Mesoscopic Cooperative Emission From a Disordered System

Abstract

We study theoretically the cooperative light emission from a system of $N\gg 1$ classical oscillators confined within a volume with spatial scale, $L$, much smaller than the radiation wavelength, $λ_0=2πc/ω_0$. We assume that the oscillators frequencies are randomly distributed around a central frequency, $ω_0$, with some characteristic width, $Ω\llω_0$. In the absence of disorder, that is $Ω=0$, the cooperative emission spectrum is composed of a narrow subradiant peak superimposed on a wide superradiant band. When $Ω\neq 0$, we demonstrate that if $N$ is large enough, the subradiant peak is not simply broadened by the disorder but rather splits into a system of random narrow peaks. We estimate the spectral width of these peaks as a function of $N, L, Ω$, and $λ_0$. We also estimate the amplitude of this mesoscopic structure in the emission spectrum.