Rotary dynamics of solitons in radially periodic optical lattices

We investigate the dynamics of strongly localized solitons trapped in remote troughs of radially periodic lattices with Kerr-type self-focusing nonlinearity. The rotary motion of solitons is found to be more stable for larger nonlinear wavenumbers, lower rotating velocity, and shorter radius of the trapping troughs. When the lattice is shrunk or expanded upon propagation, the solitons can be trapped in the original trough and move outward or inward, with their rotating linear velocity inversely proportional to the radius of the trapping troughs.     

The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity

By virtue of the method of multiple-scale and the quasi-discreteness approach, we have discussed the nonlinear vibration equation of a 3D discrete monatomic lattice with its nearest-neighbours interaction. The 3D simple cubic lattices have the same localized modes as a 1D discrete monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop solitons in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/6$a_{0}$ in the Brillouin zone, as well as has 3D vortices in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/$a_{0}$ in the Brillouin zone.     

Multi-soliton energy transport in anharmonic lattices

We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons (see Phys. Rev. Lett. 83 (1999) 296), our analysis reveals a novel physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-component nonlinear models.     

Surface solitons in trilete lattices

Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrödinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter—actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.     

Gap solitons in an anharmonic diatomic lattice

Localized stationary modes with frequency in the forbidden region of the elastic vibrations of a diatomic anharmonic lattice are studied by the coupled-wave method. The mechanisms responsible for the brightening of the lattice in the cases of narrow and wide forbidden frequency bands are determined and an analytical expression is found for the stationary gap solitons. Fiz. Tverd. Tela (St. Petersburg) 39, 158–162 (January 1997)     

Rotary solitons in bessel optical lattices

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, in addition to 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.     

Random-phase solitons in nonlinear periodic lattices

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices.     

Coupled matter-wave solitons in optical lattices

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (V_eff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well V_eff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of V_eff(LOL) increases as k increases and that of V_eff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution they exhibit decay and revival.     

Surface solitons in chirped photonic lattices

We study surface modes at the edge of a semi-infinite chirped photonic lattice in the framework of an effective discrete nonlinear model. We demonstrate that the lattice chirp can change dramatically the conditions for the mode localization near the surface, and we find numerically the families of discrete surface solitons in this case. Such solitons do not require any minimum power to exist provided the chirp parameter exceeds some critical value. We also analyze how the chirp modifies the interaction of a soliton with the lattice edge.     

Multivortex solitons in triangular photonic lattices

We introduce a novel class of stable lattice solitons with a complex phase structure composed of many single-charge discrete vortices in a triangular photonic lattice. We demonstrate that such nonlinear self-trapped states are linked to the resonant Bloch modes, which bear a honeycomb pattern of phase dislocations.     

Asymmetric dark solitons in nonlinear lattices

New types of stable discrete solitons are discovered. They represent the first example of asymmetric dark solitons and shock waves with a nonzero background. Both types of solutions exhibit a strong intrinsic phase dynamics. Their domains of existence and criteria of stability are identified. Numerical experiments support the analytical findings.     

Reduced-symmetry two-dimensional solitons in photonic lattices

We demonstrate theoretically and experimentally a novel type of localized beam supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.     

Derivation of transport equations for anharmonic lattices

Non-equilibrium properties of dielectric crystals are described using a Green function approach which represents transport phenomena by correlation functions of the equilibrium system. The equation which is equivalent to a Boltzmann equation for phonons is the integral equation for the vertex part corrections. Including all irreducible diagrams quadratic in the cubic and linear in the quartic anharmonicities the vertex part equation is reduced to a form which could be used as a starting point for numerical studies of microscopic models. The vertex part is also used to express the space and time variation of the phonon density and the frequency change of the phonons in response to an external displacement field. We also relate the integral equation for the vertex part to a form of the transport equation which is used in Landau's theory of quantum liquids.     

Observation of multivortex solitons in photonic lattices

We report on the first observation of topologically stable spatially localized multivortex solitons generated in optically induced hexagonal photonic lattices. We demonstrate that topological stabilization of such nonlinear localized states can be achieved through self-trapping of truncated two-dimensional Bloch waves and confirm our experimental results by numerical simulations of the beam propagation in weakly deformed lattice potentials in anisotropic photorefractive media.     

Interface thermal resistance between dissimilar anharmonic lattices

We study interface thermal resistance (ITR) in a system consisting of two dissimilar anharmonic lattices exemplified by the Fermi-Pasta-Ulam and Frenkel-Kontorova models. It is found that the ITR is asymmetric; namely, it depends on how the temperature gradient is applied. The dependence of the ITR on the coupling constant, temperature, temperature difference, and system size is studied. Possible applications in nanoscale heat management and control are discussed.     

Almost compact breathers in anharmonic lattices near the continuum limit

Certain strictly anharmonic one-dimensional lattices support discrete breathers over a macroscopic localized domain that in the continuum limit becomes exactly compact. The discrete breather tails decay at a double-exponential rate, so such systems can store energy locally, especially since discrete breathers appear to be stable for amplitudes below a sharp stability threshold. The effective width of other solutions broadens over time, but, under appropriate conditions, only after a positive waiting time. The continuum limit of a planar hexagonal lattice also supports a compact breather.     

Long-range effects on superdiffusive algebraic solitons in anharmonic chains

Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices were recently generalized to the case of dispersive long-range interactions (LRI) of the Kac-Baker form. The variance of the soliton position shows a stronger than linear time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with nearest-neighbour interactions (NNI). Since the superdiffusion seems to be generic for nontopological solitons, we want to illuminate the role of the soliton shape on the superdiffusive mechanism. Therefore, we concentrate on an FPU-like lattice with a certain class of power-law long-range interactions where the solitons have algebraic tails instead of the exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI).Despite of structurally similar Langevin equations which hold for the soliton position and width of the two soliton types, the algebraic solitons reach the superdiffusive long-time limit with a characteristic t^3/2 time-dependence much faster than exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor of π smaller for algebraic solitons. Our results appear to be generic for nonlinear excitaitons in FPU-chains, because the same superdiffusive time-dependence was also observed in simulations with discrete breathers.     

Spatiotemporal surface solitons in two-dimensional photonic lattices

We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.