Journal Article10.1109/50.822799
Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices
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TL;DR: In this article, a general relation between a sampled point and its nearby points is derived and the derived relation and the generalized Douglas scheme are extended to fourth order accuracy irrespective of the existence of the step-index interfaces.
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Abstract: A general relation, considering the interface conditions, between a sampled point and its nearby points is derived. Making use of the derived relation and the generalized Douglas scheme, the three point formulas in the finite-difference modeling of step-index optical devices are extended to fourth order accuracy irrespective of the existence of the step-index interfaces. With numerical analysis and numerical assessment, several frequently used formulas are investigated.
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Citations
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A New Full-Vectorial Higher Order Finite-Difference Scheme for the Modal Analysis of Rectangular Dielectric Waveguides
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Comparative study of several time-domain methods for optical waveguide analyses
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