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Boundary conditions for the finite difference beam propagation method based on plane wave solutions of the Fresnel equation

  • Each particular implementation of the beam propagation method (BPM) requires a special procedure allowing for radiation to leave the computational window. We propose a new approach to constructing the finite difference schemes of the BPM at the boundary of the computational window. These schemes are independent of the computed fields and allow for a similar treatment of both interior and boundary points. The new approach can be further improved by correcting the field values at the boundary points according to Hadley's method. The algorithm is easy to implement for both two- and three-dimensional structures. The new method considerably reduces computation times because the propagation matrices remain constant in longitudinally invariant sections, thus avoiding repeated LU-decompositions. The basic idea-establishing the finite difference scheme such that locally exact, approximate, or plausible solutions are recovered-may be of interest for other efforts to solve partial differential equations by the finite difference method.

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Metadaten
Author:M. Lohmeyer, Mikhail Shamonin (Chamonine)ORCiDGND, P. Hertel
DOI:https://doi.org/10.1109/3.552269
ISSN:0018-9197
Parent Title (English):IEEE Journal of Quantum Electronics
Document Type:Article
Language:English
Year of first Publication:1997
Release Date:2023/11/11
Tag:Boundary conditions; Computational modeling; Finite difference methods; Matrix decomposition; Maxwell equations; Optical propagation; Partial differential equations; Refractive index; Shape; Sparse matrices
Volume:33
Issue:2
First Page:279
Last Page:286
Institutes:Fakultät Elektro- und Informationstechnik
Fakultät Elektro- und Informationstechnik / Labor Intelligente Materialien und Strukturen
Begutachtungsstatus:peer-reviewed
Publication:Externe Publikationen
research focus:Produktion und Systeme
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG