Section 2.3.4.4. Stress- (strain-) induced Raman scattering

Stress-induced Raman scattering is an example of the case when the external `force' is a higher-rank tensor. In the case of stress, we deal with a symmetric second-rank tensor. Since symmetric stress (T) and strain (S) tensors have the same symmetry and are uniquely related via the fourth-rank elastic stiffness tensor (c),it is immaterial for symmetry purposes whether stress- or strain-induced effects are considered. The linear strain-induced contribution to the susceptibility can be written as so that the respective strain coefficients (conventional symmetric scattering) transform evidently as i.e. they have the same symmetry as the piezo-optic or elasto-optic tensor. Reducing this representation into irreducible components , we obtain the symmetry-restricted form of the linear strain-induced Raman tensors. Evidently, their matrix form is the same as for quadratic electric-field-induced Raman tensors. In centrosymmetric crystals, strain-induced Raman scattering (in any order in the strain) is thus allowed for even-parity modes only.