Variational solutions for Hermite-Gaussian solitons in nonlocal nonlinear media

The physical features exhibited by Hermite-Gaussian （HC） beams propagating in nonlocal nonlinear media with Gaussian-shaped response are discussed with an approximate variational method.Using direct numerical simulations,we find that the beam properties in the normalized system are different with the change of the degree of nonlocality.It is shown that initial HG profiles break up into several individual beams with propagation when the degree of nonlocality α is small.HG beams can propagate stably when a is large enough.

Elliptical Gaussian solitons in synthetic nonlocal nonliear media

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a ＂double-self-focusing＂ synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality. Based on the variational approach, it obtains the approximately analytical solution of such Gaussian elliptical solitons. It also computes the stability of the solitons by numerical simulations.

Gaussian solitons in nonlocal media:variational analysis

Exact solutions of Gaussian solitons in nonlinear media with a Gaussian nonlocal response are obtained.Using the variational approach,we obtain the approximate solutions of such solitons when the degree of the nonlocality is arbitrary.Specifically,we study the conditions for Gaussian solitons that propagate in weakly and highly nonlocal media.We also compare the variational result with the known exact solutions for weakly and highly nonlocal media.

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity

We investigate the properties of fundamental,multi-peak,and multi-peaked twisted solitons in three types of finite waveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity.Two opposite soliton selfbending signals are considered for different families of solitons.Power thresholdless fundamental and multi-peaked solitons are stable in the low power region.The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals.When solitons tend to self-bend toward the waveguide lattice,stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region.Three-peaked twisted solitons are stable in the lower(upper)cutoff region for a shallow(deep)lattice depth.Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.

Solitons in optical lattices with nonlocal nonlinearity

The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.

Break Up of <i>N</i>-Soliton Bound State in a Gradient Refractive Index Waveguide with Nonlocal Nonlinearity

We study the propagation of N-soliton bound state in a triangular gradient refractive index waveguide with nonlocal nonlinearity. The study is based on the direct numerical solutions of the model and subsequent eigenvalues evolution of the corresponding Zakharov-Shabat spectral problem. In the waveguide with local nonlinearity, the velocity of a single soliton is found to be symmetric around zero and therefore the soliton oscillates periodically inside the waveguide. If the nonlocality is presence in the medium, the periodic motion of soliton is destroyed due to the soliton experiences additional positive acceleration induced by the nonlocality. In the waveguide with the same strength of nonlocality, a higher amplitude soliton experiences higher nonlocality effects, i.e. larger acceleration. Based on this soliton behavior we predict the break up of N-soliton bound state into their single-soliton constituents. We notice that the splitting process does not affect the amplitude of each soliton component.

Vortex and Gaussian Solitons of (3+1)-Dimensional Spatially Modulated Cubic-Quintic-Septimal Nonlinear Schrdinger Equation with External Potential

Based on the variable separation principle and the similarity transformation, vortex soliton solution of a （3＋1）-dimensional cubie-quintic-septimal nonlinear Schrodinger equation with spatially modulated nonlinearity under the external potential are obtained in the spatially modulated cubic-quintic-septimal nonlinear media. If the topological charge m = 0 and m ≠0, Gaussian solitons and vortex solitons can be constructed respectively. The shapes of vortex soliton possess similar structures when the value of l - m is same. Moreover, all phases of vortex solitons exist m-jump with the change of every jump as 2π/m-jumps, and thus totally realize the azimuthal change of 21r around their cores.

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.

Elegant Ince-Gaussian breathers in strongly nonlocal nonlinear media

A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear SchrSdinger equation.

The propagation of dipole solitons in highly nonlocal medium

This paper studies the propagation of dipole solitons in highly nonlocal medium by using the variational method. It finds that the dipole solitons will be stable when the input power obeys a restrict value. When the incident power does not satisfy the stable conditions, the nonlocal accessible dipole solitons will undergo linear harmonic oscillation. It shows such evolution behaviours in detail.

Generation of breathing solitons in the propagation and interactions of Airy–Gaussian beams in a cubic–quintic nonlinear medium

Using the split-step Fourier transform method, we numerically investigate the generation of breathing solitons in the propagation and interactions of Airy–Gaussian（AiG） beams in a cubic–quintic nonlinear medium in one transverse dimension. We show that the propagation of single AiG beams can generate stable breathing solitons that do not accelerate within a certain initial power range. The propagation direction of these breathing solitons can be controlled by introducing a launch angle to the incident AiG beams. When two AiG beams accelerated in opposite directions interact with each other,different breathing solitons and soliton pairs are observed by adjusting the phase shift, the beam interval, the amplitudes,and the light field distribution of the initial AiG beams.

Surface superlattice solitons in nonlocal nonlinear media

We analyse surface solitons at the interface between a one-dimensional photonic superlattice and a uniform medium with weak nonlocal nonlinearity. We demonstrate that in deep lattices there exist three kinds of surface solitons when the propagation constant exceeds a critical value, including two on-site solitons and one off-site soliton. These three kinds of surface solitons have unique dynamical properties. If the relative depth of the superlattice is low, there is only one kind of off-site soliton; however, the solitons of this kind can propagate stably, unlike their deep superlattice counterparts. Dipole surface solitons are also investigated, and the stable domain is given.

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.

Bound states of spatial optical dark solitons in nonlocal media

It is shown that multiple dark solitons can form bound states in a series of balance distances in nonlocal bulk media. Dark solitons can either attract or repel each other depending on their separated distance. The stability of such bound states are studied numerically. There exist unstable degenerate bound states decaying in different ways and having different lifetimes.

Dipole Solitons in Nonlinear Media with an Exponential-Decay Nonlocal Response

By applying the variational approach,the analytical expression of dipole solitons is obtained in nonlinear media with an exponential-decay nonlocal response.The relations of the soliton power versus the propagation constant and the soliton width are given.Some numerical simulations are carried out.The results show that the analytical expression is in excellent agreement with the numerical results for the strongly nonlocal case.

Adiabatic evolution of optical beams of arbitrary shapes in nonlocal nonlinear media

We discuss evolution of Hermite–Gaussian beams of different orders in nonlocal nonlinear media whose characteristic length is set as different functions of propagation distance,using the variational approach.It is proved that as long as the characteristic length varies slowly enough,all the Hermite–Gaussian beams can propagate adiabatically.When the characteristic length gradually comes back to its initial value after changes,all the Hermite–Gaussian beams can adiabatically restore to their own original states.The variational results agree well with the numerical simulations.Arbitrary shaped beams synthesized by Hermite–Gaussian modes can realize adiabatic evolution in nonlocal nonlinear media with gradual characteristic length.

Elegant Ince-Gaussian breathers in strongly nonlocal nonlinear media

A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell’s mode in an elliptic coordinate system,and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function.We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schro¨dinger equation.

具有竞争非线性损耗介质中非局域光孤子的研究

利用JUNG P S等提出的竞争非局域模型,研究了高斯光束在竞争非局域非线性损耗介质中的传输特性。利用变分法得到孤子参数之间的解析关系式,在此基础上给出无损耗情况下亮孤子临界功率和亮孤子势能函数。利用势能函数分析了无损耗情况下亮孤子宽度和入射功率的关系。当损耗较小时,入射功率在小于、等于和大于临界功率情况下,亮孤子均以准呼吸子形式传输,在传输过程中光束宽度逐渐增大。该变分结论与数值结论相符。最后,利用平方算子迭代法求出无损耗时的孤子解,并把该孤子解作为分步傅里叶算法的初始输入仿真了小损耗和小增益时的光束传输特性。当有小增益时,亮孤子也以准呼吸子形式传输,传输过程中光束宽度逐渐减小。研究结果表明,损耗或增益的存在对光束传输影响的效果很明显,可以利用材料的损耗或增益对光束整形。

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