Polariton Theory of Raman Scattering. III. Effect of Exciton and Band Properties on the Frequency Dependence of the Cross Section

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Abstract
In the present work, a polariton approach is employed to derive cross sections for resonant Raman scattering mediated by dipole-forbidden and quadrupole-allowed excitons. The results are contrasted with those in the dipole-allowed case. We investigate differences in polariton dispersion and in the nature of the discrete-state and continuum contributions in the various cases, and demonstrate how these influence the resonance properties of the cross section. We find that, in general, continuum effects dominate in forbidden scattering, while continuum-discrete interference is strongest in allowed scattering. Considerably sharper onsets to resonance are predicted for the quadrupole case, as compared to the dipole. Resonance properties are shown to depend as well, often strongly, on the values of various crystalline parameters, such as the exciton effective mass and the frequency of the phonons involved in the scattering. The predictions are illustrated via detailed numerical computations for a hydrogenic exciton model, and parameters appropriate to insulators such as CdS.