Gaussian decomposition of beams and other functions

TR Number
Date
1989-06-15
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Physics
Abstract

The Gabor expansion of a function f_(x) decomposes it into a double sum over integers m and n of a product of basis functions g(x_m X) and Fourier_series exponentials exp(2πi n/X) for given spacing X. The choice of basis function determines the coefficients a m n of the expansion. If f_(x) is band limited, the double sum can for all practical purposes be replaced by a single sum over Gaussian basis functions. This is extremely useful for expansion of multidimensional functions such as beams in phase space. Conditions of validity are given, and several examples illustrate the technique.

Description
Keywords
Beams, Gaussian, Gabor expansion
Citation
Dewolf, D. A. (1989). Gaussian decomposition of beams and other functions. Journal of Applied Physics, 65(12), 5166-5169. doi: 10.1063/1.343144