Spinning solitons in cubic-quintic nonlinear media

We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.     

Regular and stochastic motion of dissipative optical solitons

Investigations of the motion of dissipative optical solitons and their complexes in wide-aperture nonlinearly optical (with coherent pump radiation) and laser (with incoherent pump radiation) systems have been reviewed. An important characteristic of dissipative solitons is the topology of the energy fluxes, which determines the internal structure of individual solitons and makes it possible to certainly separate the cases of the weak and strong interactions between the solitons. It has been shown that the character of the regular motion of dissipative soliton structures in a homogeneous system is determined by the symmetry of the transverse distributions of the intensity and energy flux; the motion of asymmetric structures is curvilinear. This is also valid for complexes of three-dimensional dissipative optical solitons, “laser bullets.” The extreme possibilities of localization of solitons are determined by quantum noises. The corresponding Brownian motion of the center of the dissipative optical soliton is characterized by a much lower level of the statistic dispersion of the coordinates of its center and velocity than that in the case of conservative solitons.     

Dissipative plasmon‐solitons in multilayer graphene

Nonlinear properties of a multi‐layer stack of graphene sheets are studied. It is predicted that such a structure may support dissipative plasmon‐solitons generated and supported by an external laser radiation. Novel nonlinear equations describing spatial dynamics of the nonlinear plasmons driven by a plane wave in the Otto configuration are derived and the existence of single and multi‐hump dissipative solitons in the graphene structure is predicted.     

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.     

Multi-peak solitons in PT-symmetric Bessel optical lattices with defects

This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity–time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μ _c for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ > μ _c . In the self-defocusing case, solitons exist only when μ < μ _c . Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.     

Temperature effect on the evolution and stability of rigid screening spatial soliton in biased photorefractive crystal

Based on the temperature dependence of two-wave mixing, temperature effects on the dynamical evolution and stability of rigid screening (RS) bright solitons in a photorefractive dissipative system based on two-wave mixing have been investigated numerically. Our results indicate that the stability of bright RS solitons depends strongly on the crystal temperature. The RS solitons are stable to small temperature perturbations. They will not evolve into stable rigid screening solitons, however, and their intensity and width vary with the propagation distance if the temperature deviation is large enough. The potential applications of the temperature properties of these RS solitons in optical attenuators or repeaters are discussed.     

First principle theory for cavity solitons in semiconductor microresonators

Cavity solitons are similar to spatial solitons, appearing as localized bright dots in the transverse intensity profile of the electromagnetic field, but they arise in dissipative systems. In this paper we consider a broad-area vertical-cavity semiconductor microresonator, driven by an external coherent field, at room temperature. The active material is constituted by a Multiple Quantum Well GaAs/AlGaAs structure (MQW). We present a set of nonlinear dynamical equations for the electric field and the carrier density valid for both a passive and an active (i.e. with population inversion) configuration. The complex nonlinear susceptibility is derived on the basis of a full many-body theory, with the Coulomb enhancement treated in the Padé approximation. The linear stability analysis of the homogeneous steady states is performed with a generalised approach, and numerical simulations demonstrating the existence of spatial patterns and cavity solitons in experimentally achievable parameter regions are given for the two configurations. Received 18 January 2001     

Evolution and stability of spatial solitons in a photorefractive two-wave mixing system

The dynamical evolution and stability of bright dissipative holographic solitons in biased photorefractive materials in which the self-trapping beam obtains a gain from the pump beam via two-wave mixing has been investigated numerically. Results show that these solitons are stable relative to small perturbations. Adjusting some system parameters, such as the bias field and the angle between beams, can easily control the generation of such solitons. Potential applications in optical switches or repeaters are discussed.     

Dissipative dynamics of dark solitons in elongated Bose--Einstein condensates

The dissipative dynamic stability is investigated of dark solitons in elongated Bose--Einstein condensates that can be described by the Gross--Pitaevskii equation including an additional term. Based on the direct perturbation theory for the nonlinear Schr?dinger equation, the dependence of the soliton velocity on time is explicitly given, and the shape of dark solitons remaining unchanged under the dissipative condition is confirmed theoretically for the first time. It is found that the dynamically stable dark solitons turn out to be thermodynamically unstable.     

Holographic solitons in photorefractive dissipative systems

A new kind of holographic soliton is proposed for a photorefractive dissipative system consisting of a biased photorefractive crystal and a strong pump beam with a uniform spatial distribution in both transverse dimensions. The self-trapping beam in the system can evolve into a spatial soliton when it couples coherently with the pump beam by two-wave mixing. Unlike the holographic solitons recently proposed by Cohen et al. [Opt. Lett. 27, 2031 (2002)], the most unique features of the present solitons are that they have a fixed amplitude and width that are determined completely by the system parameters and that their existence conditions are independent of the polarity of the bias field. Numerical simulations show that these solitons are stable relative to small perturbations.     

Helical solitons in vector modified Korteweg–de Vries equations

We study existence of helical solitons in the vector modified Korteweg–de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems, including plasma and chains of particles connected by elastic springs. By using the dynamical system methods such as the blow-up near singular points and the construction of invariant manifolds, we construct helical solitons by the efficient shooting method. The helical solitons arise as the result of co-dimension one bifurcation and exist along a curve in the velocity-frequency parameter plane. Examples of helical solitons are constructed numerically for the non-integrable equation and compared with exact solutions in the integrable vector mKdV equation. The stability of helical solitons with respect to small perturbations is confirmed by direct numerical simulations.     

Structure of Energy Fluxes in Topological Three-Dimensional Dissipative Solitons

The internal structure of dissipative topological solitons has been revealed by example of three-dimensional dissipative optical solitons with one open and one closed dislocation lines of a wavefront. This structure is manifested in the existence of critical points, lines, and surfaces in the field of electromagnetic energy fluxes (Poynting vector). The conservation of the topological characteristics of such solitons, which can be formed in a homogeneous laser medium with saturated amplification and absorption or in lasers with quite large longitudinal and transverse dimensions, provides additional capabilities for information applications.     

Hard soliton excitation regime: Stability investigation

The problem of the stability of one-dimensional solitons in the hard regime of soliton excitation, where the matrix element of the four-wave interaction has an additional smallness, is studied. It is that shown for optical solitons striction can weaken the Kerr nonlinearity. It is shown that solitons with a finite amplitude discontinuity at the critical soliton velocity, equal to the minimum phase velocity of linear waves, are unstable while solitons with a soft transition remain stable with respect to one-dimensional perurbations. Two-and three-dimensional solitons near threshold are unstable with respect to modulation perturbations. Zh. éksp. Teor. Fiz. 116, 299–317 (July 1999)     

Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials

It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by cubic attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also stabilize various species of fundamental and vortical solitons against the supercritical collapse, driven by the double-attractive cubic-quintic nonlinearity (however, solitons remain unstable in the case of the pure quintic nonlinearity). Two types of OLs are considered, producing similar results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential. Soliton families are obtained by means of a variational approximation, and as numerical solutions. The stability of all families, which include fundamental and multi-humped solitons, vortices of oblique and straight types, vortices built of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov criterion. The model applies to optical media and BEC in “pancake” traps.     

On three-dimensional dissipative optical solitons: Collisions of laser bullets and topological solitons

Results of numerical simulation of collisions of two fundamental laser bullets—three-dimensional solitons formed in a medium with saturable amplification and absorption and frequency dispersion—are presented. A new collision regime resulting in the formation and the propagation of a switching wave is revealed. The existence of a metastable topological (with a wave front dislocation and an annular intensity distribution) three-dimensional dissipative optical soliton is demonstrated.     

一维光伏空间灰孤子及其稳定性研究

从考虑背景光的光伏作用后的光束在光伏媒质中传播的方程出发,证明了在折射率改变为正的光伏媒质中也可以形成灰孤子。光束以灰孤子状态在光伏晶体中传播时,其横向相位必须具有一个与光强分布有关的形式分布,表达式为φ（s）=v[η-∫y^-2（η）dη],其中v是灰孤子的横向运动速度,η是无量纲化坐标,y（η）是归一化的光场振幅。分别讨论了光束灰度、光强振幅、信号光与背景光的有效Glass系数之比R对一维的光伏空间灰孤子宽度、横向总相移和横向运动速度的影响,并分析了光伏灰孤子的稳定性。当光束的灰度m为0时,这一理论可直接退化为光伏暗孤子的理论。     

非局域暗孤子及其稳定性分析

由于其在通信领域潜在的应用前景, 非局域空间孤子一直是研究热点. 但空间非局域暗孤子由于其边界的特殊性, 对其特别是稳定性方面研究甚少. 提出了非局域暗孤子稳定性分析理论, 并对热非线性体介质中1+1维基态和二阶暗孤子的稳定性进行了数值分析和研究, 得到了稳定性图. 从稳定性分析图可知: 在热非线性体介质中, 1+1维基态暗孤子在其存在区域总是稳定的, 而1+1维二阶暗孤子是震荡不稳定的, 其不稳定区域的宽度与传播常数以及介质的非局域程度有关. 为了验证非局域暗孤子稳定性分析理论的正确性, 对加噪声初始输入的传输进行数值模拟得到了传输图, 传输图表明稳定性分析理论的正确性. 关键词： 非局域 稳定性 暗孤子     

非局域表面暗孤子及其稳定性分析

非局域体介质中的暗孤子及表面亮孤子由于在光通信领域的潜在应用而受到极大关注,然而到目前为止却没有对非局域表面暗孤子的研究.在线性介质和非局域非线性介质的分界面上,数值模拟得到了1+1维非局域基态和二阶表面暗孤子,研究了它们的波形与传播常数和介质非局域程度的关系,基于它们的稳定性分析进行了理论推导和数值模拟.稳定性分析结果表明:1+1维非局域基态表面暗孤子在其存在区域总是稳定的,而二阶表面暗孤子是区域不稳定的,其不稳定区域的宽度与传播常数以及介质的非局域程度有关系,且受传播常数的影响更大.加噪声的初始输入传输图验证了稳定性分析结果的正确性.     

On the formation of envelope solitons with tube ended by spherical beads

In this paper it is suggested the possibility of using a simple device to explore the propagation of short transverse perturbations in specimens of three linearly aligned elements (bead, tube and bead). By using time signal analysis and frequency spectroscopy some properties of the transmitted wave packets are experimentally analyzed in the acoustic domain. It is clearly demonstrated that the shape and the velocity of propagation of the waves do not change with distance. The amplitude may vary depending on the dissipation effect. These properties allow us to identify the wave packets as “envelope solitons”. The influence of the elasticity of these materials composing the beads and the tube on the generation of envelope solitons is also investigated.     

Spatiotemporal discrete Ginzburg-Landau solitons in two-dimensional photonic lattices

In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, spatiotemporal dissipative solitons which are highly confined inside two-dimensional photonic lattices are found numerically. The domains of existence in the relevant parameter space, of in-phase (unstaggered) on-site (single-peaked), inter-site (double-peaked), and flat-top-like (four-peaked) spatiotemporal dissipative solitons are determined. We show that the on-site solitons are stable in the whole domain of their existence and we find the stability domains of both inter-site and flat-top-like solitons. We describe the complex instability-induced scenarios of the dynamics of spatiotemporal discrete Ginzburg-Landau solitons in two-dimensional photonic lattices.