Mesoscopic Cooperative Emission from a Disordered System

We study theoretically the cooperative light emission from a system of N ≫ 1 classical oscillators confined within a volume with spatial scale, L, much smaller than the radiation wavelength, λ0 = 2πc/ω0. We assume that the oscillators frequencies are randomly distributed around a central frequency, ω0, with some characteristic width, Ω ≪ ω0. 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 6= 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 λ0. We also estimate the amplitude of this mesoscopic structure in the emission spectrum.