Time-domain analysis of the dynamics of Frenkel excitons in disordered systems

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Abstract
The dynamics of Frenkel excitons in disordered systems is studied in the time domain. Particular emphasis is placed on the evolution of the integrated fluorescence in the forward direction following pulsed, broadband excitation. Methods for calculating the fluorescence by integrating the coupled equations of motion for the dipole-moment correlation functions are outlined. In a system without traps, the integrated fluorescence is related to the sine and cosine transforms of the line-shape function. Numerical results are presented for the case of a Gaussian distribution of transition frequencies. The effects of traps on the fluorescence are investigated for a three-dimensional periodic array of ions with a random distribution of trapping centers. The asymptotic decay rates are calculated numerically and compared with lowest-order perturbation theory and a theory based on the coherent-potential approximation. The failure of the perturbation-theoretic calculation when the single-ion trapping rate is comparable to the exciton bandwidth is pointed out. The coherent-potential approximation gives reasonable results at all trap concentrations over a wide range of the ratio of trapping rate to bandwidth.