Generalization of the crystalline optical activity dispersion relations for arbitrary propagation direction of electromagnetic waves

This study suggests an alternative method concerning the derivation of the dispersion relations in crystalline optical activity for the arbitrary propagation direction of the electromagnetic waves. The solution is based on the dipole–dipole interactions between the valence electrons that are represented by the harmonic oscillators. The following theoretical description of the optical activity uses the modified Rosenfeld relations. The rotational strengths of the quantum-mechanical transitions in the normal modes of vibrations are obtained following simple calculations of a sum of two independent components. The specific model of three coupled oscillators, which seems to be sufficient for the description of the optical activity of crystals having space groups of symmetry D34 or D36, is solved as the example and the dispersion relations are derived for the optical rotatory power and circular dichroism. The results are applied on the example of trigonal selenium, for which the optical rotatory power ratio in the direction perpendicular and in the direction parallel to the optic axis is calculated. The calculated relation is compared with a similar relation derived by Chandrasekhar. The validity of both relations is then discussed.