49 research outputs found
Localization of transverse waves in randomly layered media at oblique incidence
We investigate the oblique incidence of transverse waves on a randomly
layered medium in the limit of strong disorder. An approximate method for
calculating the inverse localization length based on the assumptions of zero
energy flux and complete phase stochastization is presented. Two effects not
found at normal incidence have been studied: dependence of the localization
length on the polarization, and decrease of the localization length due to the
internal reflections from layers with small refractive indexes. The inverse
localization length (attenuation rate) for P-polarized radiation is shown to be
always smaller than that of S-waves, which is to say that long enough randomly
layered sample polarizes transmitted radiation. The localization length for
P-polarization depends non-monotonically on the angle of propagation, and under
certain conditions turns to infinity at some angle, which means that typical
(non-resonant) random realizations become transparent at this angle of
incidence (stochastic Brewster effect).Comment: 12 pages, 1 figure, accepted for publication in Physical Review
Localization of Classical Waves in Weakly Scattering Two-Dimensional Media with Anisotropic Disorder
We study the localization of classical waves in weakly scattering 2D systems
with anisotropic disorder. The analysis is based on a perturbative
path-integral technique combined with a spectral filtering that accounts for
the first-order Bragg scattering only. It is shown that in the long-wavelength
limit the radiation is always localized, and the localization length is
independent of the direction of propagation, the latter in contrast to the
predictions based on an anisotropic tight-binding model. For shorter
wavelengths that are comparable to the correlation scales of the disorder, the
transport properties of disordered media are essentially different in the
directions along and across the correlation ellipse. There exists a
frequency-dependent critical value of the anisotropy parameter, below which
waves are localized at all angles of propagation. Above this critical value,
the radiation is localized only within some angular sectors centered at the
short axis of the correlation ellipse and is extended in other directions.Comment: 10 pages, 5 figure
Reflection coefficient and localization length of waves in one-dimensional random media
We develop a novel and powerful method of exactly calculating various
transport characteristics of waves in one-dimensional random media with (or
without) coherent absorption or amplification. Using the method, we compute the
probability densities of the reflectance and of the phase of the reflection
coefficient, together with the localization length, of electromagnetic waves in
sufficiently long random dielectric media. We find substantial differences
between our exact results and the previous results obtained using the random
phase approximation (RPA). The probabilty density of the phase of the
reflection coefficient is highly nonuniform when either disorder or absorption
(or amplification) is strong. The probability density of the reflectance when
the absorption or amplification parameter is large is also quite different from
the RPA result. We prove that the probability densities in the amplifying case
are related to those in the absorbing case with the same magnitude of the
imaginary part of the dielectric permeability by exact dual relationships. From
the analysis of the average reflectance that shows a nonmonotonic dependence on
the absorption or amplification parameter, we obtain a useful criterion for the
applicability of the RPA. In the parameter regime where the RPA is invalid, we
find the exact localization length is substantially larger than the RPA
localization length.Comment: 16 pages, 9 figure
Propagation of wave packets in randomly stratified media
The propagation of a narrow-band signal radiated by a point source in a
randomly layered absorbing medium is studied asymptotically in the
weak-scattering limit. It is shown that in a disordered stratified medium that
is homogeneous on average a pulse is channelled along the layers in a narrow
strip in the vicinity of the source. The space-time distribution of the pulse
energy is calculated. Far from the source, the shape of wave packets is
universal and independent of the frequency spectrum of the radiated signal.
Strong localization effects manifest themselves also as a low-decaying tail of
the pulse and a strong time delay in the direction of stratification. The
frequency-momentum correlation function in a one-dimensional random medium is
calculated.Comment: 11 pages, 3 figures, Revtex-4. Submitted to Phys. Rev.
Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials
We summarize the results of our comprehensive analytical and numerical
studies of the effects of polarization on the Anderson localization of
classical waves in one-dimensional random stacks. We consider homogeneous
stacks composed entirely of normal materials or metamaterials, and also mixed
stacks composed of alternating layers of a normal material and metamaterial. We
extend the theoretical study developed earlier for the case of normal incidence
[A. A. Asatryan et al, Phys. Rev. B 81, 075124 (2010)] to the case of off-axis
incidence. For the general case where both the refractive indices and layer
thicknesses are random, we obtain the long-wave and short-wave asymptotics of
the localization length over a wide range of incidence angles (including the
Brewster ``anomaly'' angle). At the Brewster angle, we show that the long-wave
localization length is proportional to the square of the wavelength, as for the
case of normal incidence, but with a proportionality coefficient substantially
larger than that for normal incidence. In mixed stacks with only
refractive-index disorder, we demonstrate that p-polarized waves are strongly
localized, while for s-polarization the localization is substantially
suppressed, as in the case of normal incidence. In the case of only thickness
disorder, we study also the transition from localization to delocalization at
the Brewster angle.Comment: 15 pages, 11 figures, accepted for publication in PR
Light scattering from an amplifying medium bounded by a randomly rough surface: A numerical study
We study by numerical simulations the scattering of -polarized light from
a rough dielectric film deposited on the planar surface of a semi-infinite
perfect conductor. The dielectric film is allowed to be either active or
passive, situations that we model by assigning negative and positive values,
respectively, to the imaginary part of the dielectric constant of
the film. We study the reflectance and the total scattered energy
for the system as functions of both and the angle of
incidence of the light. Furthermore, the positions and widths of the enhanced
backscattering and satellite peaks are discussed. It is found that these peaks
become narrower and higher when the amplification of the system is increased,
and that their widths scale linearly with . The positions of the
backscattering peaks are found to be independent of , while we find
a weak dependence on this quantity in the positions of the satellite peaks.Comment: Revtex, 9 pages, 9 figure
Statistical Properties of the Reflectance and Transmittance of an Amplifying Random Media
Statistical properties of the transmittance () and reflectance () of an
amplifying layer with one-dimensional disorder are investigated analytically.
Whereas the transmittance at typical realizations decreases exponentially with
the layer thickness just as it does in absorbing media, the average
and \ are shown to
be infinite even for finite due to the contribution of low-probable
resonant realizations corresponding to the non-Gaussian tail of the
distribution of . This tail differs drastically from that in the case of
absorption. The physical meaning of typical and resonant realizations is
discussed.Comment: 5 pages (RevTeX
Enhanced Transmission Due to Disorder
The transmissivity of a one-dimensional random system that is periodic on
average is studied. It is shown that the transmission coefficient for
frequencies corresponding to a gap in the band structure of the average
periodic system increases with increasing disorder while the disorder is weak
enough. This property is shown to be universal, independent of the type of
fluctuations causing the randomness. In the case of strong disorder the
transmission coefficient for frequencies in allowed bands is found to be a non
monotonic function of the strength of the disorder. An explanation for the
latter behavior is provided.Comment: 9 pages, RevTeX 3.0, 4 Postscript figure
Study of transmission and reflection from a disordered lasing medium
A numerical study of the statistics of transmission () and reflection
() of quasi-particles from a one-dimensional disordered lasing or amplifying
medium is presented. The amplification is introduced via a uniform imaginary
part in the site energies in the disordered segment of the single-band tight
binding model. It is shown that is a non-self-averaging quantity. The
cross-over length scale above which the amplification suppresses the
transmittance is studied as a function of amplification strength. A new
cross-over length scale is introduced in the regime of strong disorder and weak
amplification. The stationary distribution of the backscattered reflection
coefficient is shown to differ qualitatively from the earlier analytical
results obtained within the random phase approximation.Comment: 5 pages RevTex (twocolumn format), 5 EPS figures, considerably
modifie