Polariton theory of first-order Raman scattering in finite crystals for transparent and absorbing frequency regions

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Abstract
A new treatment is given of first-order Raman scattering in bounded insulators using the polariton picture. A novel feature of the work is the use of polariton states which have the correct asymptotic behavior as incoming or outgoing photons in the region exterior to the crystal, and are properly matched, via boundary conditions to the usual polaritons (coupled exciton-photon states) in the region interior. We recover in this polariton treatment, essentially the results of lowest-order perturbation theory for the scattering cross section with some significant modifications in part depending on whether allowed or forbidden exciton-phonon interaction is involved. Inter alia our work shows that the exterior-photon density-of-states factors appear in the cross section thereby resolving previous uncertainty regarding use of polariton group or energy velocities in the absorption region. Calculations are given of frequency dependence of Raman-scattering cross sections for incident frequencies below and above the energy gap, for allowed and forbidden electron-phonon coupling, and for correlated (exciton) and Bloch (free) electron-hole pairs. These are compared with experiment for CdS and GaP.

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