Optical Response of Exciton-Phonon System I —Absorption Spectrum and Urbach-Martienssen Rule—

Stochastic theory of the first and second order optical response 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 modes which interact dominantly with the exciton. In this paper, the dynamical coherent potential approximation is extended to this non-Hamiltonian system and the low energy side of the optical absorption spectrum due to the exciton is studied. It is shown that the multiphonon sidebands are merged into the exponential tail with the increase of the temperature and/or the transfer of the exciton. This exponential tail originates from the thermal distribution of the relevant modes and from the broadening of the phonon sidebands due to the exciton transfer and the interaction with the reservoir of irrelevant lattice vibrations.