Modal analysis of homogeneous optical waveguides by the boundary integral formulation and the Nyström method

Abstract

The optical field in a weakly guiding homogeneous waveguide satisfies scalar Helmholtz equations in both the core and the cladding and the transmission conditions on the boundary. Two different systems of boundary integral equations are derived for numerical solutions of the discrete propagation constants of the optical field; one of them is in the form of Fredholm integral equations of the second kind, and the other is a mixed first and second kind. The Nyström method is used to solve the boundary integral equations numerically. The numerical results show that the two boundary integral formulations are both very efficient in the numerical simulations of homogeneous waveguides but that the second kind is superior because it controls spurious modes better.