Asymptotic analysis of planar and cylindrical inhomogeneous waveguides

Abstract

The problem of determining the eigenvalues of an inhomogeneous waveguide, subject to boundary conditions at an interface with an exterior homogeneous medium (cladding) is considered. A recently developed asymptotic method is summarised. Previous work dealt with planar waveguides; here we incorporate the extensions necessary to accommodate cylindrical waveguides, as encountered in optical fibres. The method uses a nonlinear transformation between variables to reduce a given differential equation to canonical form; this transformation has more tractable asymptotic properties than the original differential equation.