Wave propagation through a coherently amplifying random medium

TL;DR

This paper presents a comprehensive numerical analysis of wave propagation in a one-dimensional coherently amplifying disordered medium, revealing new regimes and behaviors of transmittance and reflectance influenced by amplification.

Contribution

It introduces a detailed numerical study of wave behavior in amplifying disordered media, identifying new regimes and analyzing the limitations of the random phase approximation.

Findings

Transmittance is non-self-averaging with a well-defined mean.

Stationary distribution of super reflection differs from RPA predictions in strong disorder and amplification.

Phase distribution analysis explains discrepancies with analytical models.

Abstract

We report a detailed and systematic numerical study of wave propagation through a coherently amplifying random one-dimensional medium. The coherent amplification is modeled by introducing a uniform imaginary part in the site energies of the disordered single-band tight binding Hamiltonian. Several distinct length scales (regimes), most of them new, are identified from the behavior of transmittance and reflectance as a function of the material parameters. We show that the transmittance is a non-self-averaging quantity with a well defined mean value. The stationary distribution of the super reflection differs qualitatively from the analytical results obtained within the random phase approximation in strong disorder and amplification regime. The study of the stationary distribution of the phase of the reflected wave reveals the reason for this discrepancy. The applicability of random phase approximation is discussed. We emphasize the dual role played by the lasing medium, as an amplifier as well as a reflector.