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

TL;DR

This paper extends perturbation theory to analyze fast two-beam collisions with weak cubic loss in higher-dimensional linear optical media, revealing shape changes and universal amplitude shift behaviors confirmed by numerical simulations.

Contribution

It generalizes the analysis of beam collisions with cubic loss from one to higher spatial dimensions, providing new theoretical insights and validation through simulations.

Findings

Beam shapes change transversely during collision.

Amplitude shift has a universal longitudinal component.

Theoretical predictions agree well with numerical simulations.

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.