Abstract-This is a numerical investigation of a recently proposed formulation called coupled transverse-mode integral equation (CTMIE) for analyzing EM field properties in general 2-D dielectric waveguide devices. The device is first approximated by stack of piece-wise 1-D horizontally layered structures. Transverse field components on the interface between waveguide slices are unknown functions, which are governed by a coupled integral equation. When unknowns are expanded as a linear combination of given functions, CTMIE is converted to a coupled block matrix equation. We study three waveguide devices, in detail, to understand the relation between modeling parameters and accuracy and convergent rate of the solutions. Examples include a step waveguide junction, a multi-mode interferometer power cross coupler and a linearly tapered waveguide. All results are verified with independent calculations using other proven methods.
Abstract-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.
We propose a rigorous full-vector integral-equation formulation for analyzing modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic mode field is completely determined by the y-component electric and magnetic field functions on the interfaces between slices. These interfacial functions are governed by a system of vector-coupled transverse-mode integral equations (VCTMIE) whose kernels are made of orthonormal sets of both TE-to-y and TM-to-y modes from each slice. To solve for the unknown functions, we construct sets of suitable expansion functions and turn VCTMIE into a nonlinear matrix equation via orthogonal projection. The eigenvectors of the matrix provide the mode field solutions of the complex dielectric waveguide.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.