Solitons in nonlinear lattices

TL;DR

This comprehensive survey reviews theoretical and experimental results on solitons supported by nonlinear lattices in optics and BEC, highlighting their properties, stability challenges, and novel existence thresholds across dimensions.

Contribution

It provides the first detailed overview of solitons in purely nonlinear lattices, emphasizing their unique creation mechanisms and stability properties in various physical systems.

Findings

Existence of a finite threshold norm for 1D solitons in NLs

Distinct creation mechanism of solitons in NLs versus linear lattices

Stability challenges for multidimensional solitons in nonlinear lattices

Abstract

This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions can be drawn. In particular, a novel fundamental property of 1D solitons, which does not occur in the absence of NLs, is a finite threshold value of the soliton norm, necessary for their existence. In multidimensional settings, the stability of solitons supported by the spatial modulation of the nonlinearity is a truly challenging problem, for the theoretical and experimental studies alike. In both the 1D and 2D cases, the mechanism which creates solitons in NLs is principally different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.