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The polarization properties of the light transmitted through an optically anisotropic stratified medium are discussed in terms of a 2 × 2 matrix approach, which can be followed in all cases when the intensity of the reflected waves is negligible. The starting point of the treatment is Berreman’s equation, involving a 4 × 4 matrix. A generalized Jones vector is obtained by applying a suitable transformation to Berreman’s vector. An equation for the propagation of the Jones vector is easily derived. It involves another 4 × 4 matrix, obtained from the Berreman one, whose elements describe the propagation and the mutual coupling of forward-and backward-traveling solutions. In particular, the upper 2 × 2 block corresponds to the Jones matrix of the problem. The Jones equation is solved by making use of an interaction-matrix treatment derived from the perturbation methods of quantum mechanics. A transfer matrix is obtained, describing the effect of the optical medium on the transmitted light. Such a procedure holds and gives good results, for the arbitrary incidence of light. Simple, analytical expressions for the transfer-matrix elements are obtained for quasi-normal incidence of light. This approximation retains its validity for incidence angles as large as 30° (in air). The case of the twisted nematic cell is discussed in detail. The effect of multiple reflections at the surfaces of the optical medium (or at interfaces between adjacent media) is shown to be correctly accounted for within the proposed approach.
© 1988 Optical Society of America
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