Field analysis of dielectric waveguide devices based on coupled transverse-mode integral equation - Mathematical and numerical formulations

We propose an integral-equation formulation for analyzing EM field of 2-D dielectric waveguide devices. The complex 2-D device is first divided into slices of 1-D horizontally layered structures. The entire EM solutions are determined by transverse field functions on the interfaces between slices. These functions are governed by a system of integral equations whose kernels are constructed from layer modes of each slice. These unknown tangential field functions are expanded as some linear combination of known basis functions. Various waveguide devices such as multi-mode interferometers, waveguide crossing and quasi-adiabatic tapered waveguides can be formulated and studied using present formulation.