A method of calculating 2×2 reflection and transmission-coefficient matrices for a multilayer birefringent system, developed for use in a plane stratified magnetoplasma, is applied to an optical system. The diagonal matrix elements refer to the direct reflection and transmission coefficients of the two characteristic or normal modes, and off-diagonal elements refer to inter-mode coupling between them. For waves normally incident on the plane stratified system, in the positive or negative z directions, corresponding reflection and transmission-coefficient matrices, R± and T±, are defined in terms of suitably normalized wave fields. A reciprocity theorem is established wherein it is shown that the matrices R+ and R- are symmetric, and the matrix T+ is the transpose of T-, provided that the dielectric tensors of the layers composing the system are either (a) all symmetric, or (b) all gyrotropic (magnetoactive), having a common principal axis that is generally the external magnetic-field direction. Optically inactive, isotropic layers may be included in either class, but care must be taken in defining characteristic modes for such layers. Some applications are discussed, including the feasibility of constructing light valves.
C. ALTMAN and S. G. LIPSON, "Reciprocity Relations in Light Propagation through a Multilayer Birefringent System," J. Opt. Soc. Am. 61, 1373-1379 (1971)