Fast Hankel Transform Algorithms for Optical Beam Propagation

Report No. ARL-TR-2492
Authors: Timothy M. Pritchett
Date/Pages: December 2001; 29 pages
Abstract: Essential for the development of low-f-number eye and sensor protection systems is an accurate model for the propagation of a widely diverging laser beam through a nonlinear medium. This problem may be solved numerically with the well-known 'split-step' procedure, in which the effects of propagation are computed separately from those arising from nonlinear absorption and refraction. For a cylindrically symmetric beam, the propagation phase of each step in the process is most conveniently calculated in the Hankel transform domain; each step thus requires numerical computation of a discrete Hankel transform followed by an inverse transform. Accordingly, we seek an algorithm for efficient numerical computation of the Hankel transform that preserves the transform's invertibility. This report summarizes the relevant properties of the Hankel transform and of the closely related Fourier transform, it reviews existing fast Hankel transform algorithms (proposing several modest improvements in one), and it evaluates those methods in terms of their suitability for the beam propagation application of interest.
Distribution: Approved for public release
  Download Report ( 0.348 MBytes )
If you are visually impaired or need a physical copy of this report, please visit and contact DTIC.

Last Update / Reviewed: December 1, 2001