Fast Hankel Transform Algorithms for Optical Beam Propagation
Army Research Laboratory Adelphi United States
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Essential for the development of low-f-number eye and sensor protectionsystems is an accurate model for the propagation of a widely diverginglaser beam through a nonlinear medium. This problem may be solved numericallywith the well-known split-step procedure, in which the effectsof propagation are computed separately from those arising from nonlinearabsorption and refraction. For a cylindrically symmetric beam, the propagationphase of each step in the process is most conveniently calculatedin the Hankel transform domain each step thus requires numerical computationof a discrete Hankel transform followed by an inverse transform.Accordingly, we seek an algorithm for efficient numerical computation ofthe Hankel transform that preserves the transforms invertibility. This reportsummarizes the relevant properties of the Hankel transform and ofthe closely related Fourier transform, it reviews existing fast Hankel transformalgorithms proposing several modest improvements in one, and itevaluates those methods in terms of their suitability for the beam propagationapplication of interest.