First and Second Order Optical Responses in Exciton-Phonon System

Abstract

Stochastic theory of the first and second order optical responses is presented for a system of exciton-phonon complex. The dynamical motion of the whole lattice system is projected onto the stochastic motion of the relevant mode which interacts dominantly with the exciton. The dynamical coherent potential approximation is extended to this non-Hamiltonian system and the low energy side of the absorption spectrum due to the exciton is studied. It is shown that the multi-phonon sidebands are merged into the exponential tail with the increase of the temperature or/and transfer of the exciton. This exponential tail originates from the thermal equilibrium distribution of the relevant mode and from the broadening of the phonon sidebands due to the interaction with the reservoir of the irrelevant lattice vibrations or due to the increase of the exciton transfer. The dynamical coherent potential approximation is further extended to the second order optical response in the exciton-phonon system and the emission spectrum of this system is calculated. The broadening of the Raman lines reflects the relaxation of the relevant mode in the final state and the luminescence, on the other hand, are shown to depend sensitively on the exciton transfer as well as the radiative decay rate and the relaxation of relevant phonons. The spectra show how these lines shift to the high energy side and are broadened with the increase of the transfer of the exciton. The relative magnitude of the Raman and luminescence components depends not only on the ratio of radiative decay to the relaxation but also on the incident photon frequency Ω_l. This means that we can observe the coexistence of these components over a wide value of the ratio by choosing Ω_l suitably and determine the decay and relaxation constant. The study of the second order optical response in the exciton-phonon system is thus shown to provide us with information on the relaxation Process and on the characteristic constants of the exciton-phonon system.