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Proceedings Paper

The finite-difference matrix for beam propagation: eigenvalues and eigenvectors
Author(s): Alan H. Paxton
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Paper Abstract

The partial differential equation for the three dimensional propagation of a light beam may be solved numerically by applying finite-difference techniques. We consider the matrix equation for the finite-difference, alternating direction implicit (ADI), numerical solution of the paraxial wave equation for the free-space propagation of light beams. The matrix is tridiagonal. It is also a Toeplitz matrix; Each diagonal descending from left to right is constant. Eigenvalues and eigenvectors are known for such matrices. The equation can be solved by making use of the orthogonality property of the eigenvectors.

Paper Details

Date Published: 22 April 2016
PDF: 4 pages
Proc. SPIE 9727, Laser Resonators, Microresonators, and Beam Control XVIII, 97271O (22 April 2016); doi: 10.1117/12.2214399
Show Author Affiliations
Alan H. Paxton, Air Force Research Lab. (United States)

Published in SPIE Proceedings Vol. 9727:
Laser Resonators, Microresonators, and Beam Control XVIII
Alexis V. Kudryashov; Alan H. Paxton; Vladimir S. Ilchenko, Editor(s)

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