Spatiotemporal accessible solitons in fractional dimensions

TL;DR

This paper presents exact solutions for spatiotemporal solitons in fractional-dimensional nonlocal media, revealing complex vortex and necklace structures, with potential applications in quantum well excitons.

Contribution

It introduces exact analytical solutions for accessible solitons in fractional dimensions, including vortex and necklace configurations, verified by simulations.

Findings

Exact soliton solutions in fractional dimensions derived

Solutions include vortex and necklace-shaped modes

Model applicable to excitons in quantum wells

Abstract

We report solutions for solitons of the "accessible" type in globally nonlocal nonlinear media of fractional dimension (FD), viz., for self-trapped modes in the space of effective dimension $2<D\le3$ with harmonic-oscillator potential whose strength is proportional to the total power of the wave field. The solutions are categorized by a combination of radial, orbital and azimuthal quantum numbers $(n,l,m)$. They feature coaxial sets of vortical and necklace-shaped rings of different orders, and can be exactly written in terms of special functions that include Gegenbauer polynomials, associated Laguerre polynomials, and associated Legendre functions. The validity of these solutions is verified by direct simulation. The model can be realized in various physical settings emulated by FD spaces; in particular, it applies to excitons trapped in quantum wells.