Light propagation in absorbing crystals possessing optical activity

Abstract

A light beam in an absorbing crystal may be looked upon as travelling under the superposed effects of the various 'elementary properties' associated with the medium,viz., linear birefringence, linear dichroism, optical rotation and circular dichroism. For any general direction of propagation, this postulate yields completely (a) the states of polarisation of the two waves (specified conveniently by two corresponding points on the Poincare sphere), and (b) their velocities and absorption coefficients (expressed conveniently as functions of their states of polarisation). The treatment is closely parallel to that for inactive absorbing crystals (Pancharatnam, 1955)-since for each direction, linear and circular birefringence combine to give elliptic birefringence, while linear and circular dichroism similarly combine to yield elliptic dichroism. The case of biaxial media with negligible or no circular dichroism is dwelt upon at length. The waves along an optic axis are not circularly polarised: they may even be in two non-orthogonal linearly polarised states (if the dichroism exceed twice the rotatory power). For directions in the near vicinity of an optic axis the waves are in two elliptic states of unequal ellipticity with their major axes not crossed. For other directions, however, the orientations of the major axes-as also the velocities and absorption coefficients of the waves-become substantially the same as for an inactive absorbing crystal; but the ellipticity for each state now approximates to the sum of the corresponding ellipticities obtaining in the inactive absorbing crystal and the active transparent crystal-thus becoming negligible only when the inclination to both the optic axes becomes notable.