Spatial soliton switching in quasi-continuous optical arrays

Asymmetric soliton mobility in competing linear-nonlinear parity-time-symmetric lattices

We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such a range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest to form moving soliton pairs.

Giant Goos-Hänchen shifts and radiation-induced trapping of Helmholtz solitons at nonlinear interfaces

Giant Goos-Hänchen shifts and radiation-induced trapping are studied at the planar boundary separating two focusing Kerr media within the framework of the Helmholtz theory. The analysis, valid for all angles of incidence, reveals that interfaces exhibiting linear external refraction can also accommodate both phenomena. Numerical evidence of these effects is provided, based on analytical predictions derived from a generalized Snell's law.

Controlling soliton refraction in optical lattices

We show in the framework of the 1D nonlinear Schrödinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.

Walking-vector-soliton caging and releasing

We address the formation and propagation of vector solitons in optical lattices in the presence of anisotropy-induced walk-off between ordinary and extraordinary polarized field components. Stable vector solitons trapped by the lattice form above a threshold power, while decreasing the lattice depth below a critical value results in the abrupt release of the caged solitons that then move across the lattice and may get trapped in a desired lattice channel.

Spatial soliton tunneling, compression and splitting

We numerically investigate the tunneling of spatial solitons through a focusing Kerr nonlinear optical lattice with longitudinal potential barrier, and find that the position of input beams apparently affects the tunneling behaviors of spatial solitons, which exhibit compression or splitting when passing through the barrier, and that the transverse modulation frequency of lattice and the intensity of input beams strongly affect the ability of tunneling. Based on these properties, we present a scheme for compressing soliton and splitting soliton into stable twin beams. The obtained results may have promising applications in all-optical devices based on spatial solitons.

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows one to predict the stability and instability strength.

Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity

We put forward new properties of lattice solitons in materials and geometries where both the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear refractive index modulations results in new soliton properties, including modifications of the soliton stability and transverse mobility, as well as shape transformations that may be controlled, e.g., by varying the light intensity.

Drift instability and tunneling of lattice solitons

We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be "mathematically unstable" but "physically stable." We also derive an analytic upper bound for the critical velocity for tunneling, which is valid even when the standard Peierls-Nabarro potential approach fails.

Soliton dynamics and interactions in dynamically photoinduced lattices

The dynamics of a spatial soliton pulse and interactions under the presence of a linear periodic wave (PW), which dynamically induces a photonic lattice, is investigated. It is shown that appropriate selections of the characteristic parameters of the PW result in different soliton propagation and interaction scenarios, suggesting a reconfigurable soliton control mechanism. The quasiparticle perturbation method is utilized for providing a dynamical system, governing the soliton parameters evolution, for single- and two-soliton propagation under generic conditions for the PW. Results of the perturbation method are shown in good agreement with direct numerical simulations.

Soliton control in fading optical lattices

We predict new phenomena, such as soliton steering and soliton fission, in optical lattices that fade away exponentially along the propagation direction. Such lattices, featuring tunable decay rates, arise in photorefractive crystals in the wavelength range 360-400 nm. We show that the predicted phenomena offer different opportunities for soliton control.

Topological dragging of solitons

We put forward properties of solitons supported by optical lattices featuring topological dislocations and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.

Matter-wave solitons in nonlinear optical lattices

We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N = N(min), necessary for the existence of solitons. The VA predicts N(min) very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N = N(min) are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A, the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

Soliton mobility in nonlocal optical lattices

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discover that the nonlocality of the nonlinear response can profoundly affect the soliton mobility, hence all the related phenomena. Such behavior manifests itself in significant reductions of the Peierls-Nabarro potential with an increase in the degree of nonlocality, a result that opens the rare possibility in nature of almost radiationless propagation of highly localized solitons across the lattice.

Anderson localization of solitons in optical lattices with random frequency modulation

We report on the phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with the growth of the frequency fluctuation level. The localization process is strongly sensitive to the lattice depth since in shallow lattices walking solitons experience random refraction and/or multiple scattering in contrast to relatively deep lattices, where solitons are typically immobilized in the vicinity of local minimums of modulation frequency.

Soliton dragging by dynamic optical lattices

We report on the phenomenon of controllable soliton dragging by dynamic optical lattices induced by three imbalanced interfering plane waves. Because of such an imbalance, the transverse momentum of the lattice does not vanish, and thus the dynamic lattice can cause soliton dragging. The dragging rate is shown to depend on the amplitude and on the angle of incidence of the third plane wave making the optical lattice.

Polarization instability, steering, and switching of discrete vector solitons

We study the dynamics of discrete vector solitons in arrays of weakly coupled birefringent optical waveguides with cubic nonlinear response. We start with a modulational instability analysis, followed by approximate analytical solutions in the form of strongly localized modes. Next, we compute the effective Peierls-Nabarro potential for these modes and obtain the spatial average of the power transfer between both polarizations modes as a function of their relative phase. Finally, we combine the concepts of polarization mode instability with discreteness-induced beam trapping by the array, and demonstrate numerically the amplification of a weak signal by a strong pump of the other polarization, combined with simultaneous discretized all-optical switching.

Soliton spiraling in optically induced rotating Bessel lattices

We address soliton spiraling in optical lattices induced by multiple coherent Bessel beams and show that the dynamic nature of such lattices makes it possible for them to drag different soliton structures, setting them into rotation. We can control the rotation rate by varying the topological charges of lattice-inducing Bessel beams.

Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices

We consider parametric amplification of two-dimensional spatial soliton oscillations in longitudinally modulated harmonic and Bessel lattices in Kerr-type saturable medium. We show that soliton center oscillations along different axes in two-dimensional lattices are coupled, which gives rise to a number of interesting propagation scenarios including periodic damping and excitation of soliton oscillations along perpendicular axes, selective amplification of soliton oscillations along one transverse axis, and enhancement of soliton spiraling.

Stable ring-profile vortex solitons in bessel optical lattices

Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.

Multicolor vortex solitons in two-dimensional photonic lattices

We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable almost in the entire domain of their existence, and that the instability domain decreases with the increase of the lattice depth. We also show the generation of the solitons, and the feasibility of the concept of lattice soliton algebra.

Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices

We address azimuthally modulated Bessel optical lattices imprinted in focusing cubic Kerr-type nonlinear media, and reveal that such lattices support different types of stable solitons whose complexity increases with the growth of lattice order. We reveal that the azimuthally modulated lattices cause single solitons launched tangentially to the guiding rings to jump along consecutive sites of the optical lattice. The position of the output channel can be varied by small changes of the launching angle.

Stabilization of vector solitons in optical lattices

We address the properties and dynamical stability of one-dimensional vector lattice solitons in a Kerr-type cubic medium with harmonic transverse modulation of the refractive index. We discovered that unstable families of scalar lattice solitons can be stabilized via cross-phase modulation (XPM) in the vector case. It was found that multihumped vector solitons that are unstable in uniform media where the XPM strength is higher than that of self-phase modulation can also be stabilized by the lattice.

Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice

We investigate the existence and stability of three-dimensional spatiotemporal solitons in self-focusing cubic Kerr-type optical media with an imprinted two-dimensional harmonic transverse modulation of the refractive index. We demonstrate that two-dimensional photonic Kerr-type nonlinear lattices can support stable one-parameter families of three-dimensional spatiotemporal solitons provided that their energy is within a certain interval and the strength of the lattice potential, which is proportional to the refractive index modulation depth, is above a certain threshold value.

Tunable soliton self-bending in optical lattices with nonlocal nonlinearity

We address the phenomenon of soliton self-bending in Kerr-type nonlocal nonlinear media with an imprinted transverse periodic modulation of the linear refractive index. We show that the imprinted optical lattice makes possible to control the mobility of soliton by varying the depth and the frequency of the linear refractive index modulation.

Soliton eigenvalue control in optical lattices

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.

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.

Stable soliton complexes in two-dimensional photonic lattices

We show that two-dimensional photonic Kerr nonlinear lattices can support stable soliton complexes composed of several solitons packed together with appropriately engineered phases. This may open up new prospects for encoding pixellike images made of robust discrete or lattice solitons.

Resonant phenomena in nonlinearly managed lattice solitons

The formation of nonlinearly managed spatial solitons in Kerr-type nonlinear media with transverse periodic modulation of the refractive index is considered. The phenomenon of resonant enhancement of lattice soliton amplitude oscillations is reported. We show how the tunable discreteness and competition between such characteristic scales as the beam width and the lattice period influence propagation dynamics and properties of breathing lattice solitons.

Packing, unpacking, and steering of multicolor solitons in optical lattices

We discuss potential applications of multicolor solitons supported by periodic lattices imprinted in quadratic nonlinear media. Such lattice solitons can be packed together with appropriate relative phases to form stable soliton trains that can be treated as bit sequences. We describe controllable splitting of the trains into their soliton constituents and the angle- and power-controlled steering and trapping of solitons moving across the lattice into the desired guiding channel.

Parametric amplification of soliton steering in optical lattices

We report on the effect of parametric amplification of spatial soliton swinging in Kerr-type nonlinear media with longitudinal and transverse periodic modulation of the linear refractive index. The parameter areas are found where the soliton center motion is analogous to the motion of a parametrically driven pendulum. This effect has potential applications for controllable soliton steering.

Multicolor lattice solitons

We report on the existence of multicolor solitons supported by periodic lattices made from quadratic nonlinear media. Such lattice solitons bridge the gap between continuous solitons in uniform media and discrete solitons in strongly localized systems and exhibit a wealth of new features. We discovered that, in contrast to uniform media, multipeaked lattice solitons are stable. Thus they open new opportunities for all-optical switching based on soliton packets.