Response Functions in the Theory of Raman Scattering by Vibrational and Polariton Modes in Dielectric Crystals

The paper begins with a tutorial introduction to the theory of inelastic light scattering by polaritons in dielectric crystals. The treatment is based on a simple two-oscillator model which represents the ionic and electronic motions of a crystal. The model contains a third-order anharmonicity which allows an incident laser beam to mix with the oscillator fluctuations and produce scattered light of frequency different from the incident frequency. The magnitude of the oscillator fluctuations is determined by an application of the Nyquist of fluctuation-dissipation theorem, using the response functions of the oscillators for externally applied forces. The simple model gives results for light scattering cross sections which agree with more rigorous derivations in the existing literature. The response function approach is generalized to apply to crystals having many ionic resonances and of uniaxial or orthorhombic structure. The general formulas reduce in appropriate special cases to results already published. Experimental and theoretical work on light scattering by polaritons and by pure phonons is reviewed in the context of both the two-oscillator model and the general theory. Particular attention is given to resonance scattering in an attempt to achieve consistency between the differing theoretical treatments in the literature. The subject matter of the review overlaps some topics in nonlinear optics, and contact is made with the theories of the electrooptic effect and stimulated Raman scattering.