Improved coupled-mode theory for reciprocal anisotropic waveguides

An improved coupled-mode theory for a reciprocal anisotropic multiwaveguide system is derived. The general reciprocal anisotropic medium is described by a symmetric permittivity tensor that can have nonzero off-diagonal elements. The derivation is based on the generalized reciprocity relation. The coupled-mode equations are applicable to both lossy (gain) and lossless systems. For the special case of lossless systems, it is shown that the matrices in the coupled-mode equation are Hermitian, so that energy conservation is observed exactly. For the special case of a single anisotropic waveguide, the results also reduce to the previously derived solutions by D. Marcuse (1975). The improved coupled-mode theory in an anisotropic multiwaveguide system is illustrated with numerical examples.>