Multipoles and vortex multiplets in multidimensional media with inhomogeneous defocusing nonlinearity

TL;DR

This paper predicts and analyzes stable, complex multidimensional self-trapped modes in media with inhomogeneous defocusing nonlinearity, including various multipole and vortex configurations, using numerical and analytical methods.

Contribution

It introduces a new class of stable, complex multidimensional modes in media with inhomogeneous defocusing nonlinearity, which were previously thought to be unstable or nonexistent.

Findings

Stable 2D dipoles and quadrupoles identified

Stable 3D octupoles and vortex pairs found

Modes are robust and analytically approximated

Abstract

We predict a variety of composite quiescent and spinning two- and three-dimensional (2D and 3D) self-trapped modes in media with a repulsive nonlinearity whose local strength grows from center to periphery. These are 2D dipoles and quadrupoles, and 3D octupoles, as well as vortex-antivortex pairs and quadruplets. Unlike other multidimensional models, where such complex bound states either do not exist or are subject to strong instabilities, these modes are remarkably robust in the present setting. The results are obtained by means of numerical methods and analytically, using the Thomas-Fermi approximation. The predicted states may be realized in optical and matter-wave media with controllable cubic nonlinearities.