205 research outputs found
Exact localization length for s-polarized electromagnetic waves incident at the critical angle on a randomly-stratified dielectric medium
The interplay between Anderson localization and total internal reflection of
electromagnetic waves incident near the critical angle on randomly-stratified
dielectric media is investigated theoretically. Using an exact analytical
formula for the localization length for the Schr\"odinger equation with a
Gaussian -correlated random potential in one dimension, we show that
when the incident angle is equal to the critical angle, the localization length
for an incident wave of wavelength is directly proportional to
throughout the entire range of the wavelength, for any value of
the disorder strength. This result is different from that of a recent study
reporting that the localization length at the critical incident angle for a
binary multilayer system with random thickness variations is proportional to
in the large region. We also discuss the characteristic
behaviors of the localization length or the tunneling decay length for all
other incident angles. Our results are confirmed by an independent numerical
calculation based on the invariant imbedding method.Comment: 12 pages, 3 figure
Resonant absorption of electromagnetic waves in transition anisotropic media
We study the mode conversion and resonant absorption phenomena occurring in a
slab of a stratified anisotropic medium, optical axes of which are tilted with
respect to the direction of inhomogeneity, using the invariant imbedding theory
of wave propagation. When the tilt angle is zero, mode conversion occurs if the
longitudinal component of the permittivity tensor, which is the one in the
direction of inhomogeneity in the non-tilted case, varies from positive to
negative values within the medium, while the transverse component plays no
role. When the tilt angle is nonzero, the wave transmission and absorption show
an asymmetry under the sign change of the incident angle in a range of the tilt
angle, while the reflection is always symmetric. We calculate the reflectance,
the transmittance and the absorptance for several configurations of the
permittivity tensor and find that resonant absorption is greatly enhanced when
the medium from the incident surface to the resonance region is hyperbolic than
when it is elliptic. For certain configurations, the transmittance and
absorptance curves display sharp peaks at some incident angles determined by
the tilt angle.Comment: 15 pages, 11 figure
Excitation of surface waves on the interfaces of general bi-isotropic media
We study theoretically the characteristics of surface waves excited at the
interface between a metal and a general bi-isotropic medium, which includes
isotropic chiral media and Tellegen media as special cases. We derive an
analytical dispersion relation for surface waves, using which we calculate the
effective index and the propagation length numerically. We also calculate the
absorptance, the cross-polarized reflectance and the spatial distribution of
the electromagnetic fields for plane waves incident on a bilayer system
consisting of a metal layer and a bi-isotropic layer in the Kretschmann
configuration, using the invariant imbedding method. The results obtained using
the invariant imbedding method agree with those obtained from the dispersion
relation perfectly. In the case of chiral media, the effective index is an
increasing function of the chirality index, whereas in Tellegen media, it is a
decreasing function of the Tellegen parameter. The propagation length for
surface waves in both cases increase substantially as either the chirality
index or the Tellegen parameter increases. In Tellegen media, it diverges to
infinity when the effective index goes to zero, whereas in chiral media, it
does when the parameters approach the cutoff values where quasi surface waves
are excited. We investigate the characteristics of quasi surface waves excited
when the chirality index is sufficiently large.Comment: 15 pages, 13 figure
Anderson localization and Brewster anomaly of electromagnetic waves in randomly-stratified anisotropic media
Anderson localization of -polarized waves and the Brewster anomaly
phenomenon, which is the delocalization of -polarized waves at a special
incident angle, in randomly-stratified anisotropic media are studied
theoretically for two different random models. In the first model, the random
parts of the transverse and longitudinal components of the dielectric tensor,
between which the longitudinal component is the one in the stratification
direction, are assumed to be uncorrelated, while, in the second model, they are
proportional to each other. We calculate the localization length in a precise
way using the invariant imbedding method. From analytical considerations, we
provide an interpretation of the Brewster anomaly as a phenomenon arising when
the wave impedance is effectively uniform. Similarly, the ordinary Brewster
effect is interpreted as an impedance matching phenomenon. We derive the
existence condition for the Brewster anomaly and concise analytical expressions
for the localization length, which are accurate in the weak disorder regime. We
find that the Brewster anomaly can arise only when disorder is sufficiently
weak and only in the second model with a positive ratio of the random parts.
The incident angle at which the anomaly occurs depends sensitively on the ratio
of the random parts and the average values of the tensor components. In the
cases where the critical angle of total reflection exists, the angle at which
the anomaly occurs can be either bigger or smaller than the critical angle.
When the transverse and longitudinal components are uncorrelated, localization
is dominated by the the transverse component at small incident angles. When
only the longitudinal component is random, the localization length diverges as
as the incident angle goes to zero and is also argued to
diverge for all in the strong disorder limit.Comment: 15 pages, 4 figure
Giant enhancement of reflectance due to the interplay between surface confined wave modes and nonlinear gain in dielectric media
We study theoretically the interplay between the surface confined wave modes
and the linear and nonlinear gain of the dielectric layer in the Otto
configuration. The surface confined wave modes such as surface plasmons or
waveguide modes are excited in the dielectric-metal bilayer by obliquely
incident waves. In the purely linear case, we find that the interplay
between linear gain and surface confined wave modes can generate a large
reflectance peak with its value much greater than 1. As the linear gain
parameter increases, the peak appears at smaller incident angles, and the
associated modes also change from surface plasmons to waveguide modes. When the
nonlinear gain is turned on, the reflectance shows very strong multistability
near the incident angles associated with surface confined wave modes. As the
nonlinear gain parameter is varied, the reflectance curve undergoes complicated
topological changes and sometimes displays separated closed curves. When the
nonlinear gain parameter takes an optimally small value, a giant amplification
of the reflectance by three orders of magnitude occurs near the incident angle
associated with a waveguide mode. We also find that there exists a range of the
incident angle where the wave is dissipated rather than amplified even in the
presence of gain. We suggest that this can provide the basis for a possible new
technology for thermal control in the subwavelength scale.Comment: 11 pages, 6 figure
Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media
Bi-isotropic media, which include isotropic chiral media and Tellegen media
as special cases, are the most general form of linear isotropic media where the
electric displacement and the magnetic induction are related to both the
electric field and the magnetic intensity. In inhomogeneous bi-isotropic media,
electromagnetic waves of two different polarizations are coupled to each other.
In this paper, we develop a generalized version of the invariant imbedding
method for the study of wave propagation in arbitrarily-inhomogeneous
stratified bi-isotropic media, which can be used to solve the coupled wave
propagation problem accurately and efficiently. We verify the validity and
usefulness of the method by applying it to several examples, including the wave
propagation in a uniform chiral slab, the surface wave excitation in a bilayer
system made of a layer of Tellegen medium and a metal layer, and the mode
conversion of transverse electromagnetic waves into longitudinal plasma
oscillations in inhomogeneous Tellegen media. In contrast to the case of
ordinary isotropic media, we find that the surface wave excitation and the mode
conversion occur for both s and p waves in bi-isotropic media.Comment: 17 pages, 4 figure
Resonant absorption and amplification of circularly-polarized waves in inhomogeneous chiral media
It has been found that in the media where the dielectric permittivity
or the magnetic permeability is near zero and in transition
metamaterials where or changes from positive to negative
values, there occur a strong absorption or amplification of the electromagnetic
wave energy in the presence of an infinitesimally small damping or gain and a
strong enhancement of the electromagnetic fields. We attribute these phenomena
to the mode conversion of transverse electromagnetic waves into longitudinal
plasma oscillations and its inverse process. In this paper, we study analogous
phenomena occurring in chiral media theoretically using the invariant imbedding
method. In uniform isotropic chiral media, right-circularly-polarized and
left-circularly-polarized waves are the eigenmodes of propagation with
different effective refractive indices and , whereas in the chiral
media with a nonuniform impedance variation, they are no longer the eigenmodes
and are coupled to each other. We find that both in uniform chiral slabs where
either or is near zero and in chiral transition metamaterials where
or changes from positive to negative values, a strong absorption or
amplification of circularly-polarized waves occurs in the presence of an
infinitesimally small damping or gain. We present detailed calculations of the
mode conversion coefficient, which measures the fraction of the electromagnetic
wave energy absorbed into the medium, for various configurations of
and with an emphasis on the influence of a nonuniform impedance. We
propose possible applications of these phenomena to linear and nonlinear
optical devices that react selectively to the helicity of the circular
polarization.Comment: 10 pages, 5 figures, Optics Express 24, 1794 (2016
Broadband wide-angle absorption enhancement due to mode conversion in cold unmagnetized plasmas with periodic density variations
We study theoretically the mode conversion and the associated resonant
absorption of p-polarized electromagnetic waves into longitudinal plasma
oscillations in cold, unmagnetized and stratified plasmas with periodic spatial
density variations. We consider sinusoidal density configurations for which the
frequency band where mode conversion occurs is well included within a
transmission band of the one-dimensional plasma photonic crystal. We calculate
the mode conversion coefficient, which measures the fraction of the
electromagnetic wave energy absorbed into the plasma, and the spatial
distribution of the magnetic field intensity for various values of the wave
frequency and the incident angle using the invariant imbedding theory of mode
conversion. We find that the absorption is greatly enhanced over a wide range
of frequency and incident angle due to the interplay between the mode
conversion and the photonic band structure. The enhancement occurs because for
frequencies within a transmission band, the wave reflection is strongly
suppressed and the waves penetrate more deeply into the inhomogeneous region,
thereby increasing the possibility for them to reach many resonance points
where the dielectric permittivity vanishes.Comment: 11 pages, 5 figure
Optical conductivity associated with solitons in the Peierls state as modified by zero-point-motion disorder
We extend previous work to consider the effect of the soliton on the density
of states and conductivity of quasi-one-dimensional Peierls systems with
quantum lattice fluctuations, modeled by a random static disorder. Two features
have been verified over an order of magnitude variation in the disorder. (1)
The soliton density of states and the leading edges of both the soliton-to-band
and the band-to-band conductivities have universal scaling forms. (2) The
soliton-to-band conductivity has the remarkable feature that the leading edge
is accurately predicted by the joint density of states while the trailing edge
tracks the rigid-lattice conductivity. Or, in other words, disorder dominates
the leading edge, while matrix element effects are predominant for the trailing
edge
Theory of solitons, polarons and multipolarons in one dimension: An alternative formulation
We develop an alternative formulation of the theory of solitons, polarons and
multipolarons in quasi-one-dimensional degenerate and non-degenerate conducting
polymers, starting from the continuum Hamiltonian introduced by Brazovskii and
Kirova. Based on a convenient real-space representation of the electron Green
function in one dimension, we present a simple method of calculating the Green
function and the density of states in the presence of a single soliton or
polaron defect, using which we derive exact expressions for the soliton,
polaron and multipolaron excitation energies and the self-consistent gap
functions for an arbitrary value of the electron-phonon coupling constant. We
apply our results to -polyacetylene.Comment: 13 pages, 1 figure, to appear in Physical Review
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