Accession Number : ADP008192

Title :   Accurate Solution of the Helmholz Equation by Lanczos Orthogonalization for Media with Loss or Gain,

Corporate Author : LAWRENCE LIVERMORE NATIONAL LAB CA

Personal Author(s) : Ratowsky, R. P. ; Fleck, J. A., Jr ; Feit, M. D.

Report Date : APR 1992

Pagination or Media Count : 2

Abstract : The Helmholtz equation plays a central role in the description of propagation phenomena in optics and acoustics. The paraxial approximation to the Helmholtz equation, also known as the paraxial wave equation, has long been the instrument of choice for performing calculations because it is amenable to solution by accurate marching techniques. The generation of accurate solutions to the unapproximated Helmholtz equation by marching, on the other hand, requires the evaluation of a square root operator applied to some initial field. By using an orthogonalization procedure due to Lanczos one can generate a low-dimensional representation, valid over a sufficiently short propagation step, which accurately diagonalizes the square root operator. A shortcoming of this Lanczos propagation scheme is that it is restricted to Hermitian operators, which prohibits its use with imaginary refractive indices, representing gain or loss. This restriction excludes a wide class of interesting propagation applications. Even when loss is not explicitly included in the problem, it is customary to include loss in a border region along the grid boundary to prevent power from reflecting from the boundaries back into the interior of the computational grid. We will describe a generalization of the previous Lanczos Helmholtz solver that allows general complex refractive index distributions to be considered.

Descriptors :   *LIGHT TRANSMISSION, *REFRACTION, ACOUSTICS, BOUNDARIES, EQUATIONS, GAIN, GRIDS, OPTICS, POWER, REFRACTIVE INDEX, SELECTION, SQUARE ROOTS, WAVE EQUATIONS, FOURIER ANALYSIS.

Subject Categories : Optics

Distribution Statement : APPROVED FOR PUBLIC RELEASE