The electromagnetic field generated in a nonabsorbing anisotropic multilayer by a plane incident wave with given wave vector is considered. By taking into account the fact that the field within a given layer is a superposition of four proper waves, namely, four waves that propagate without changing their polarization state, the field is associated with a four-dimensional complex vector space. In this space a new algebra is defined such that the norm of a vector gives the energy flux density of the corresponding field, and the scalar product of two proper waves is zero. This allows one (1) to simply derive the amplitudes of the four proper waves for any layer, (2) to explicitly write the reflection and transmission coefficients of a structure whose layers are uniaxial media with arbitrary direction of the optical axis, and (3) to deduce the propagation equations for the four waves in the limiting case of a plane stratified medium with continuous variation of the dielectric tensor. Similar equations are found in the literature only for some very particular cases and are generally used to obtain approximate solutions for the wave equation. Here the general case is considered. The given equations contain as specific cases most of the already known approximations and give a unifying method for their discussion and generalization. In particular, they contain the geometrical-optics approximation (GOA) for uniaxial stratified media with arbitrary directions of the optical axis and of the incidence angle, as well as a generalization of the GOA, where the coupling between the ordinary and extraordinary waves is taken into account. The theory developed here has a wide range of applications in many fields of physics, as for instance the propagation of electromagnetic waves in magnetoactive plasmas, the optical properties of liquid crystals, and more generally the optics of anisotropic media.

• Received 21 February 1989

DOI:https://doi.org/10.1103/PhysRevA.40.6014