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Proceedings Paper

Helmholtz beam propagation by the method of Lanczos reduction
Author(s): Joseph A. Fleck Jr.
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Paper Abstract

The solution of the Helmholtz wave equation requires the application of an exponentiated square root operator to an initial field. This operation is greatly facilitated by the introduction of a representation in which the aforementioned operator is diagonal. The Lanczos method allows this diagonalization to be performed in a low dimensional space, e.g., of the order of 4-6, if one is interested in advancing the field over a limited propagation step of length Az. Although some boundary conditions may be ill-posed for the unapproximated Helmholtz equation, in the sense that certain plane wave components cannot propagate in the forward direction, the Lanczos method damps all of these components exponentially, thus guaranteeing the correctness of the solution.

Paper Details

Date Published: 1 December 1991
PDF: 12 pages
Proc. SPIE 1583, Integrated Optical Circuits, (1 December 1991); doi: 10.1117/12.50893
Show Author Affiliations
Joseph A. Fleck Jr., Lawrence Livermore National Lab. (United States)

Published in SPIE Proceedings Vol. 1583:
Integrated Optical Circuits
Ka Kha Wong, Editor(s)

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