Generalized WKB method for the analysis of light propagation in inhomogeneous anisotropic optical waveguides

The generalization of the WKB method for light propagation in planar uniaxially anisotropic inhomogeneous optical waveguides is presented. Both ordinary and extraordinary ray paths and phases along the rays in the medium inhomogeneous in the direction perpendicular to the optic axis are derived. These results are used to formulate the dispersion equations for graded-index anisotropic optical waveguides such as the LiNbO3:Ti waveguide. Analytical continuation from the real to the complex effective index of refraction enables one to include leaky modes into the analysis. A simple expression for the leaky-mode loss coefficient is given. Both the polarization conversion and energy leakage effects are well described by this method.