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Fast two-beam collisions in a linear optical medium with weak cubic loss in spatial dimension higher than 1. (English) Zbl 07507197

Summary: We study the dynamics of fast two-beam collisions in linear bulk optical media with weak cubic loss in spatial dimension higher than 1. The cubic loss arises due to two-photon absorption. We first generalize the perturbation theory that was developed for analyzing two-pulse collisions in spatial dimension 1 to spatial dimension 2. We then use the generalized two-dimensional 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. The same behavior holds for collisions between pulsed optical beams in spatial dimension 3. We check these analytic predictions along with other predictions concerning the effects of anisotropy in the initial condition by extensive numerical simulations with the weakly perturbed linear propagation model. The agreement between the perturbation theory and the simulations is very good. Thus, our study extends and generalizes the results of previous works, which were limited to spatial dimension 1. The results are very useful for multiwavelength optical communication systems.

MSC:

78A60 Lasers, masers, optical bistability, nonlinear optics
35Q55 NLS equations (nonlinear Schrödinger equations)
35B20 Perturbations in context of PDEs
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