Semidiscrete Vortex Solitons

Abstract

A possibility of creation of stable optical solitons combining one continuous and one discrete coordinates, with embedded vorticity, in an array of planar waveguides with intrinsic cubic–quintic (CQ) nonlinearity is demonstrated. The same system may be realized in terms of the spatiotemporal light propagation in an array of tunnel‐coupled optical fibers with the CQ nonlinearity. In contrast with zero‐vorticity states, semidiscrete vortex solitons do not exist without the quintic term in the nonlinearity. Two types of the solitons, viz., intersite‐centered (IC) and onsite‐centered (OC) ones, with even and odd numbers N of actually excited sites in the discrete direction, are identified. The modes carrying the embedded vorticity S=1 and 2 are considered. In accordance with their symmetry, the vortex solitons of the OC type exhibit an intrinsic core, whereas the IC solitons with small N may have a coreless structure. Facilitating their creation in the experiment, the modes reported in the present work may be much more compact states than their counterparts considered in other systems, and they feature strong anisotropy. They can be set in motion in the discrete direction, provided that the coupling constant exceeds a certain minimum value. Collisions between moving vortex solitons are also considered.

Vortex Quantum Droplets under Competing Nonlinearities

“…It is noteworthy to mention that the notion of semi-discrete vortex droplets has recently garnered attention in optical systems characterized by competitive nonlinearity. [109,110] (b) (c) Likewise, 1D cigar-shaped potential traps can be used to build an effective 2D lattice, with weak tunnel coupling between its sites. Thus, atoms may freely move along each trap and hop through the tunneling effect between neighboring traps.…”

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings

“…The objective of this article is to produce a relatively brief summary of results for multidimensional (chiefly, two-dimensional) discrete and semi-discrete solitons, which were considered in less detail in previous reviews and, on the other hand, draw growing interest in the context of the current work with 2D and 3D solitons in diverse physical contexts [27,28]. Furthermore, the presence of the two or three coordinates makes it also possible to define semi-discrete states as ones that are discrete in one direction and continuous in the perpendicular one [81][82][83][84].…”