Solitons in nonlinear lattices

TLDR

The review focuses on solitons in nonlinear lattices arising in nonlinear optics, photonic crystals, plasmonics, and Bose‑Einstein condensates, highlighting their existence, stability, mobility, and the particular challenges of multidimensional stability compared to linear lattices. The article surveys theoretical and experimental studies of solitons and complex nonlinear wave patterns in nonlinear lattices, aiming to assess their properties and prospects for experimental realization. The authors analyze solitons in one, two, and three dimensions, drawing on a comprehensive collection of theoretical results and experimental settings that illustrate how nonlinear lattices directly generate solitons rather than through Bloch‑mode bifurcations. Most reviewed results are theoretical, yet the field yields general conclusions, including a novel finite‑norm threshold for one‑dimensional solitons that does not exist without nonlinear lattices.

Abstract

This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by 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 also surveyed, 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. The solitons are considered in one, two, and three dimensions. 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 one-dimensional 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 theoretical and experimental studies alike. In both the one-dimensional and two-dimensional cases, the mechanism that creates solitons in NLs in principle is different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.