Effective regulation of the interaction process among three optical solitons

The interaction between three optical solitons is a complex and valuable research direction,which is of practical application for promoting the development of optical communication and all-optical information processing technology.In this paper,we start from the study of the variable-coefficient coupled higher-order nonlinear Schodinger equation(VCHNLSE),and obtain an analytical three-soliton solution of this equation.Based on the obtained solution,the interaction of the three optical solitons is explored when they are incident from different initial velocities and phases.When the higher-order dispersion and nonlinear functions are sinusoidal,hyperbolic secant,and hyperbolic tangent functions,the transmission properties of three optical solitons before and after interactions are discussed.Besides,this paper achieves effective regulation of amplitude and velocity of optical solitons as well as of the local state of interaction process,and interaction-free transmission of the three optical solitons is obtained with a small spacing.The relevant conclusions of the paper are of great significance in promoting the development of high-speed and large-capacity optical communication,optical signal processing,and optical computing.

The impact of temperature on the evolution and self-deflection of spatial optical solitons in photovoltaic photorefractive media

The temperature effects on the evolution and self-deflection of bright spatial optical solitons in photo-voltaic photorefractive media were investigated by taking into account diffusion effects. The numerical results show that the evolution of the bright solitary beam depends strongly on the crystal temperature. It is also found that the bending distance of the bright solitary beam centre increases and reaches its maximum value at a characteristic temperature, and then decreases as temperature rises and ap-proaches zero at low and high temperatures. Both the maximum value and characteristic temperature increase with the input power density. The self-deflection of bright solitary beam is further studied by a perturbation technique, and the results are found to be in good agreement with that obtained by the numerical method. The diffusion process and the dark irradiance dominate the temperature depend-ence of bending distance in most values of temperature besides at the characteristic temperature and in the higher temperature regime. The diffusion process will mainly dominate the temperature dependence at the characteristic temperature and the dark irradiance will dominate in the higher tem-perature range.

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.

Temporal Behavior of Low-Amplitude Grey Spatial Solitons in Biased Two-Photon Photorefractive Crystals

The temporal property of grey screening spatial solitons due to two-photon photorefractive effect in lowamplitude regime is analyzed. The results indicate that a broad solitons is generated at the beginning, and as time evolves, the intensity width of grey solitons decreases monotonically to a minimum value toward steady state. In the same propagation time, the FWHM of solitons decreases with p increasing or m decreasing. Moreover, the formation time of solitons is independent of p and m. The time is close to a constant determined by the dielectric relaxation time.

The (1+1)-dimensional spatial solitons in media with weak nonlinear nonlocality

We study the propagation of （l＋l）-dimensional spatial soliton in a nonlocal Kerr-type medium with weak non- locality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schr6dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect （and also diminished for the linear defocusing effect）. In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through.

Self-Similar Hermite-Gaussian Spatial Solitons in Two-Dimensional Nonlocal Nonlinear Media

We study analytically and numerically the propagation of spatial solitons in a two-dimensional stronglynonlocal nonlinear medium. Exact analytical solutions in the form of self-similar spatial solitons are obtained involvinghigher-order Hermite-Gaussian functions. Our theoretical predictions provide new insights into the low-energy spatialsoliton transmission with high fidelity.

Quasistable bright dissipative holographic solitons in photorefractive two-wave mixing system

The dynamical evolution of both signal and pump beams are traced by numerically solving the coupled-wave equation for a photorefractive two-wave mixing system. The direct simulations show that, when the intensity ratio of the pump beam to the signal beam is large enough, the pump beam presents a common decaying behaviour without modulational instability （MI）, while the signal beam can evolve into a quasistable spatial soliton within a regime in which the pump beam is depleted slightly. The larger the ratio is, the longer the regime is. Such quasistable solitons can overcome the initial perturbations and numerical noises in the course of propagation, perform several cycles of slow oscillation in intensity and width, and persist over tens of diffraction lengths. From physical viewpoints, these solitons actually exist as completely rigorous physical objects. If the ratio is quite small, the pump beam is apt to show MI, during which the signal beam experiences strong expansion and shrinking in width and a drastic oscillation in intensity, or completely breaks up. The simulations using actual experimental parameters demonstrate that the observation of an effectively stable soliton is quite possible in the proposed system.

Effects of temperature on screening bright-dark the stability of separate spatial soliton pair

We investigate theoretically the temperature effects on the evolution and stability of a separate screening brightdark soliton pair formed in a serial non-photovoltaic photorefractive crystal circuit. Our numerical results show that, for a stable bright-dark soliton pair originally formed in a crystal circuit at given temperatures, when one crystal temperature changes, the soliton supported by the other crystal will evolve into another stable soliton if the temperature change is quite small, whereas it will become unstable and experience larger cycles of compression or break up into beam filaments if the temperature difference is big enough. The dark soliton is more sensitive to the temperature change than the bright one.

One-Dimensional Modulational Instability of Broad Optical Beams In Photorefractive Crystals with Both Linear and Quadratic Electro-Optic Effects

We present a theoretical study of the one-dimensional modulational instability of a broad optical beam propagating in a biased photorefractive crystal with both linear and quadratic electro-optic effects(Kerr effect)under steadystate conditions.One-dimensional modulational instability growth rates are obtained by treating the space-charge field equation globally and locally.Both theoretical reasoning and numerical simulation show that both the global and local modulational instability gains are governed simultaneously by the strength and the polarity of external bias field and by the ratio of the intensity of the broad beam to that of the dark irradiance.Under a strong bias field,the results obtained using these two methods are in good agreement in the low spatial frequency regime.Moreover,the instability growth rate increases with the bias field,and the maximum instability growth occurs when ratio of light intensity to dark irradiance is 0.88.

The solutions of the strongly nonlocal spatial solitons with several types of nonlocal response functions

The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrodinger equation for several types of nonlocal responses are calculated by Ritz＇s variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the mth power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the （m ＋ 2）th power of its beam width.

Incoherently Coupled Grey-Grey Spatial Soliton Pairs in Biased Two-Photon Photovoltaic Photorefractive Crystals

The incoherently coupled grey-grey screening-photovoltaic spatial soliton pairs are predicted in biased two-photon photovoltaic photorefractive crystals under steady-state conditions. These grey-grey screening-photovoltaic soliton pairs can be established provided that the incident beams have the same polarization, wavelength, and are mutually incoherent. The grey-grey screening-photovoltaic soliton pairs can be considered as the united form of grey- grey screening soliton pairs and open or closed-circuit grey-grey photovoltaic soliton pairs.

Incoherent interaction between one- and two-dimensional solitons in noncentrosymmetric photorefractive media

The incoherent interaction between solitons with different transverse dimensions in a noncentrosymmetric photorefractive crystal is studied both in theory and in experiment. An anomalous incoherent interaction between one- and two-dimensional solitons, whose attractive and repulsive effects depend on the soliton separation, is numerically demonstrated by employing an anisotropic model. By launching a one-dimensional green beam and a two-dimensional red beam into a biased SBN：60 crystal, the hybrid-dimensional soliton interaction is performed. The experimental results are in good agreement with the numerical ones.

Two-Dimensional Spatial Solitons in Nematic Liquid Crystals

We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Oaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.

竞争向列相液晶中(1+2)维空间光孤子

基于JUNG等人提出的竞争非局域模型,研究了竞争型向列相液晶中(1+2)维空间光孤子的传输特性。利用变分法给出了孤子临界功率解析表达式,发现当热非局域程度固定时,临界功率随分子取向效应非局域程度的变化规律与随热非线性系数的变化规律一致:随着分子取向非局域程度或热非线性系数的增加,临界功率由功率不等的两个分支逐渐重合为功率相等的一支;当分子取向效应非局域程度和热非线性系数固定时,随着热非局域程度的增加,临界功率由功率相等的一支分为功率不等的两个分支。利用光束传输方法发现,只有功率不等分支上的点对应的(1+2)维空间光孤子才能稳定传输。该研究结果可为竞争非局域介质中(1+2)维空间光孤子的实验研究以及全光互联应用提供理论基础。

Rotating soliton clusters in nonlocal nonlinear media

From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise, and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0 〈 ｜θ｜ 〈 π, while along the direction of phase gradient when the relative phase difference is within the domain π 〈｜θ｜ 〈 2π

Waveguides induced by grey screening solitons

We investigate the properties of waveguides induced by one-dimensional grey screening solitons in biased photorefractive crystals. The results show that waveguides induced by grey screening solitons are always of single mode for all intensity ratios, i,e. the ratios between the peak intensity of the soliton and the dark irradiance. Our analysis indicates that the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton increase monotonically with intensity ratio increasing. On the other hand, when the soliton greyness increases, the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton decrease monotonically. Relevant examples are provided where photorefractive crystal is of the strontium barium niobate type.

Propagation characteristics of parallel dark solitons in silicon-on-insulator waveguide

The propagation characteristic of two identical and parallel dark solitons in a silicon-on-insulator(SOI)waveguide is simulated numerically using the split-step Fourier method.The parallel dark solitons imposed by the initial chirp are investigated mainly by changing their power,their relative time delay.The simulation shows that the time delay deforms the parallel dark soliton pulse,forming a bright-like soliton in the transmission process and making the transmission quality down.By increasing the power of one dark soliton,the energy of the other dark soliton can be increased,and larger increase in a soliton’s power leads to larger increase in the energy of the other.When the initial chirp is introduced into one of the dark solitons,higher energy consumption is observed.In particular,positive chirps resulting in pulse broadening width while negative chirps narrowing,with an obvious compression effect on the other dark soliton.Finally,large negative chirps are found to have a profound impact on parallel and nonparallel dark solitons.

Incoherently coupled soliton pairs in nonlocal nonlinear media

We show that incoherently coupled soliton pairs can exist in nonlocal Kerr-type nonlinear media. Such solitons can propagate in bright--bright, dark--dark, and gray--gray configurations. When the nonlocal nonlinearity is absent, these bright--bright and dark--dark soliton pairs are those observed previously in local Kerr-type nonlinear media. Our analysis indicates that for a self-focusing nonlinearity the intensity full width half maximum （FWHM） of the bright--bright pair components increases with the degree of nonlocality of the nonlinear response, whereas for a self-defocusing nonlinearity the intensity FWHM of the dark--dark and gray--gray pair components decreases with the increase in the degree of nonlocality of the nonlinear response. The stability of these soliton pairs has been investigated numerically and it has been found that they are stable.

Alternative （1＋1）-D Dark Spatial Soliton-Like Distributions in Kerr Media

In this paper, we solve numerically the nonlinear Schrodinger equation for a defocusing Kerr media with initial conditions different to the hyperbolic tangent function. We demonstrate that initial conditions with a similar position dependence than the hyperbolic tangent evolve to a hyperbolic tangent function, therefore can be considered as （1＋1）-D spatial solitons. The waveguide induced by these conditions is not single mode; it has the capacity to confine one mode more.