Numerical Modeling of Cylindrically Symmetric Nonlinear Self-Focusing Using an Adaptive Fast Hankel Split-Step Method

Author(s)

Partha P. Banerjee, University of DaytonFollow
George Nehmetallah, The Catholic University of America
Monish Ranjan Chatterjee, University of DaytonFollow

Document Type

Article

Publication Date

5-2005

Publication Source

Optics Communications

Abstract

We present a novel technique to numerically solve beam propagation problems based on the paraxial and nonparaxial scalar nonlinear Schrödinger (NLS) equation in two transverse dimensions with cylindrical symmetry. Using fast algorithms for Hankel transforms along with adaptive longitudinal stepping and transverse grid management in a symmetrized split-step technique, it is possible to accurately track a beam much closer to its physical collapse due to self-focusing for the paraxial NLS than other existing methods, notably the fast Fourier transform-based standard split-step technique. For the nonparaxial NLS, the adaptive fast Hankel transform-based split-step method with an adaptive nonparaxiality parameter yields results comparable to the more rigorous vector nonlinear wave equation.

Inclusive pages

293–300

ISBN/ISSN

0030-4018

Comments

Permission documentation is on file.

Copyright

Copyright © 2004, Elsevier

Publisher

Elsevier

Volume

249

Peer Reviewed

yes

Issue

1-3

eCommons Citation

Banerjee, Partha P.; Nehmetallah, George; and Chatterjee, Monish Ranjan, "Numerical Modeling of Cylindrically Symmetric Nonlinear Self-Focusing Using an Adaptive Fast Hankel Split-Step Method" (2005). Electrical and Computer Engineering Faculty Publications. 258.
https://ecommons.udayton.edu/ece_fac_pub/258