Simulation of Two-Dimensional Nonlinear Envelope Pulse Dynamics by a Two-Step Spatiotemporal Angular Spectrum Method
Journal of the Optical Society of America B
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.
Copyright © 1988, Optical Society of America
Optical Society of America
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.