Evaluation of photoelastic constants from first-order Raman intensities of MgF2

A formalism to connect first-order Raman intensities of MgF₂ and its photoelastic constants is developed by developing a method of writing internal coordinates in terms of displacement gradientsu _ij which are not symmetric. It is found that for crystals containing only one line inA ₁ species, the ratiosP ₁₃/P ₃₃ and (P ₁₁ +P ₁₂)/P ₃₁ can be directly evaluated from the intensities, without having to derive the intensity formulae; while (P ₁₁ +P ₁₂)/P ₁₃ is independent of the intensities as well as the refractive index of the crystal. It is a function of only the dimensional parameters. In this crystal, since the speciesB _1g andB _2g also contain only one line each, the ratio (P ₁₁ −P ₁₂)/P ₆₆ can also be directly obtained from the intensities.