Cooperative emission from a disordered system: a classical model

The effect of disorder on the collective emission from a system of classical oscillators is studied theoretically. Three types of disorder are considered: random orientation of dipole moments, finite spread in frequencies of the individual oscillators (diagonal disorder), and dipole-dipole interaction (off-diagonal disorder). We found that for sufficiently high concentration of oscillators the diagonal disorder does not completely destroy the collective character of the emission. We show that the eigenmodes of a cooperative system with disorder comprise a large number of oscillators and, due to cooperative character of the emission, their lifetime is much longer than the lifetime of an individual oscillator. Consequently, the cooperative emission spectrum of the system is not simply broadened by the disorder, but represents a superposition of relatively narrow peaks.