Super-reflection of light from a random amplifying medium with disorder in the complex refractive index : Statistics of fluctuations

TL;DR

This paper derives the probability distribution of light reflection in a one-dimensional random amplifying medium with correlated disorder, revealing enhanced backscattering and super-reflection effects due to Anderson localization and amplification.

Contribution

It introduces a novel statistical analysis of reflection fluctuations in a disordered amplifying medium with correlated real and imaginary refractive index components.

Findings

Enhanced backscattering leads to super-reflection with reflection coefficient > 1

Disorder in the imaginary part affects localization differently than in the real part

Statistics of fluctuations vary between telegraph and Gaussian noise models

Abstract

The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with {\it cross-correlated} spatial disorder in the real and the imaginary parts of the refractive index is derived using the method of invariant imbedding. The statistics of fluctuations have been obtained for both the correlated telegraph noise and the Gaussian white-noise models for the disorder. In both cases, an enhanced backscattering (super-reflection with reflection coefficient greater than unity) results because of coherent feedback due to Anderson localization and coherent amplification in the medium. The results show that the effect of randomness in the imaginary part of the refractive index on localization and super-reflection is qualitatively different.