Classical Theory of Raman Scattering

The following classical description [21], while failing to explain many of the quantitative aspects of the Raman effect, is able to capture its qualitative behavior and provides a useful basis for understanding this phenomena. As in the case of Rayleigh scattering theory, the source of the scattering is the oscillating dipole moment, 

The polarizability tensor, a, introduced in section 4.1.2, is a measure of the facility of the electron distribution to distortion by an imposed electric field. The structure of the electron distribution will generally be anisotropic, giving rise to intrinsic birefringence. This optical anisotropy reflects the average electron distribution whereas vibrational and rotational modes of the molecules making up a sample will cause the polarizability to fluctuate in time. These modes are discrete, and considering a particular vibrational frequency, vk, the oscillating polarizability can be modeled as 

Taking the electric field to be o sin27rvf, the induced dipole moment is then 

Using this model, the intensity of light generated by a specific Raman scattering process will simply by the modulus of the electric vector it produces  

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Both quantum mechanical and classical theories of Raman scattering have been developed. The quantum mechanical treatment of Kramers and Heisenberg 5) preceded the classical theory of Cabannes and Rochard 6). 

The classical theory of Raman scattering offered a mechanistic way of understanding the Raman effect but was unable to provide information on the intensity of Raman... 

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