Reflection coefficient and localization length of waves in one-dimensional random media

TL;DR

This paper introduces an exact method to calculate wave transport properties in one-dimensional random media, revealing significant deviations from previous approximations and establishing dual relationships between absorption and amplification effects.

Contribution

The authors develop a novel exact approach for calculating transport characteristics, including reflectance and localization length, in 1D random media with absorption or amplification, surpassing the limitations of the RPA.

Findings

Exact probability densities differ from RPA predictions under strong disorder or absorption.

Probability density of reflection phase is highly nonuniform with strong disorder or absorption.

Localization length is larger than RPA estimates when RPA is invalid.

Abstract

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.