The exact finite difference method: A new approach to the calculation of leak modes in multilayer waveguide structures

Abstract

A new approach to the calculation of electromagnetic modes in optical waveguides (OWGs), which is based on the exact finite difference method (EFDM) representing a combination of the finite difference method and the transmission matrix technique, is described. The efficacy of the EFDM is demonstrated in application to the calculation of leak modes in multilayer planar OWGs of the ARROW type, featuring antiresonance reflection from a multilayer shell (rather than the total internal reflection from the shell-core interface as in the usual OWGs). The proposed method can be used for calculations of both the electromagnetic modes in dielectric OWGs and the quantum states of electrons in multibarrier semiconductor heterostructures. The parameters of a nine-layer OWG calculated using the EFDM are compared to the published data obtained by solving a dispersion equation within the framework of the transmission matrix technique. The results of calculations of the spectrum of radiative losses for the first (leak) TE mode in planar OWGs with various numbers of layers are presented.