An alternative method of dispersion relations derivation in the crystalline optical activity in the direction perpendicular to the optic axis

An alternative method of the dispersion relations derivation in the crystalline optical activity based on the application of the modified Rosenfeld relation in the models of coupled oscillators is generalized for the propagation of the electromagnetic wave in the direction perpendicular to the optic axis. The rotational strengths of the quantum mechanical transitions in the normal modes of vibrations are calculated by relatively easy way as the sum of two independent components. As an example, the solution of specific three coupled oscillators model, which seems to be sufficient for the description of the optical activity of crystals with space groups of symmetry D34 or D36, is presented. The dispersion relations for both aspects of the crystalline optical activity - optical rotatory dispersion and circular dichroism - are derived. The results are applied on the calculation of the optical activity ratio in the directions perpendicular and parallel to the optic axis for trigonal selenium.