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Opto-Electronics Review

Editor-in-Chief: Jaroszewicz, Leszek

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1896-3757
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Volume 19, Issue 2

Issues

Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

S. Sujecki
Published Online: 2011-04-08 | DOI: https://doi.org/10.2478/s11772-011-0019-1

Abstract

A rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of the refractive index profile. The results show that the approximations reach O(h2) truncation error only asymptotically for sufficiently small values of the mesh size.

Keywords: finite differences; optical waveguides; guided waves

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About the article

Published Online: 2011-04-08

Published in Print: 2011-06-01


Citation Information: Opto-Electronics Review, Volume 19, Issue 2, Pages 145–150, ISSN (Online) 1896-3757, DOI: https://doi.org/10.2478/s11772-011-0019-1.

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© 2011 SEP, Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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