The origin of optical dephasing times and line shape functions for electronic transitions to localized and delocalized states in solids

Abstract

A theory for optical dephasing times and the homogeneous component of the absorption line shape function to localized states and to the k=o levels of Frenkel exciton states is presented. The theory is based upon exchange between two or more optical transitions which are separated by a small frequency difference. Exchange averaging of the optical transition is brought about via phonon–exciton scattering which couples the optical transitions. This process causes both a temperature dependent line broadening and a temperature dependent frequency shift in the optical spectrum when quadratic phonon–exciton coupling terms are present. The optical dephasing time in such cases result from energy differences of the phonon branch in the ground and excited states and consequently it need not necessarily reflect the complete loss of coherence of the exciton wavepacket at k=o. A simple criterion is derived that allows one to determine whether the phonon–exciton interaction causes an optical transition line shape function to reflect random frequency modulation by the exchange of low frequency phonon or vibrational quanta. The theory allows the phonon–exciton scattering times for individual modes to be determined from an analysis of the frequency shift and line broadening relationships in favorable cases. This information coupled with knowledge of the exciton dispersion allows one to semiquantitatively determine the effect individual phonon and vibrational modes have on the exciton coherence time at a particular temperature.