On the phenomenological theory of light propagation in optically active crystals

Abstract

In the usual treatment of the optical activity of crystals, the displacement vector of the light wave is expressed as a function of the electric vector-this being done with the aid of the dielectric tensor and the gyration vector. The treatment is made more concise and tractable by using the inverse vector function and expressing the electric vector in terms of the displacement vector, since it is the latter which necessarily lies on the wave-front; this can be done by using the inverse of the dielectric tensor (which defines the index ellipsoid), and an inverse gyration vector (which determines the rotatory power for the particular direction of propagation considered). The inverse gyration-vector (like the gyration-vector) is itself a function of the direction of propagation, being related to it by a modified gyration tensor- which consequently determines the rotatory power for all directions.