in the
case of resonance with the modes of a sphere. In the paper
published in 1967, it was shown that hypothetical media with a
simultaneously negative permittivity and permeability have a
number of unusual properties. Here, in particular, the phase and
group velocities of light propagation have the opposite directions
of propagation and the refraction index takes negative values. In
the case of $\varepsilon >0$, $\mu >0$ ( this is the case of usual
media ) the wave vector {\bf {k}} and Umov-Poynting vector ${\bf
S}={\bf E}\times {\bf H}$ have the same direction of propagation.
In this case the vector {\bf {k}}, {\bf {E}} and {\bf {H}} form a
right-handed system; thus Veselago referred to such materials as
``right-handed'' (RH). In the case of $\varepsilon <0$, $\mu <0$
the direction of propagation {\bf {k}} is reversed with respect to
the direction of energy flow. In this case the vector {\bf {k}},
{\bf {E}} and {\bf {H}} form a left-handed system; thus Veselago
referred to such materials as ``left-handed'' (LH). \cite {Klimov}
The Doppler effect has an unusual form in such media. For example,
when the distance between the source and receiver diminishes, the
frequency picked by the receiver will be less than the source
frequency as compared to usual media. The Vavilov-Cherenkov effect
is also drastically modified: the energy flow from the particle
moving faster than the phase velocity in LH medium propagates in
backward direction, while in RH medium we have the forward
radiation.\cite {Klimov}
The influence of the interface between LH and RH media on the
radiation propagation is described by the reflection and the
refraction laws, which differ substantially from the laws which
are peculiar to the usual media. When a wave in a RH material hits
an interface with a LH medium, it will have negative angle of
refraction, i. e., the refracted wave will be on the same side of
the normal as the incident wave. It is due to the fact that the
refraction index is negative for LH media. Moreover, the refracted
wave can be absent at all if the absolute values of the refraction
indices of LH and RH media are equal\cite{Veselago}.\cite {Klimov}
Until quite recently the existence of LH media remained unproved.
This fact has not stimulated further investigation of such media.
With the recent experimental demonstration of principal
possibility of creation of LH media on the base of composite
materials\cite{Lagarkov,Pendry,Smith,Shelby1,Shelby2}, now it is
relevant to investigate the influence of LH media on more
complicated processes, such as spontaneous emission in more
detail.\cite {Klimov}
Purcell was the first who pointed out that the spontaneous decay
rates can be modified in a resonant cavity. This idea received a
strong proof in the experiments with atoms in microwave
cavities\cite{Goy,Jhe} and with and with Eu$^{3+}$ ions in liquid
microdroplets\cite{Lin}. In \cite{Bykov,Yablonovich,John} it was
shown that spontaneous emission can be substantially inhibited in
three-dimensional periodic dielectric structures ( photonic
crystals ). The influence of a semi-infinite active media on
spontaneous emission was investigated in \cite{Kocharovsky}. This
investigation showed that the instability of the ground state of
an atom arises, and the radiation reaction force changes its sign
in comparison with the usual ( passive ) media. In the present
paper the processes of spontaneous emission of an atom placed near
a body ( sphere ) made of the LH material and placed in the RH
medium will be considered, and it will be shown that these
processes drastically differ from those near usual RH body. From
the physical point of view any body influences spontaneous
emission of an atom through the reflected electromagnetic waves
modifying the dynamics of the radiating system.\cite {Klimov}
The real part of the refractive index $n(\omega )$ of a nearly
transparent and passive medium is usually taken to have only
positive values. Through an analysis of a current source radiating
into a $1$D ``left-handed'' material (LHM) where the permittivity
and permeability are simultaneously less than zero, we determine
the analytic structure of $n(\omega )$, demonstrating frequency
regions where the sign of ${\rm Re}[n(\omega )]$ must, in fact, be
negative. The regime of negative index, made relevant by a recent
demonstration of an effective LHM, leads to unusual
electromagnetic wave propagation and merits further
exploration.\cite{DR Smith}
In a paper published in 1968, Veselago predicted that
electromagnetic plane wave in a medium having simultaneously
negative permittivity and permeability would propagate in a
direction opposite to that of the flow of energy. This result
follows not from the wave equation, which remains unchanged in the
absence of equations, but rather from the individual Maxwell curl
equations. The curl equation for the electric field provides an
unambiguous ``right-handed'' ( RH ) rule between the directions of
the electric field ${\bf E}$, the magnetic induction ${\bf B}$,
and the direction of the propagation vector ${\bf k}$. The
direction of energy flow, however, given by ${\bf E}\times {\bf
H}$, forms a right-handed system only when the permeability is
greater than zero. When the permeability is negative, the
direction of propagation is reversed with respect to the direction
of energy flow. The vectors ${\bf E}, {\bf H}$, and ${\bf k}$ form
a left-handed system. Thus, Veselago referred to such materials as
``left-handed'' ( LH ).\cite{DR Smith}
Veselago went on to argue, using steady-state solutions to
Maxwell's equations, that a LH medium has a negative refractive
index ($n$). We show that the designation of negative refractive
index is unique to LH systems. An isotropic negative index
condition has the important property that it exactly reverses the
propagation paths of rays within it; thus, LH materials have the
potential to form highly efficient low reflectance surfaces by
exactly cancelling the scattering properties of other
materials.\cite{DR Smith}
The dispersion relation of the surface polaritons of a
semi-infinite dispersive medium, which is left-handed ( having
negative permittivity and permeability ) over a frequency range,
are obtained. The possibility of experimentally observing the
surface polaritons by attenuated total reflection is
demonstrated.\cite{Ruppin2}
The peculiar properties of a medium, in which both the
permittivity and the permeability assume negative values, have
been demonstrated theoretically by Veselago. Such a medium is
called ``left-handed'' because for an electromagnetic plane wave
propagating inside it, ${\bf E}\times {\bf H}$ lies in the
direction opposite to that of the wavevector. Recently, an
artificial material, which is left-handed over a band of
frequencies in the microwave region, has been built, using two
dimensional arrays of split-ring resonators and
wires\cite{Smith}PRL2000. Further development of this technique
will probably lead to the production of isotropic left-handed
materials. Our aim here is to investigate the surface polariton
modes that exist near the boundary of such a left-handed medium,
and to discuss a method by which they can be detected. For the
medium at $x>0$ we will employ dispersive forms of $\varepsilon $
and $\mu $ similar to those that have been achieved with
artificial structures. A dielectric constant of the form
$\varepsilon (\omega )=1-\frac{\omega _{p}^{2}}{\omega ^{2}}$ with
the plasma frequency $\omega _{p}$ in the GHZ range, can be
realized by using a network of thin wires\cite{Pendry}1998. A
magnetic permeability of the form $\mu (\omega )=1-\frac{F\omega
^{2}}{\omega ^{2}-\omega _{0}^{2}}$ with the resonance frequency
in the GHZ range, can be achieved by using a periodic arrangement
of split ring resonantors\cite{Pendry}1999. A combination of the
two structures yields a left-handed medium.\cite{Ruppin2}
\section{Application of LH materials}
An isotropic negative index condition has the important property
that it exactly reverses the propagation paths of rays within it;
thus, LH materials have the potential to form highly efficient low
reflectance surfaces by exactly cancelling the scattering
properties of other materials.\cite{DR Smith}
In the present paper the processes of spontaneous emission of an
atom placed near a body ( sphere ) made of the LH material and
placed in the RH medium will be considered, and it will be shown
that these processes drastically differ from those near usual RH
body. From the physical point of view any body influences
spontaneous emission of an atom through the reflected
electromagnetic waves modifying the dynamics of the radiating
system.\cite {Klimov}
The influence of the interface between LH and RH media on the
radiation propagation is described by the reflection and the
refraction laws, which differ substantially from the laws which
are peculiar to the usual media. When a wave in a RH material hits
an interface with a LH medium, it will have negative angle of
refraction, i. e., the refracted wave will be on the same side of
the normal as the incident wave. It is due to the fact that the
refraction index is negative for LH media. Moreover, the refracted
wave can be absent at all if the absolute values of the refraction
indices of LH and RH media are equal\cite{Veselago}.\cite {Klimov}
With a conventional lens sharpness of the image is always limited
by the wavelength of light. An unconventional alternative to a
lens, a slab of negative refractive index material, has the power
to focus all Fourier components of a $2$D image, even those that
do not propagate in a radiative manner. Such ``superlenses'' can
be realized in the microwave band with current technology. Our
simulations show that a version of the lens operating at the
frequency of visible light can be realized in the form of a thin
slab only a few nanometers across.\cite{JB Pendry}
\section{Design of LH materials}
All potential methods of construction of left-handed materials are
now of intense interest, and in this letter we investigate the
properties of a layered material, consisting of alternating layers
in which $\varepsilon <0$ ( but $\mu >0$ ) and layers in which
$\mu <0$ ( $\varepsilon >0$ ). In practice one or both layers
might be a metamaterial, but we shall suppose that they are
homogeneous materials with true $\varepsilon$ and $\mu$.\cite
{Fredkin}
We demonstrate a composite medium, based on a periodic array of
interspaced conducting nonmagnetic split ring resonators and
continuous wires, that exhibits a frequency region in the
microwave regime with simultaneously negative values of effective
permeability $\mu _{eff}(\omega )$ and permittivity $\varepsilon
_{eff}(\omega )$. This structure forms a `` left-handed '' medium,
for which it has been predicted that such phenomena as the Doppler
effect, Cherenkov radiation and even Snell's law are inverted. It
is now possible through microwave experiments to test for these
effects using this new metamaterial. However, these effects (
different propagation characteristics stemming from the sign
change of the group velocity, including reversal of both the
Doppler shift and Cherenkov radiation, anomalous refraction and
even reversals of radiation pressure to radiation tension ) could
not be experimentally verified since, as Veselago pointed out,
substances with $\mu <0$ were not available. Negative $\mu
_{eff}(\omega )$ has been shown to be possible when a polariton
resonance exists in the permeability, such as in the
antiferromagnets MnF$_{2}$ and FeF$_{2}$, or certain insulating
ferromagnets. However, a negative permeability with low losses
coexisting with a negative $\varepsilon $ has not been
demonstrated. The split ring resonator (SRR) medium recently
introduced by Pendry has now given us the opportunity to make a
material with negative permeability, from which a left-handed
medium can be constructed, as we demonstrate in what
follows.\cite{Smith}
The absence of naturally occurring materials with negative $\mu$
made further discussion of LH media academic until recently, when
a composite medium was demonstrated in which, over a finite
frequency band, both the effective permittivity $\varepsilon
(\omega )$ and the effective permeability $\mu (\omega )$ were
shown to be simultaneously less than zero. This physical medium
was composed of distinct conducting elements, the size and spacing
of which were on a scale much smaller than the wavelengths in the
frequency range of interest. Thus, the composite medium could be
considered homogeneous at the wavelengths under consideration.
With this practical demonstration, it is now relevant to discuss
in more detail the phenomena associated with wave propagation in
LH materials, as both novels devices and interesting physics may
result. Here we are concerned with the interaction of waves with
time-dependent current sources in LH media.\cite{DR Smith}
We present numerical results on the transmission properties of the
left-handed materials ( LHMs ) and split ring resonators (SRRs).
\cite{Markos}
The composite medium used in Ref.[2] made use of an array of metal
posts to create a frequency region with $\varepsilon _{eff}<0$,
interspersed with an array of split ring resonators (SRRs) having
a frequency region with $\mu _{eff}<0$. The SRR medium and the
wire array medium, both introduced by Pendry {\it et
al.}\cite{Boas,Pendry,Veselago}, have been extensively studied
previously.\cite{DR Smith}
Pendry: split ring resonator (SRR); (1999) IEEE trans. Microwave
Theory Tech. {\bf 47}, 2075 (1999).
Smith: based on a periodic array of interspaced conducting
nonmagnetic split ring resonators and continuous wires. (2000)
\section{My words}
Quite recently, a kind of composite medium ( the so-called
left-handed medium ) having a frequency band where the {\it
effective permittivity} ( $\varepsilon$ ) and the {\it effective
permeability} ( $\mu$ ) are simultaneously negative attracts
attentions of many researchers in various fields such as materials
science, condensed matter physics, optics and electromagnetism. In
1968, Veselago first considered this peculiar medium and showed
that it possesses a negative index of refraction. It follows from
the Maxwell's equations that in this medium the Poynting vector
and wave vector of electromagnetic wave would be antiparallel, i.
e., the vector {\bf {k}}, the electric field {\bf {E}} and the
magnetic field {\bf {H}} form a left-handed system; thus Veselago
referred to such materials as ``left-handed (LH)'', and
correspondingly, the ordinary medium in which {\bf {k}}, {\bf {E}}
and {\bf {H}} form a right-handed system may be termed the
``right-handed'' media. Other authors call this class of materials
``negative index media (NIM)'', ``double negative media (DNM) ''
and Veselago's media. It is readily verified that in such medium
having both $\varepsilon$ and $\mu$ negative, there exist a number
of peculiar electromagnetic properties, for instance, many
dramatically different propagation characteristics stem from the
sign change of the group velocity, including reversal of both the
Doppler shift and Cherenkov radiation, anomalous refraction,
modified spontaneous emission rates and even reversals of
radiation pressure to radiation tension. In experiments, this
artificial negative electric permittivity media may be obtained by
using the array of long metallic wires, which simulates the plasma
behavior at microwave frequencies, and the artificial negative
magnetic permeability media may be built up by using small
resonant metallic particles ( split ring resonator ) with very
high magnetic polarizability. |