Decay of the resonance fluorescence following pulsed excitation of a weakly disordered excitonic system

Abstract

A study is made of the decay of the resonance fluorescence following pulsed excitation of a weakly disordered system whose optical excitations are Frenkel excitons. The disorder is characterized by a Gaussian distribution of optical transition frequencies with no correlation between different sites. The duration of the resonant pulse is taken to be short in comparison with the reciprocal of the optical linewidth, and the wavelength of the light is assumed to be large in comparison with either the size of the array or the exciton mean free path associated with the disorder. In the limit where σ, the standard deviation of the Gaussian distribution, is much less than the exciton bandwidth, the integrated intensity of the fluorescence decays non-exponentially and is characterized by universal functions of σ x t, where x= 4 3 , 2, and 4 in one, two, and three dimensions, respectively. Analytic approximations to the scaling functions in two and three dimensions are presented.