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

Autor(en): Lohmeyer, M
Shamonin, M
Hertel, P
Stichwörter: beam propagation method; Engineering; Engineering, Electrical & Electronic; finite differences; GUIDES; integrated optics; LIGHT-PROPAGATION; Optics; Physics; Physics, Applied; Quantum Science & Technology; transparent boundary conditions
Erscheinungsdatum: 1997
Herausgeber: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Journal: IEEE JOURNAL OF QUANTUM ELECTRONICS
Volumen: 33
Ausgabe: 2
Startseite: 279
Seitenende: 285
Zusammenfassung: 
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.
ISSN: 00189197
DOI: 10.1109/3.552269

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