Coherent Random Lasing and "Almost Localized" Photon Modes

TL;DR

This paper investigates the formation of high-quality, long-lived photon modes in weakly disordered dielectric media, analyzing their properties, probabilities, and relevance to random lasing phenomena without introducing resonant scatterers.

Contribution

It provides a detailed quantitative analysis of random resonators and

Findings

Identifies conditions for the formation of high-Q photon modes in disordered media.

Quantifies the probability and density of such resonators considering disorder correlations.

Connects the existence of these modes to the phenomenon of random lasing.

Abstract

A pulse of light, injected into a weakly disordered dielectric medium, typically, will leave its initial location in a short time, by diffusion. However, due to some rare configurations of disorder, there is a possibility of formation of high quality resonators which can trap light for a long time. We present a rather detailed, quantitative study of such random resonators and of the "almost localized" states that they can support. After presenting a brief review of the earlier work on the subject, we concentrate on a detailed computation of the "prefactor": knowledge of the latter is crucial for varifying the viability of the random rasonators and their areal density. Both short range disorder (white noise) and correlated disorder are studied, and the important effect of the correlation radius, $R_c$, on the probability of formation of resonators with a given quality factor $Q$ is discussed. The random resonators are "self-formed", in the sense that no sharp features (like Mie scatterers or other "resonant entities") are introduced: our model is a featureless dielectric medium with fluctuating dielectric constant. We point out the relevance of the random resonators to the recently discovered phenomenon of coherent "random" lasing and review the existing work on that subject. We emphasize, however, that the random resonators exist already in the {\em passive} medium: gain is only needed to "make them visible".