Unified analysis of guided and radiation modes in anisotropic slab waveguide

The radiation modes of an anisotropic dielectric waveguide have been analyzed in the case where nondiagonal terms of the permittivity tensor vanish and the TE and TM modes can be separated. This paper presents a unified treatment of the radiation and guided modes of an anisotropic slab waveguide with arbitrary permittivity and permeability tensors. In the analysis the propagation of the electromagnetic field in the transverse direction is expressed in terms of a linear combination of normal modes in that direction, and the orthogonality condition of the electromagnetic modes is expressed by the amplitude vector of the normal mode. This permits replacement of the orthogonality condition of degenerate modes with the geometric orthogonality of amplitude vectors and the use of the Schmidt orthogonalization procedure. In the transition region from radiation modes to guided modes it is shown that there exist degenerate radiation modes with various degrees of degeneracy inherent to the anisotropic waveguide. Numerical examples of the application of the present method are given.