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.

[IEEE ]

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J. Lightwave Technol. (3)

J. Yamauchi, J. Shibayama, O. Saiti, O. Uchiyama and H. Nakano, "Improved finite-difference beam propagation method based on the generalized Douglas scheme and its application to semivectorial analysis", J. Lightwave Technol., vol. 14, pp. 2401- 2406, 1996.

G. R. Hadley, "Low-truncation-error finite difference equations for photonic simulation I: Beam propagation", J. Lightwave Technol., vol. 16, pp. 134- 141, 1998.

C. Vassallo and J. M. van der Keur, "Comparison of a few transparent boundary conditions for finite-difference optical mode-solvers", J. Lightwave Technol., vol. 15, pp. 397- 402, 1997.

Opt. Lett. (1)

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