An integral equation method for electromagnetic scattering of guided modes by boundary deformations of dielectric slab waveguides

An integral equation method is proposed for analyzing scattering and mode conversion of guided modes by boundary deformations of a dielectric slab waveguide. Integral equations are derived for the tangential electromagnetic fields on the deformed boundaries only, using the integral expressions of fields and the fundamental properties which the integral over a closed path has. Mode conversion coefficients for guided and radiation modes are easily obtained from the solutions of the integral equations. Using the mode conversion coefficients, physical quantities such as radiation loss, reflected mode power, and total scattered power, are calculated. Numerical examples are presented for the two-dimensional models of the typical boundary deformations in optical fibers caused by a fusion splice.