Polariton-Phonon Interaction in Molecular Crystals

Abstract

A general theory is presented concerning the interaction between the polaritons and the acoustic phonons in molecular crystals. Using a one‐phonon approximation to truncate the hierarchy of the Green's functions involved and disregarding mixing of different polariton bands, we derive an expression for the dielectric permeability of the crystal. The absorption coefficient for the coupled polariton‐phonon spectrum is found to have an asymmetric Lorentzian lineshape even if the frequency dependence of the energy shift and spectral width is neglected. The damping function causing the asymmetry of the spectral line depends entirely on the coupling between the dressed electron subsystem and the phonon field. Expressions are developed for the energy shift and spectral width of the resonance line, and their temperature dependence is discussed. Far from the resonance peak, the frequency and temperature dependence of the absorption coefficient is established. In the transparent region of frequencies of the crystal, the expression for the absorption coefficient consists of two terms that have delta‐function distributions and are peaked at different frequency regions, depending on whether or not the polariton and the phonon fields are coupled. In the limiting case where retardation can be ignored, the bare exciton‐phonon interaction is discussed. The average energy of the crystal resulting from the polariton‐phonon interaction at finite temperatures has been derived in a closed form.