Simulation of Two-Dimensional Nonlinear Envelope Pulse Dynamics by a Two-Step Spatiotemporal Angular Spectrum Method

Author(s)

H. K. Sim, University of Iowa
Adrianus Korpel, University of Iowa
Karl E. Lonngren, University of Iowa
Partha P. Banerjee, University of DaytonFollow

Document Type

Article

Publication Date

9-1988

Publication Source

Journal of the Optical Society of America B

Abstract

We present an extension of our previous nonlinear beam-simulation method to the propagation and interaction of pulse envelopes. The extra time dimension is applied in the context of a dispersive nonlinear medium that is described by a Klein–Gordon equation with an added cubically nonlinear, self-focusing term. Pulse propagation in this medium is modeled as the evolution of a spatiotemporal spectrum—i.e., the frequency-dependent angular spectrum of the pulse envelope—traversing a sequence of self-induced, thin, weak phase filters. Preliminary simulation experiments show agreement with known behavior in the absence of nonlinearity, confirm the existence of an (apparently unstable) stationary solution, and demonstrate mutual pulse attraction with subsequent destruction, initial survival following oblique collision, and mutual repulsion of out-of-phase pulses.

Inclusive pages

1900-1909

ISBN/ISSN

0030-3941

Comments

Permission documentation is on file.

Copyright

Copyright © 1988, Optical Society of America

Publisher

Optical Society of America

Volume

5

Peer Reviewed

yes

Issue

9

eCommons Citation

Sim, H. K.; Korpel, Adrianus; Lonngren, Karl E.; and Banerjee, Partha P., "Simulation of Two-Dimensional Nonlinear Envelope Pulse Dynamics by a Two-Step Spatiotemporal Angular Spectrum Method" (1988). Electrical and Computer Engineering Faculty Publications. 199.
https://ecommons.udayton.edu/ece_fac_pub/199