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Finite Difference Beam Propagation Algorithms

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Abstract

Beam Propagation Methods (BPM) provide powerful numerical tools to study the lightwave propagation in photonic devices. The standard version of the beam propagation method III and methods based on the Fresnel approximation 12-11 are not suitable for the design of these devices. Several propagation algorithms solving the Helmholtz equation by matrix diagonalizations have been developed /8,9/, which of course are very cumbersome as eigenvectors and eigenvalues have to be calculated, and on the Lanczos method /10/, where the radiation field is not adequately described because this technique is based on the dominant eigenvalues and eigenvectors. The wide angle beam propagation method II1/ is an advance in simulation techniques, though the accuracy cannot be checked easily. We present an explicit and an implicit algorithm, which do not require the paraxial (Fresnel) approximation, and the lateral discretization can be extremely dense. Moreover the truncation error of the expansions can easily be determined. For this reason an optimum propagation step can be assessed analytically. Both methods satisfy energy conservation in lossless waveguides and are unconditionally stable.

© 1994 Optical Society of America

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