Open AccessArbitrary-order interface conditions for slab structures and their applications in waveguide analysis
Author(s) -
Yih-Peng Chiou,
Cheng-Han Du
Publication year - 2010
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.18.004088
Subject(s) - slab , truncation (statistics) , truncation error , computation , waveguide , taylor series , convergence (economics) , optics , interface (matter) , finite difference method , finite difference , electric field , field (mathematics) , physics , transverse plane , computer science , mathematical analysis , mathematics , algorithm , quantum mechanics , surface tension , gibbs isotherm , structural engineering , engineering , machine learning , geophysics , pure mathematics , economics , economic growth
We extend the continuity relations of field derivatives across an abrupt interface to arbitrary orders for transverse electric and magnetic waves in slab structures. Higher-order finite-difference formulation is then obtained by combining the systematically-obtained interface conditions with Taylor series expansion. Generalized Douglas scheme is also adopted to further enhance the convergence of truncation errors by two orders. We apply the derived finite-difference formulation, up to nine-points in this paper, to solve the guided modes in simple a slab waveguide and multiple quantum well waveguides. The results shows the truncation error is much higher, up to tenth order, as expected. Using those higher-order schemes, accurate results are obtained with much fewer sampled points, and hence with tremendously less computation time and memory.