Fast two-beam collisions in a linear optical medium with weak cubic loss in spatial dimension higher than 1

Abstract

We study the dynamics of fast two-beam collisions in linear optical media with weak cubic loss in spatial dimension higher than 1. For this purpose, we extend the perturbation theory that was developed for analyzing two-pulse collisions in spatial dimension 1 to spatial dimension 2. We use the extended two-dimensional version of the perturbation theory to show that the collision leads to a change in the beam shapes in the direction transverse to the relative velocity vector. Furthermore, we show that in the important case of a separable initial condition for both beams, the longitudinal part in the expression for the amplitude shift is universal, while the transverse part is not universal. Additionally, we demonstrate that the same behavior holds for collisions between pulsed optical beams in spatial dimension 3. We check these predictions of the perturbation theory along with other predictions concerning the effects on the collision of partial beam overlap and anisotropy in the initial condition by extensive numerical simulations with the weakly perturbed linear propagation model in spatial dimensions 2 and 3. The agreement between the perturbation theory and the simulations is very good. Therefore, our study significantly extends and generalizes the results of previous works, which were limited to spatial dimension 1.

arXiv comment66 pages, 14 figures

References in corpus (9)

• Light propagation and localization in modulated photonic lattices and waveguides
• Classification of the line-soliton solutions of KPII
• Diverging probability density functions for flat-top solitary waves
• Radiation dynamics in fast soliton collisions in the presence of cubic loss
• Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems
• Enhancement of transmission quality in soliton-based optical waveguide systems by frequency dependent linear gain-loss and the Raman self-frequency shift
• Collision-induced amplitude dynamics of fast 2D solitons in saturable nonlinear media with weak nonlinear loss
• Universality of the amplitude shift in fast two-pulse collisions in weakly perturbed linear physical systems
• Collision-induced amplitude dynamics of pulses in linear waveguides with the generic nonlinear loss

Cited by in corpus (2)

• Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss
• Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2