Vortical light bullets in second-harmonic-generating media supported by a trapping potential

TL;DR

This paper demonstrates the existence and stability of three-dimensional vortical light bullets in a quadratic nonlinear medium with a trapping potential, supported by variational approximation and collision studies.

Contribution

It introduces a 3D model with a harmonic-oscillator potential supporting stable vortical solitons, a significant advancement over free-space instability.

Findings

Vortical light bullets are stable within a broad parameter range.

Shape oscillations occur above the stability boundary.

Vortex collisions are inelastic at low velocities, breaking into multiple vortices.

Abstract

We introduce a three-dimensional (3D) model of optical media with the quadratic ($\chi ^{(2)}$) nonlinearity and an effective 2D isotropic harmonic-oscillator (HO) potential. While it is well known that 3D \chi^2 solitons with embedded vorticity ("vortical light bullets") are unstable in the free space, we demonstrate that they have a broad stability region in the present model, being supported by the HO potential against the splitting instability. The shape of the vortical solitons may be accurately predicted by the variational approximation (VA). They exist above a threshold value of the total energy (norm) and below another critical value, which determines a stability boundary. The existence threshold vanishes is a part of the parameter space, depending on the mismatch parameter, which is explained by means of the comparison with the 2D counterpart of the system. Above the stability boundary, the vortex features shape oscillations, periodically breaking its axisymmetric form and restoring it. Collisions between vortices moving in the longitudinal direction are studied too. The collision is strongly inelastic at relatively small values of the velocities, breaking the two colliding vortices into three, with the same vorticity. The results suggest a possibility of the creation of stable 3D optical solitons with the intrinsic vorticity.