The Symmetry and Optical Phenomena

Abstract

The explicit forms of the broken (by a electric field E, magnetic field H and spatial dispersion of wave vector k) point symmetry groups of a crystal are given. For these groups the dielectric permeability tensors: εij (ω, E), éij (ω, H) and εi j (ω, k) -the particular cases of eij (ω, E, H, k) -are written out (the susceptibility tensors x,, (ω, E), χij (ω, H) and χij (ω, k) take the same forms). In order to illustrate the results obtained the electrooptical phenomena (connected with the tensors (ω, E)) are discussed.

The Optical Method of Determining the Point Symmetries

“…They allow to solve the question whether our medium is dispersive or not. If it is dispersive -the advantage of the proposed method is that, by varying the external fields, one can isolate the contributions coming from the external field as well as those related to the dispersive character of the medium and, therefore, determine unambiguously (as contrasted with the previous proposals for dispersive media [8]) the symmetry of the crystal.…”

“…Equation (1) is invariant under the operation of the inversion of the direction field, F → F , i f t h e t e n s o r ε i j determined by the K(F) groups and is not invariant if it is determined by the J(F) groups [2,3]. As a consequence the roots of Eq.…”

“…(1) which correspond to the above tensors and to determine the symmetry group using, in turn, table I of Ref. [3]. This is accomplished in the present paper, see Tables…”

“…T h e l a t t e r i s f i x e d b y t h e s y m m e t r y g r o u pK o f t h e medium or by the broken symmetry group K(F) [3], if the medium is placed in external field F; -the relation between the elements of ε-tensor.…”

“…The way out of this situation is to supply ourselves with the sufficient number of the different forms of the tensor eij; this can be achieved by breaking initial symmetry with the help of external field. The relevant results for εij were given in Tables II and III in the paper [3]. Therefore, it remains to analyse the solutions of Eq.…”