Theory of First-Order Raman Scattering in Insulators

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Abstract
We have formulated a theory of the first-order Raman effect in insulating crystals in which the true electromagnetic modes of the crystal (polaritons) are scattered by the lattice vibrations. The purpose of this paper is to extend an earlier calculation, where only the scattering of the exciton portion of the polariton was considered, to include also the contribution from the scattering of the Coulomb-correlated free particle-hole pairs that clothe the electromagnetic field in the crystal. A Green's-function technique is employed which expresses the Raman scattering rate in terms of the appropriate particle-hole scattering matrix. The exciton contribution to the Raman tensor, along with that from the continuum portion of the particle-hole excitation spectrum, thus appears, without the need for the explicit introduction of exciton variables. When the frequency of the incident light is near the excitation energy of an exciton, the exciton contribution to the Raman tensor is strongly enhanced, as Ganguly and Birman have pointed out. As discussed earlier, consideration of the polariton nature of the normal modes is necessary in order to examine the frequency dependence of the exciton contribution to the Raman efficiency in the resonance region. In this work, we find that the contribution to the Raman tensor from the particle-hole continuum decreases sharply as the exciton frequency is approached from below. The physical origin of this phenomenon and the frequency dependence of the various contributions to the Raman efficiency are discussed.

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