Solitons in nonlinear lattices

By Y. Kartashov, Boris A. Malomed, L. Torner. 2010

768 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cbcd698fd71ac298a7df7fed825b4ff71a2e4287

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Citations in the corpus

Light propagation and localization in modulated photonic lattices and waveguides (2011, background): “In this Section, we overview nonlinear photonic lattices with spatial modulation of the refractive index, identifying novel features in light propagation and localization as compared to conventional straight lattices [31,291,63,235,294,144,124,125] and lattices with spatial modulation of the nonline”
Nonlinear waves in PT -symmetric systems (2016, background): “Equation (153) can be considered as a PT -symmetric deformation of conservative nonlinear lattice models studied intensively during the last decade [see Kartashov, Malomed, and Torner (2011) for a review].”
Commentary (invited update) to article"Spatiotemporal optical solitons", by B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005) (2016, background): “This direction is related to a still broader area of studies of solitons in media with effective potentials induced by spatial modulation of the nonlinearity [10].”
Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics (2014, background): “Soliton solutions in periodic media have been widely studied and we refer the reader to the recent comprehensive reviews for details [253,254,6].”
(INVITED) Vortex solitons: Old results and new perspectives (2019, background): “[168] Y.”