An asymptotic theory of clad inhomogeneous planar waveguides. I. Eigenfunctions and the eigenvalue equation

Abstract

Asymptotic representations are obtained for the eigenfunctions of the differential equation describing scalar waves in a clad inhomogeneous planar waveguide, which has two turning points and finite boundaries. These representations are valid to all asymptotic orders in the large parameter, which is proportional to wavenumber. This is achieved, in contrast to augmented WKB theory, by finding transformations on the independent variable which map the eigenfunction exactly into known solutions of canonical differential equations. The resulting transformation equations are nonlinear but have tractable asymptotic properties.