title: Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. I. Mathematical formulation.
abstract: 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.
authors.affiliation: Institute of Electro-optical Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan. hchang@mail.nsysu.edu.tw
authors.forename: Hung-Wen
authors.initials: HW
authors.lastname: Chang
authors.forename: Tso-Lun
authors.initials: TL
authors.lastname: Wu
authors.forename: Meng-Huei
authors.initials: MH
authors.lastname: Sheng