Phase randomness in a one-dimensional disordered absorbing medium

Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is obtained, which shows that absorption suppresses the fluctuations of the phase. The applicability of the random phase approximation is discussed.Comment: submitted to Phys.Rev.

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

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