TE and TM modes in a cylindrical liquid-crystal waveguide

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Abstract
We consider a cylindrical waveguide consisting of an inhomogeneous anisotropic liquid-crystal core embedded in an infinite homogeneous isotropic cladding. The wave equations for the pure modes are uncoupled but may have complex coefficients owing to the inhomogeneity and anisotropy of the liquid crystal. A simple numerical method is proposed for solving these equations. For the configuration considered, numerical results for the TE modes agree exactly with the analytical solution. For the TM modes, no analytical solution is available, and the unusual result obtained is that the phase of the fields inside the core depends on the distance from the cylinder axis.