Collisions between discrete spatiotemporal Ginzburg-Landau solitons

We report systematic results of collisions between discrete spatiotemporal Ginzburg-Landau solitons in waveguide arrays. Depending on the value of the kick parameter (collision momentum), four generic outcomes are identified in the case of collision of two identical solitons located at equal distances from the edge of the waveguide array: (a) merger of the solitons into a single one, at small values of the kick parameter, (b) creation of an extra soliton at intermediate values of the collision momentum, (c) quasi-elastic interactions at both intermediate values of the kick parameter (for relatively small values of the cubic gain) and at large values of the kick parameter (for relatively high values of cubic gain), and (d) soliton spreading at relatively large values of the collision momentum but only in the case of relatively small values of the cubic gain. In the case of collision of two non-identical solitons located at different distances from the edge of the waveguide array four generic outcomes were identified too: (e) soliton bouncing, accompanied by a sharp modification of soliton velocities during the interaction process, for relatively small values of the collision momentum, (f) soliton creation at intermediate values of the kick parameter and for relatively low values of the cubic gain, (g) soliton spreading (in time) at intermediate values of the collision momentum and for relatively high values of the cubic gain, and (h) quasi-elastic interactions at large values of the the kick parameter.     

Collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices

Systematic results of collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices are reported. The generic outcomes are identified for (i) the collision of two identical solitons located in the corner, at the edge, and in the center of the photonic lattice, and for (ii) the collision of two non-identical corner and edge solitons located at different distances from the boundaries of the photonic lattice. Depending on the values of the kick (collision momentum) and of the nonlinear (cubic) gain, the collision scenarios include soliton merging, creation of an extra soliton, soliton bouncing, soliton spreading, and quasi-elastic (symmetric) interactions.     

Two-Dimensional Laguerre--Gaussian Asymmetric Soliton Family in Strongly Nonlocal Media

We demonstrate the existence of a broad class of higher-order Laguerre Gaussian asymmetric spatial optical solitons in strongly nonlocal nonlinear media. Furthermore, we discuss specific values （q = 0） of the modulation depth parameter for different rational values of the topological charge in detail. Our results show that higherorder asymmetry spatial sofiton family can exist in various forms, such as two-dimensional defect haff-solitons, asymmetric single-layer and multi-layer necklace solitons.     

Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-harmonic generation in photonic crystal fibers

We use cross-correlation frequency-resolved optical gating to obtain spectral-temporal portraits of ultrashort Raman solitons in photonic crystal fibers at telecommunication wavelengths. Power-dependent Raman frequency shifts of 200 nm in 63 mm of fiber are observed accompanied by spectral broadening and 2.5-times soliton compression. Complete time-frequency dynamics at the fundamental wavelength thus visualized enables us to explain the details of the intermodally phase-matched third harmonic generation by the propagating solitons.This revised version was published online in August 2005 with a corrected cover date.     

Evolution and Stability of Dark Holographic Solitons in Photorefractive Dissipative Systems

The dynamics evolution of dark holographic solutions in a dissipative system is investigated numerically provided that the double balance, i.e. diffraction is balanced by nonlinearity and loss is balanced by gain, is satisfied. The influence of the system parameters, such as the linear loss of the crystal, the external biased field and the angel between input beams, on the stable propagation of soliton beams is discussed numerically. Results show that such solitons can be easily amplified or absorbed by adjusting these system parameters. Furthermore, numerical simulations indicate that dissipative dark holographic solitons are stable for small perturbation on amplitude.     

Waveguides induced by steady-state gray solitons in biased photorefractive-photovoltaic crystals

We carry out a theoretical investigation of the properties of waveguides induced by photorefractive one-dimensional steady-state gray spatial solitons (i.e., screening solitons, photovoltaic solitons, and screening-photovoltaic solitons). We demonstrate that waveguides induced by photorefractive steady-state gray spatial solitons are only a single guided mode for both all soliton graynesses and all values of ρ, where ρ is the ratio between the soliton peak intensity and the dark irradiance, and moreover, waveguides induced by gray photovoltaic solitons for closed-circuit condition are also only a single guided mode for all electric current densities. We find that the confined energy near the center of a photorefractive steady-state gray spatial soliton increases with ρ and decreases with an increase in the soliton grayness. We also find that the confined energy near the center of a gray photovoltaic soliton for closed-circuit condition increases with the electric current density. On the other hand, waveguides induced by gray screening-photovoltaic solitons are gray screening soliton-induced waveguides when the bulk photovoltaic effect is neglectable and are gray photovoltaic soliton-induced waveguides when the external bias field is absent.     

Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices

We demonstrated that linearly and nonlinearly amplitude-modulated (chirped) harmonic lattices can support odd and even solitons in both focusing and defocusing saturable media. The modulated lattice modifies the profiles and enlarges the stability domains of solitons, comparing with the unchirped one. Twisted solitons, or “soliton trains” whose profiles exhibit multi-peak structures can also be supported by linearly and nonlinearly chirped lattices. In sharp contrast with periodic lattices, chirped lattices remarkably broaden the existence and stability domains of twisted solitons, especially for solitons with more components. While even solitons in focusing media and twisted solitons in defocusing media are unstable, odd and twisted solitons in focusing media are stable in relatively wide parameter windows. Chirped lattice can be used as a linear guidance to realize the oscillation of solitons which is impossible in unchirped lattice.     

Soliton formation in hollow-core photonic bandgap fibers

The formation of solitons upon compression of linearly chirped pulses in hollow-core photonic bandgap fibers is investigated numerically. The dependence of soliton duration on the chirp and power of the input pulse and on the dispersion slope of the fiber is investigated, and the validity of an approximate scaling relation is tested. It is concluded that compression of input pulses of several ps duration and sub-MW peak power can lead to a formation of solitons with ∼100 fs duration and multi-megawatt peak powers. The dispersion slope of realistic hollow-core fibers appears to be the main obstacle for forming still shorter solitons.     

光诱导准一维光子晶格中离散空间光孤子的相互作用

基于分步束传播法数值分析了离散空间光孤子在准一维光诱 导光子晶格中的相干与非相干相互作用过程. 结果表明: 对于相干孤子, 同相时相互吸引, 反相时相互排斥. 然而, 由于非线性响应的各向异性, 横向排布的非相干孤子会因间隔波导数目的增加而由相互吸引变为相互排斥. 并且, 沿对角方向排布的两个非相干孤子在孤子相 互作用力和布拉格反射的共同影响下, 会呈现出"钟摆式"振荡传输现象. 研究结果有助于进一步理解非线性各向异性对离散孤子相互作用的影响机制, 并为后续实验研究提供理论参考.     

Dipole and quadrupole solitons in optically-induced two-dimensional defocusing photonic lattices

Dipole and quadrupole solitons in a two-dimensional optically induced defocusing photonic lattice are theoretically predicted and experimentally observed. It is shown that in-phase nearest-neighbor and out-of-phase next-nearest-neighbor dipoles exist and can be stable in the intermediate intensity regime. There are also different types of dipoles that are always unstable. In-phase nearest-neighbor quadrupoles are also numerically obtained, and may also be linearly stable. Out-of-phase, nearest-neighbor quadrupoles are found to be typically unstable. These numerical results are found to be aligned with the main predictions obtained analytically in the discrete nonlinear Schrödinger model. Finally, experimental results are presented for both dipole and quadrupole structures, indicating that self-trapping of such structures in the defocusing lattice can be realized for the length of the nonlinear crystal (10 mm).     

Mobility of discrete solitons in quadratically nonlinear media

We study the mobility of solitons in lattices with quadratic (chi(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulations, we demonstrate that, in contrast with their cubic (chi(3)) counterparts, the discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D), in any direction. We identify parametric regions where an initial kick applied to a soliton leads to three possible outcomes: staying put, persistent motion, or destruction. On the 2D lattice, the solitons survive the largest kick and attain the largest speed along the diagonal direction.     

Stabilization of three-dimensional light bullets by a transverse lattice in a Kerr medium with dispersion management

We demonstrate a possibility to stabilize three-dimensional spatiotemporal solitons (“light bullets”) in self-focusing Kerr media by means of a combination of dispersion management in the longitudinal direction (with the group-velocity dispersion alternating between positive and negative values) and periodic modulation of the refractive index in one transverse direction (out of the two). Assuming the usual model based on the paraxial nonlinear Schrödinger equation for the local amplitude of the electromagnetic field, the analysis relies upon the variational approximation (results of direct three-dimensional simulations will be reported in a follow-up). A predicted stability area is identified in the model’s parameter space. It features a minimum of the necessary strength of the transverse modulation of the refractive index, and finite minimum and maximum values of the soliton’s energy. The former feature is also explained analytically.     

Oscillations of the soliton parameters in nonlinear interference phenomena

Applying the inverse scattering transform method, we show that a soliton modified by an amplitude or phase filter can evolve into several solitons. The oscillation period upon subsequent propagation follows from the wavenumbers of the emerging solitons and the radiation. Our results clarify spectral variations observed in recent supercontinuum experiments.     

Solitary Wave Evolution of Optical Planar Vortices in Self-Defocusing Photorefractive Media

Solitary wave evolution of optical planar vortices in isotropie self-defoeusing photorefractive media is investigated in detail. We demonstrate that the formation of a planar vortex soliton intensively depends on the diameter and maximum intensity of the input vortex Seam. The exact solutions of planar vortex solitons are obtained due to the Petviashvili iteration method. It is found that, with the increasing soliton maximum intensity, the soliton core will be gradually diminished to a minimum value.     

Generation of phase nuclei by solitons of the new “undulator” type in martensitic phase transitions of crystalline materials

The microdynamics of large-amplitude nonlinear lattice vibrations of plutonium and uranium materials has been investigated at high reactor temperatures in the ranges of martensitic phase transitions. Topologically new large-amplitude solitons of the “undulator” type have been revealed. Transverse and longitudinal “undulator” solitons in crystals with hexagonal and cubic symmetry, depending on the direction of motion, have different kinematic and amplitude characteristics, which differ from the characteristics of the previously known solitons. The transverse “undulator” solitons, like electrons in undulators, are observed with periodic atomic displacements orthogonal to the direction of soliton propagation. The longitudinal “undulator” solitons with displacements of atoms in the direction of soliton propagation are characterized by periodic delays with two-step velocities on the trajectory in a certain analogy with two-period engineering undulator devices. It has been shown that, at high energies, such “undulator” solitons of two types generate nuclei of a new phase in early stages of structural phase transitions.     

Interaction of two-dimensional spatial incoherent solitons in photorefractive medium

We present a review of our recent theoretical and experimental results on the interaction of incoherent two-dimensional solitary beams in PR SBN crystals. We show that the inherent anisotropy of PR nonlinearity strongly affects the interaction between solitons. Theoretical and experimental results reveal that solitons interacting in a plane perpendicular to the direction of external biasing field always attract, whereas those colliding in a plane of the field exhibit anomalous behaviour. They may experience both attractive and repulsive forces, depending on their mutual separation. We also show that this anisotropy results in the complicated topology of soliton trajectories, featuring periodic collisions, prolonged mutual spiraling and collapse, depending on the initial conditions. Received: 16 November 1998 / Revised version: 12 February 1999 / Published online: 12 April 1999     

Raman perturbation and surface core soliton in hollow photonic crystal fiber

Effect of Raman scattering and higher order dispersion are investigated in case of surface core or gap solitons, known to exist in hollow core photonic crystal fibers. The necessary conditions for the existence of the soliton are analyzed in the parameter plane. It is observed that these conditions are compatible with the famous Vakhitov-Kolokolov (VK) criterion. In the later part the system of partial differential equations are solved by ETDRK method from which the shapes of the pulses are investigated as it travels along the z direction. Both the terms, intrapulse Raman scattering and higher order dispersion have important effect on the propagation characteristics     

Rotating surface soliton complexes in annular waveguides

We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a π-phase difference between neighboring spots. It is shown that the multipole-mode solitons can rotate steadily upon propagation, and the existence domain is strongly affected by the rotation frequency. The rotation may enhance the stabilization of surface multipole-mode solitons.     

Raman gap solitons

We show that an intense pump pulse, detuned far from the Bragg resonance of a nonlinear periodic structure, can excite a gap soliton at a wavelength within the band gap that corresponds to the Raman shift of the medium. This Raman gap soliton is a stable, long-lived, quasistationary excitation that exists within the grating even after the pump pulse has passed. We find both stationary solitons as well as slow Raman gap solitons with velocities as low as 1% of the speed of light. The predicted phenomena should be observable in fiber Bragg gratings and other nonlinear photonic band gap structures.     

Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons

We report results of the first analysis of collisions between stable fundamental (alias spinless) and vortical (spinning) three-dimensional dissipative solitons in a model of a laser cavity. The systematic analysis is carried out for values S=1 and S=2 of the vorticity of the latter soliton. With the increase of the collision momentum, Χ, the same generic scenarios are observed in either case: merger into a single fundamental soliton at both small and relatively large values of Χ, and the formation of two fundamental solitons in an intermediate interval of variation of the collision momentum Χ. At very large values of Χ, the collision seems quasi-elastic, but the vortex soliton eventually splits into two nonspinning fragments.