Inverse-scattering view of modal structures in inhomogeneous optical waveguides

Abstract

To understand the physical meaning of rational reflection coefficients in inverse-scattering theory for optical waveguide design [ J. Opt. Soc. Am. A6, 1206 ( 1989)], we studied the relationship between the poles of the transverse reflection coefficient and the modes in inhomogeneous dielectrics. By using a stratified-medium formulation we showed that these poles of the spectral reflection coefficient satisfy the same equation as the guidance condition in inhomogeneous waveguides. Therefore, in terms of wave numbers, the poles are the same as the discrete modes in the waveguide. The radiation modes have continuous real values of transverse wave numbers and are represented by the branch cut on the complex plane. Based on these results, applications of the Gel’fand–Levitan–Marchenko theory to optical waveguide synthesis with the rational function representation of the transverse reflection coefficient are discussed.