Open AccessVector analysis of bending waveguides by using a modified finite-difference method in a local cylindrical coordinate system
Author(s) -
Jinbiao Xiao,
Xiaohan Sun
Publication year - 2012
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.20.021583
Subject(s) - optics , coordinate system , finite difference method , mathematical analysis , eigenvalues and eigenvectors , finite difference , boundary value problem , perfectly matched layer , bending , physics , solver , cylindrical coordinate system , taylor series , series expansion , waveguide , materials science , geometry , mathematics , mathematical optimization , quantum mechanics , thermodynamics
A vector mode solver for bending waveguides by using a modified finite-difference (FD) method is developed in a local cylindrical coordinate system, where the perfectly matched layer absorbing boundary conditions are incorporated. Utilizing Taylor series expansion technique and continuity condition of the longitudinal field components, a standard matrix eigenvalue equation without the averaged index approximation approach for dealing with the discrete points neighboring the dielectric interfaces is obtained. Complex effective indexes and field distributions of leaky modes for a typical rib bending waveguide and a silicon wire bend are presented, and solutions accord well with those from the film mode matching method, which shows the validity and utility of the established method.