Disorder-induced cavities, resonances, and lasing in randomly-layered media

TL;DR

This paper investigates disorder-induced resonances and cavities in randomly-layered media through theoretical analysis and experiments, revealing their properties, distribution, and lasing behavior in active systems.

Contribution

It introduces an algorithm to detect and characterize resonant cavities in disordered media, linking cavity properties to system size and disorder strength, and demonstrates lasing in experimental fiber systems.

Findings

Number of cavities and resonances per frequency is system-size dependent.

Lasing cavities behave as distributed feedback lasers.

Experimental spectra show peaks corresponding to theoretical resonances.

Abstract

We study, theoretically and experimentally, disorder-induced resonances in randomly-layered samples,and develop an algorithm for the detection and characterization of the effective cavities that give rise to these resonances. This algorithm enables us to find the eigen-frequencies and pinpoint the locations of the resonant cavities that appear in individual realizations of random samples, for arbitrary distributions of the widths and refractive indices of the layers. Each cavity is formed in a region whose size is a few localization lengths. Its eigen-frequency is independent of the location inside the sample, and does not change if the total length of the sample is increased by, for example, adding more scatterers on the sides. We show that the total number of cavities, $N_{\mathrm{cav}}$, and resonances, $N_{\mathrm{res}}$, per unit frequency interval is uniquely determined by the size of the disordered system and is independent of the strength of the disorder. In an active, amplifying medium, part of the cavities may host lasing modes whose number is less than $N_{\mathrm{res}}$. The ensemble of lasing cavities behaves as distributed feedback lasers, provided that the gain of the medium exceeds the lasing threshold, which is specific for each cavity. We present the results of experiments carried out with single-mode optical fibers with gain and randomly-located resonant Bragg reflectors (periodic gratings). When the fiber was illuminated by a pumping laser with an intensity high enough to overcome the lasing threshold, the resonances revealed themselves by peaks in the emission spectrum. Our experimental results are in a good agreement with the theory presented here.