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.     

Stability of solitons in parity-time-symmetric couplers

Families of analytical solutions are found for symmetric and antisymmetric solitons in a dual-core system with Kerr nonlinearity and parity-time (PT)-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of gain, loss, and intercore coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").     

Exact chirped gray soliton solutions of the nonlinear Schrödinger equation with variable coefficients

In this paper, we consider the nonlinear Schrödinger equation with variable coefficients, and by using direct transformation of variables and functions, the explicit chirped gray one- and two-soliton solutions are presented. Based on the exact solutions, we in detail analyze the propagation characteristics of the chirped gray soliton, including the stability against either the deviation from integrable condition or the initial perturbation, and interaction between the chirped gray solitons. The results show that the gray soliton can be compressed by choosing the appropriate initial chirp, and the chirped gray pulses can stably propagate along optical fibers remaining the character of solitons.     

Generation of surface soliton arrays

We discover that, at the edge of an optical lattice imprinted in a saturable nonlinear medium, one-dimensional surface solitons exist only within a band of light intensities and that they cease to exist when the lattice depth exceeds an upper threshold. We also reveal the generation of arrays of two-dimensional surface solitons mediated by the transverse modulational instability of one-dimensional solitons, a process that is found to exhibit specific features associated to properties of the optical lattice.     

Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice

We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-onedimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice.It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice.The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter,and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.     

空间调制作用下Bessel型光晶格中物质波孤立子的稳定性

利用变分法和数值计算方法研究了空间调制作用下Bessel型光晶格中玻色-爱因斯坦凝聚体系中孤立子的稳定性, 给出了存在随空间非周期变化的线性Bessel型光晶格和非线性光晶格(原子之间非线性相互作用的空间调制)时, 各种参数组合下涡旋和非涡旋孤立子的稳定性条件. 首先, 利用圆对称的高斯型试探波函数得出描述体系稳定性参数满足的Euler-Lagrange方程和变分法分析体系稳定性所需要的有效作用势能的表达式. 然后, 根据有效作用势能是否具有局域最小值判断体系是否具有稳定状态, 得出体系具有稳定状态时参数所满足的条件. 最后, 利用有限差分法求解Gross-Pitaevskii方程验证变分法结果的正确性, 所得结果和变分法结果一致. 关键词： Bessel型光晶格 非线性光晶格 孤立子 稳定性     

Surface solitons in chirped photonic lattices

We study surface modes at the edge of a semi-infinite chirped photonic lattice in the framework of an effective discrete nonlinear model. We demonstrate that the lattice chirp can change dramatically the conditions for the mode localization near the surface, and we find numerically the families of discrete surface solitons in this case. Such solitons do not require any minimum power to exist provided the chirp parameter exceeds some critical value. We also analyze how the chirp modifies the interaction of a soliton with the lattice edge.     

Oscillatory stability of quantum droplets in PT-symmetric optical lattice

We study stability and collisions of quantum droplets(QDs) forming in a binary bosonic condensate trapped in parity-time (PT)-symmetric optical lattices. It is found that the stability of QDs in the PT-symmetric system depends strongly on the values of the imaginary part W_0 of the PT-symmetric optical lattices, self-repulsion strength g, and the condensate norm N. As expected,the PT-symmetric QDs are entirely unstable in the broken PT-symmetric phase. However, the PT-symmetric QDs exhibit oscillatory stability with the increase of N and g in the unbroken PT-symmetric phase. Finally, collisions between PT-symmetric QDs are considered. The collisions of droplets with unequal norms are completely different from that in free space. Besides, a stable PT-symmetric QDs collides with an unstable ones tend to merge into breathers after the collision.     

Bessel型光晶格中自旋-轨道耦合极化激元凝聚的稳态结构

Bessel型光晶格是一种非空间周期性的柱对称的光晶格势场,其兼具无限深势阱和环状势阱的特征,在0阶Bessel光晶格势场中央形成深势阱,而在非0阶Beseel光晶格势场中能形成具有中央势垒的环状浅势阱.极化激元是一种半光半物质的准粒子,该准粒子甚至可以在室温条件下发生玻色-爱因斯坦凝聚相变,形成极化激元凝聚.另外,通过极化激元能级的腔诱导TE-TM分裂能在极化激元凝聚中实现足够强的自旋-轨道耦合作用.极化激元凝聚能在室温条件下实现,在其中又存在自旋-轨道耦合作用,其为量子物理的研究提供了全新的平台.本文把Bessel光晶格势场引入到极化激元凝聚系统,研究了存在自旋-轨道耦合作用下的旋量双组分极化激元凝聚系统的稳态结构.通过求解Gross-Pitaevskii方程给出了极化激元凝聚系统在实验室坐标系和旋转坐标系中极化激元凝聚系统的稳态结构,由于Bessel势场的引入,使得稳态结构更具有多样性.给出了实验室坐标系中在中央深势阱中存在的基础型高斯孤立子、多极孤立子和在环状浅势阱中存在环状孤立子和多极孤立子的稳态结构;给出了旋转坐标系中存在的涡旋环状孤立子,及其由于自旋-轨道相互作用引起的组...     

Nonlinear dynamical stability of gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice

We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice. Honeycomb lattices possess a unique band structure, the first and second bands intersect at a set of so-called Dirac points. Deformation can result in the merging and disappearance of the Dirac points, and support the gap solitons. We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures being in-phase or out-of-phase. We also investigate the linear stabilities and nonlinear stabilities of these gap solitons. These results have applications of the localized structures in nonlinear optics, and may helpful for exploiting topological properties of a deformed lattice.     

Surface defect gap solitons in two-dimensional optical lattices

We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.     

Dynamics and manipulation of matter-wave solitons in optical superlattices

We study the existence and stability of bright, dark, and gap matter-wave solitons in optical superlattices. Then, using these properties, we show that (time-dependent) “dynamical superlattices” can be used to controllably place, guide, and manipulate these solitons. In particular, we use numerical experiments to displace solitons by turning on a secondary lattice structure, transfer solitons from one location to another by shifting one superlattice substructure relative to the other, and implement solitonic “path-following”, in which a matter wave follows the time-dependent lattice substructure into oscillatory motion.     

Higher-order surface solitons in one-dimensional Bessel optical lattices

We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena may open a new way for soliton control and manipulation.     

光晶格势阱中二元凝聚体的矢量孤子的振荡和分裂

考虑外部囚禁势阱为光晶格势阱,研究了二元玻色-爱因斯坦凝聚体中亮-亮孤子的动力学行为.结果表明,亮-亮孤子的运动方向和振荡行为可以分别通过调节光晶格势阱的晶格常数和势阱深度来控制.进一步地,亮-亮孤子还可以被局域在光晶格势阱中,并且随着势阱深度的增加,局域孤子会产生分裂行为.     

Stable ring-profile vortex solitons in bessel optical lattices

Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.     

含自频移啁啾超短脉冲间相互作用的数值研究

采用拟解法给出了Ginzberg—Landau方程类孤波解的参数表达式.通过数值模拟对啁啾超短脉冲间的相互作用进行了研究．结果表明, 随着相邻孤子间距离的减小,它们之间的相互作用变得越来越严重．传统的不等振幅法在一定程度上可以抑制孤子间的相互作用,通过选取合适的振幅比,找到了相邻孤子间相互作用平衡的最小距离,这对提高光纤传输的比特率具有十分重要的意义．讨论了多孤子间的相互作用,找到了抑制四孤子之间相互作用的合适振幅比．     

三体相互作用下Bessel型光晶格中物质波孤立子的稳定性研究

研究了两体和三体相互作用空间调制情形下Bessel型光晶格中准二维玻色-爱因斯坦凝聚体系中物质波孤立子的稳定性.利用标准的变分法程序,得出体系有效势能的表达式,进而根据有效势能结构给出了体系的稳定性条件.结果表明,在有Bessel型光晶格和没有Bessel型光晶格的情况下,体系均能形成稳定的孤立子解,但是有晶格参与时,体系有很大范围的稳定区间.另外,稳定性受两体相互作用和三体相互作用共同支配,其中两体相互作用对体系的稳定性起主导作用,三体相互作用和相互作用的空间调制只对稳定性起调节作用,但是在特定情况下,必须要有三体相互作用或者相互作用空间调制的参与才能形成稳定的孤立子解.     

Surface defect kink solitons

We reveal the existence of dynamically stable nonlinear defect kink modes at an interface separating a defocusing Kerr medium and an imprinted semi-infinite lattice with a positive or negative defect covering single or several lattice sites. Increasing the number of defect sites equivalently results in a band-gap shift of lattice which in return alters the existence domains and stability properties of defect solitons. Comparing with the uniform semi-infinite lattice, the instability of kink soliton in lattice with a negative defect is significantly suppressed, especially for in-phase soliton. Our results provide an effective way for the realization of stable in-phase kink solitons.     

Dissipative solitons in active Bragg gratings

Motionless and moving bright dissipative solitons in an optical fiber with a Bragg grating and non-linear amplification and absorption are found numerically and studied. These solitons form a one-parameter family whose parameter—the soliton velocity—can continuously change in a certain range. The presence of saturation of the nonlinearity is necessary for stability of such solitons. Neglect of saturation of the cubic-in-field polarization of the medium results in the instability of the possible localized structures.     

三体相互作用下Bessel型光晶格中物质波孤立子的稳定性研究

研究了两体和三体相互作用空间调制情形下Bessel型光晶格中准二维玻色-爱因斯坦凝聚体系中物质波孤立子的稳定性. 利用标准的变分法程序, 得出体系有效势能的表达式, 进而根据有效势能结构给出了体系的稳定性条件. 结果表明, 在有Bessel型光晶格和没有Bessel型光晶格的情况下, 体系均能形成稳定的孤立子解, 但是有晶格参与时, 体系有很大范围的稳定区间. 另外, 稳定性受两体相互作用和三体相互作用共同支配, 其中两体相互作用对体系的稳定性起主导作用, 三体相互作用和相互作用的空间调制只对稳定性起调节作用, 但是在特定情况下, 必须要有三体相互作用或者相互作用空间调制的参与才能形成稳定的孤立子解.