Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component

TL;DR

This paper demonstrates that two-dimensional vector solitons in media with attractive cubic nonlinearity can be stabilized against collapse by either a linear or nonlinear lattice acting on a single component, leveraging cross-phase modulation effects.

Contribution

It reveals that a lattice acting on one component suffices for stabilization of vector solitons, a novel insight into controlling collapse in multi-component nonlinear media.

Findings

Linear lattice stabilizes almost entire existence domain of vector solitons.

Nonlinear lattice stabilizes solitons when the affected component's norm is comparable or larger.

Cross-phase modulation enables stabilization even when only one component is influenced by the lattice.

Abstract

The subject of the work is the stabilization of two-dimensional (2D) two-component (vector) solitons, in media with the attractive cubic nonlinearity, against the collapse by a linear lattice (LL, which is induced by a periodic modulation of the refractive index in optics, or created as an optical lattice in BEC), or by a nonlinear lattice (NL, induced by a periodic modulation of the nonlinearity coefficient). We demonstrate that, due to the XPM (cross-phase-modulation) coupling between the components, the LL or NL acting on a single component is sufficient for the stabilization of vector solitons, that include a component for which the self-focusing medium is uniform. In the case of the LL, the vector solitons are stable almost in their entire existence domain, while the NL can only stabilize the solitons in which the component affected by the lattice carries the norm which is comparable to, or larger than the norm of the component in the uniform medium.