Two-dimensional Airy waves and three-wave solitons in quadratic media

TL;DR

This paper explores the dynamics and interactions of two-dimensional Airy waves and three-component solitons in quadratic media, revealing stable solutions, vortex imprinting, and diverse collision behaviors in optical and Bose-Einstein systems.

Contribution

It introduces exact stable solutions for 2D Airy waves in quadratic media and systematically studies their interactions and collision outcomes.

Findings

Stable 2D Airy wave solutions are found in quadratic media.

Airy wave interactions can produce soliton pairs or debris depending on vorticity.

Collision behaviors include merger, elastic passage, and bounce-back depending on velocities.

Abstract

We address the dynamics of two-dimensional (2D) truncated Airy waves and three-component solitons in the system of two fundamental-frequency and second-harmonic fields, coupled by quadratic (chi^(2)) terms. The system models second-harmonic-generating optical media and atomic-molecular mixtures in Bose-Einstein condensates. In addition to stable solitons, the system maintains truncated-Airy-waves states in either one of the fundamental-frequency components, represented by exact solutions, which are stable, unlike the Airy waves in the degenerate (two-component) chi^(2) system. It is also possible to imprint vorticity onto the 2D Airy modes. By means of systematic simulations, we examine interactions between truncated Airy waves originally carried by different fundamental-frequency components which are bending in opposite directions, through the second-harmonic field. The interaction leads to fusion of the input into a pair of narrow solitons. This is opposed to what happens in the 1D system, where the interacting Airy waves split into a large number of solitons. The interaction of truncated Airy waves carrying identical imprinted vorticities creates an additional pair of solitons, while opposite vorticities create a set of small-amplitude "debris" in the output. Slowly moving solitons colliding with a heavy truncated Airy wave bounce back, faster ones are absorbed by it, and collisions are quasi-elastic for fast solitons. Soliton-soliton collisions lead to merger into a single mode, or elastic passage, for lower and higher velocities, respectively.