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.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.     

Dissipative solitons of the Bose-Einstein condensate of excitons

A mirrorless scheme for forming dissipative solitons has been proposed. It consists of a thin layer of a nonlinear medium excited by coherent laser radiation. The existence of dark dissipative solitons of the Bose-Einstein condensate of excitons in such a semiconductor film has been numerically demonstrated. The sizes of an excition soliton and required laser-radiation level are two orders of magnitude smaller than the respective quantities for the case of optical dissipative solitons.     

Temperature effect on dissipative holographicscreening-photovoltaic solitons in a biased dissipative system

In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic （DHSP） solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system.     

Fifth order evolution equation for long wave dissipative solitons

Third and fifth order nonlinear wave equations which arise in the theory of water waves possess solitary and periodic traveling waves. Solitary waves also arise in systems with dissipation and instability where a balance between these effects allows the existence of dissipative solitons. Here we search for a model equation to describe long wave dissipative solitons including fifth order dispersion. The equation found includes quadratic and cubic nonlinearities. For periodic solutions in a small box we characterize the rate of growth, and show that they do not blow up in finite time. Analytic solutions are constructed for special parameter values.     

Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation

For a scalar integrable model,it is generally believed that the solitons interact with each other elastically,for instance,multi-bright solitons from the nonlinear Schr(o|")dinger equation and the Korteweg-de Vries equation,etc.We obtain double-valley dark solitons from the defocusing Hirota equation by the Darboux transformation.Particularly,we report a remarkable phenomenon for the inelastic interaction of the double-valley dark solitons,in contrast to the solitons interacting with each other elastically for a scalar integrable model in previous works.Furthermore,we give the explicit conditions for the elastic collision based on the asymptotic analysis results.It is shown that the double-valley dark solitons could also admit elastic interaction under the special parameters settings.     

Three-dimensional dissipative optical solitons

A brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental (zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

全正色散多波长被动锁模耗散孤子掺镱光纤激光器

报道了一种带有周期性双折射光纤滤波器的全正色散多波长被动锁模耗散孤子掺镱光纤激光器. 通过数值模拟发现加入滤波器后激光器能输出多波长耗散孤子脉冲, 调节滤波器带宽大小可以得到不同波长个数和波长间隔的多波长锁模耗散孤子脉冲. 在激光器产生的四波长和五波长耗散孤子脉冲中观察到了耗散孤子分子, 并且通过调节滤波器参数和饱和功率可以改变多波长脉冲中耗散孤子分子的个数和波长. 这是在被动锁模光纤激光器中首次实现包含有耗散孤子分子的多波长脉冲. 另外还在实验上实现了全正色散双波长被动锁模耗散孤子的产生. 关键词： 全正色散 耗散孤子 多波长脉冲 孤子分子     

Conservative and dissipative fiber Bragg solitons (a review)

We present a comparative review of two classes of optical solitons—conservative and dissipative solitons—propagating in single-mode optical fibers in which refractive-index gratings are induced such that their period is comparable with the radiation wavelength. Fibers that have the Kerr nonlinearity and negligibly small losses and that do not gain radiation (conservative system) are described by traditional equations of the approximation of slowly varying amplitudes, and effects caused by the nonlinearity of the medium, such as nonlinear switching, optical bistability, and formation of conservative Bragg solitons are considered. It is shown that the passage beyond the scope of the approximation of slowly varying amplitudes makes it possible to describe new important effects, including localization of soliton centers near maxima of the refractive-index grating. Bright and dark conservative solitons are demonstrated, which are formed when the Kerr nonlinearity is replaced by the nonlinearity of two-level atomic systems. The properties of conservative solitons in resonance semiconductor Bragg structures with quantum wells are considered. Results of experimental studies of nonlinear effects in fibers with Bragg gratings are presented. For an active single-mode fiber with a Bragg refractive-index grating and nonlinear gain and absorption, dissipative solitons are described using the approximation of slowly varying amplitudes and inertialess nonlinearity. It is shown that the dissipative factors qualitatively change the properties of solitons compared to the conservative case. Using the Maxwell-Bloch equations, it is demonstrated that the ratio between the gain and absorption relaxation times significantly affects the stability of localized structures. The interaction of dissipative optical Bragg solitons is described. It is shown that, beyond the scope of the approximation of slowly varying amplitudes, the average velocity of propagating dissipative Bragg solitons acquires only discrete values, and formation of pairs of solitons with two values of the phase difference becomes possible. For a birefringent fiber, dissipative vector optical Bragg solitons are demonstrated.     

Holographic solitons in centrosymmetric photorefractive crystals

The conditions necessary for obtaining holographic solitons in centrosymmetric photorefractive crystals are discussed. When both the intensity modulation of the two interacting waves and the angle between the vector of each beam and the longitudinal axis are small, centrosymmetric photorefractive crystals with a positive (or negative ) effective quadratic electro-optic coefficient are able to support bright (or dark) holographic solitons. The intensity width at half maximum of bright and dark solitons is inversely proportional to the external bias field. The holographic solitons can also exit in dissipative centrosymmetric photorefractive crystals when the applied external bias field is large enough.     

Spatial solitons in Kerr and Kerr-like media

This is a review paper of basic knowledge and recent advances in the area of spatial solitons in Kerr and Kerr-like media. We consider spatial bright and dark solitons, solitons in waveguide geometries, optical bullets, vortex solitons and, briefly, dissipative cases. In our treatment, we use a Hamiltonian approach when considering stability issues.     

Temporal behavior of low-amplitude dark spatial solitons in two-photon centrosymmetric photorefractive media

We investigate the temporal behavior of low-amplitude dark spatial solitons in biased centrosymmetric crystals with two-photon photorefractive effects. The expressions of time-dependent space-charge field and dynamical evolution equation are derived. The temporal behaviors of the intensity profiles and the intensity full width at half maximum (FWHM) of dark solitons are investigated by numerical method. The results indicate that a broad soliton is generated at the beginning, and as time evolves, the intensity width of solitons decrease monotonously to a minimum value toward steady state. Within the same propagation time, the higher the ratio of soliton peak intensity to the dark irradiation intensity is, the shorter the FWHM of dark solitons is.     

Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin–orbit coupled Bose–Einstein condensate

We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation. Compared with previous results, the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling. With the modulation of the spin–orbit coupling, not only the lifetime of ring dark solitons is greatly prolonged, but also their attenuation kinetics is significantly affected. For two shallow ring dark solitons with the equal strength of the spin–orbit coupling, the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value. Due to the effect of the snake instability, ring dark solitons split into a series of ring-like clusters of vortex pairs, which perform complex oscillations. This indicates that the system is strongly dependent on the presence of the spin–orbit coupling. Furthermore, the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.     

Dynamics of Spatial Dark Solitons Trapped in the Media with Gain and TPA

The propagation of dark solitons in nonlinear media that include gain and Joss described by a nonlinear Schroedinger equation is investigated. Based on the direct approach of perturbation theorv, the width, height and other related quantities of dark solitons are obtained. It is shown that stationarv propagation of dark solitons is found to be possible in the presence of both gain and absorption. The results obtained by means of our analytic method are in excellent agreement with numerical simulations. Our results are helpful for the research into the optical soliton transmission system.     

非局域非线性介质中空间暗孤子的理论和实验研究

对非局域非线性介质中的空间暗孤子进行了研究.理论上运用牛顿迭代法求解非局域非线性薛定谔方程,得到了不同传播常数下的非局域空间暗孤子的数值解,发现在任何非局域程度以及任何传播常数条件下,都存在暗孤子的解,而且孤子的束宽与非局域程度存在一定的关系.实验上,在染料溶液中观测到了空间暗孤子在非局域非线性介质中的形成.利用输入功率所引起的非线性效应强度的变化,分析了背景光波形对暗孤子的影响,数值模拟结果与实验结果相符合. 关键词： 非局域非线性 空间暗孤子     

Soliton instabilities and vortex street formation in a polariton quantum fluid

Exciton?polaritons have been shown to be an optimal system in order to investigate the properties of bosonic quantum fluids. We report here on the observation of dark solitons in the wake of engineered circular obstacles and their decay into streets of quantized vortices. Our experiments provide a time-resolved access to the polariton phase and density, which allows for a quantitative study of instabilities of freely evolving polaritons. The decay of solitons is quantified and identified as an effect of disorder-induced transverse perturbations in the dissipative polariton gas.     

Dynamics of dark solitons in elongated Bose-Einstein condensates

We find two types of moving dark soliton textures in elongated condensates: nonstationary kinks and proper dark solitons. The latter have a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.     

Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions

We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems. It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.     

Impact of higher-order effects on pulsating and chaotic solitons in dissipative systems

We investigate numerically, both in time and frequency domains, the influence of some higher-order effects, namely the third-order dispersion, intrapulse Raman scattering, and self-steepening, on the dynamics of different pulsating and chaotic solitons in dissipative systems, which are described by a generalized complex Ginzburg-Landau equation. We show that the higher-order effects can have a dramatic impact on the dynamics of such pulses and that, for some ranges of the parameter values, they can be transformed into fixed-shape solitons. This paper is dedicated to Prof. Helmut Brand on the occasion of his 60th birthday.