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.Peer ReviewedPostprint (published version

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We report the first experimental observation of three-dimensional light bullets, excited by femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity and a periodic, transversally modulated refractive index. Stringent evidence of the excitation of light bullets is based on time-gated images and spectra which perfectly match our numerical simulations. Furthermore, we reveal a novel evolution mechanism forcing the light bullets to follow varying dispersion or diffraction conditions, until they leave their existence range and decay.

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as (1 ) r   support one-and twodimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., D   . Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough.OCIS codes: 190.5940, 190.6135 Optical solitons may form in many physical settings. By and large, in uniform conservative media, focusing and defocusing nonlinearities give rise to bright and dark solitons, respectively. The situation may change in the presence of transverse modulations of the refractive index (linear lattices), which affect the strength and sign of the effective diffraction for the propagating waves, and may result in the formation of gap solitons even in defocusing media [1,2]. However, guiding bright solitons by the defocusing nonlinearity without the help of a linear potential is commonly considered impossible. At the same time, recent advances in the technology of fabrication of nonlinear materials indicate that not only the refractive index, but also nonlinearity may be profiled, as needed, in the transverse directions. Solitons in such nonlinearity landscapes (nonlinear lattices) may have unusual properties, because the corresponding effective inhomogeneity of the material depends on the intensity of the nonlinear excitation [2]. Many effects were predicted in nonlinear [3][4][5][6][7] and mixed linear-nonlinear [8][9][10][11][12][13][14] lattices, in both one-(1D) and two-dimensional (2D) [15][16][17] settings. However, in contrast to linear lattices, localized and periodic landscapes of defocusing nonlinearities do not support bright solitons (instead, "anti-dark" modes can be built on top of a flat background [18,19]). While a dip in a uniform defocusing background may result in considerable concentration of light, a linear trapping potential is still necessary for the complete localization [20].In this Letter we show that, in contrast to the common belief, a spatially profiled defocusing nonlinearity whose strength grows toward the periphery does support bright solitons in conservative media. They exist because the growth of the nonlinearity coefficient makes the governing equation non-linearizable for decaying tails, in contrast to media with homogeneous or periodic nonlinearities, where the presence of the decaying tails places soliton into the semi-infinite spectral gap of the linearized system, in which defocusing nonlinearities cannot support localization. We consider an algebraic profile of the nonlinearity coefficient,, that supports bright solitons, multipoles, and vortices in both 1D and 2D geometries. Solitons exist when the nonlinearity growth rate  exceeds certain critical value, and they may be stable. Notice that examples of solitons w...

We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media.We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, besides the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.PACS numbers: 42.65.Tg, 42.65.Jx, 42.65

We present the experimental observation of scalar multi-pole solitons in highly nonlocal nonlinear media, including dipole-, tri-pole, quadru-pole, and necklace-type solitons, organized as arrays of out-of-phase bright spots. These complex solitons are meta-stable, but with a large parameters range where the instability is weak, enabling their experimental observation.

lar. Energy bands of the microcavity polariton graphene are readily controlled by magnetic field and influenced by the spin-orbit coupling effects, a combination leading to formation of linear unidirectional edge states in polariton topological insulators as predicted very recently. In this work we depart from the linear limit of non-interacting polaritons and predict instabilities of the nonlinear topological edge states resulting in formation of the localized topological quasisolitons, which are exceptionally robust and immune to backscattering wavepackets propagating along the graphene lattice edge. Our results provide a background for experimental studies of nonlinear polariton topological insulators and can influence other subareas of photonics and condensed matter physics, where nonlinearities and spin-orbit effects are often important and utilized for applications.

We present a progress overview focused on the recent theoretical and experimental advances in the area of soliton manipulation in optical lattices. Optical lattices offer the possibility to engineer and to control the diffraction of light beams in media with periodicallymodulated optical properties, to manage the corresponding reflection and transmission bands, and to form specially designed defects. Consequently, they afford the existence of a rich variety of new families of nonlinear stationary waves and solitons, lead to new rich dynamical phenomena, and offer novel conceptual opportunities for all-optical shaping, switching and routing of optical signals encoded in soliton formats. In this overview, we consider reconfigurable optically-induced lattices as well as waveguide arrays made in suitable nonlinear materials. We address both, one-dimensional and multi-dimensional geometries.We specially target the new possibilities made possible by optical lattices induced by a variety of existing non-diffracting light patterns, we address nonlinear lattices and soliton arrays, and we briefly explore the unique features exhibited by light propagation in defect modes and in random lattices, an area of current topical interest and of potential crossdisciplinary impact.