Excitation Spectrum of Interacting Polaritons in Dielectric Crystals

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Abstract
The excitation spectrum of interacting polariton waves in the infrared region of frequencies of dielectric crystals has been studied using the double-time Green's-function method. The Dyson equation describing the spectrum of interacting polariton fields is derived in a general form, and then the polarization operator and the polariton Green's function are evaluated in two successive approximations. Use has been made of two "equivalent" renormalized Hamiltonian representations, which are correct in the lowest and first approximations, respectively. The polariton Green's function is expressed, in the second approximation, in terms of the renormalized polariton frequencies, where the frequency of each polariton mode contains anharmonic corrections to all orders. Expressions are developed for the frequency shift and spectral width of the fundamental absorption bands. It is shown that the renormalization of the polariton frequencies directly affects the temperature dependence of the frequency shift and width of the infrared absorption bands. The retardation effects reduce the magnitudes of the anharmonic coupling functions. In the region of wave vectors where retardation may be neglected, the phonon excitation spectrum has been considered and compared with the results derived from previous studies.