Probability of Reflection by a Random Laser

TL;DR

This paper develops a theoretical framework, supported by simulations, for understanding phase-coherent light reflection in disordered media with absorption or amplification, revealing divergence at laser threshold and finite modal values.

Contribution

It introduces a random-matrix theory approach to describe reflection eigenvalues and statistical fluctuations of albedo in disordered media near laser threshold.

Findings

Reflection eigenvalues follow the Laguerre ensemble.

Albedo fluctuations diverge at laser threshold.

Modal value of albedo remains finite and depends on surface area.

Abstract

A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre ensemble of random-matrix theory. The statistical fluctuations of the albedo (the ratio of reflected and incident power) are computed for arbitrary ratio of sample thickness, mean free path, and absorption or amplification length. On approaching the laser threshold all moments of the distribution of the albedo diverge. Its modal value remains finite, however, and acquires an anomalous dependence on the illuminated surface area.