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.     

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.     

Defect solitons supported by parity-time symmetric defects in superlattices

The existence and stability of defect solitons supported by parity-time (PT) symmetric defects in superlattices are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive defects, zero defects, and negative defects. In the first gap, out-of-phase solitons are stable for positive defects or zero defects, whereas in-phase solitons are stable for negative defects. For both the in-phase and out-of-phase solitons with the positive defect and in-phase solitons with negative defect in the first gap, there exists a cutoff point of the propagation constant below which the defect solitons vanish. The value of the cutoff point depends on the depth of defect and the imaginary parts of the PT symmetric defect potentials. The influence of the imaginary part of the PT symmetric defect potentials on soliton stability is revealed.     

Observation of discrete solitons in optically induced real time waveguide arrays

We report the first experimental observation of discrete solitons in an array of optically induced waveguides. The waveguide lattice is induced in real time by illuminating a photorefractive crystal with a pair of interfering plane waves. We demonstrate two types of bright discrete solitons: in-phase self-localized states and the staggered (pi out-of-phase) soliton family. This experiment is the first observation of bright staggered solitons in any physical system. Our scheme paves the way for reconfigurable focusing and defocusing photonic lattices where low-power (mW) discrete solitons can be thoroughly investigated.     

光诱导准一维光子晶格中离散空间光孤子的相互作用

基于分步束传播法数值分析了离散空间光孤子在准一维光诱 导光子晶格中的相干与非相干相互作用过程. 结果表明: 对于相干孤子, 同相时相互吸引, 反相时相互排斥. 然而, 由于非线性响应的各向异性, 横向排布的非相干孤子会因间隔波导数目的增加而由相互吸引变为相互排斥. 并且, 沿对角方向排布的两个非相干孤子在孤子相 互作用力和布拉格反射的共同影响下, 会呈现出"钟摆式"振荡传输现象. 研究结果有助于进一步理解非线性各向异性对离散孤子相互作用的影响机制, 并为后续实验研究提供理论参考.     

Anomalous interactions of spatial gap solitons in optically induced photonic lattices

We demonstrate coherent interactions between spatial gap solitons in optically induced photonic lattices. Because of the "staggered" phase structures, two in-phase (out-of-phase) bright gap solitons can repel (attract) each other at close proximity, in contrast to soliton interaction in homogeneous media. A reversal of energy transfer direction and a transition between attractive and repulsive interaction forces can be obtained solely by changing the initial soliton separation relative to the lattice spacing.     

Dipole and quadrupole solitons in optically-induced two-dimensional defocusing photonic lattices

Dipole and quadrupole solitons in a two-dimensional optically induced defocusing photonic lattice are theoretically predicted and experimentally observed. It is shown that in-phase nearest-neighbor and out-of-phase next-nearest-neighbor dipoles exist and can be stable in the intermediate intensity regime. There are also different types of dipoles that are always unstable. In-phase nearest-neighbor quadrupoles are also numerically obtained, and may also be linearly stable. Out-of-phase, nearest-neighbor quadrupoles are found to be typically unstable. These numerical results are found to be aligned with the main predictions obtained analytically in the discrete nonlinear Schrödinger model. Finally, experimental results are presented for both dipole and quadrupole structures, indicating that self-trapping of such structures in the defocusing lattice can be realized for the length of the nonlinear crystal (10 mm).     

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.     

Higher-order solitons in amplitude-disordered waveguide arrays

We investigate the existence and stability of different families of spatial solitons in optical waveguide arrays whose amplitudes obey a disordered distribution. The competition between focusing nonlinearity and linearly disordered refractive index modulation results in the formation of spatial localized nonlinear states. Solitons originating from Anderson modes with few nodes are robust during propagation. While multi-peaked solitons with in-phase neighboring components are completely unstable, multipole-mode solitons whose neighboring components are out-of-phase can propagate stably in wide parameter regions provided that their power exceeds a critical value. Our findings, thus, provide the first example of stable higher-order nonlinear states in disordered systems.     

Kink dynamics in the highly discrete sine-Gordon system

We study kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing. Numerical simulations exhibit new properties of kinks in this case: they lose the memory of their initial velocity and propagate preferentially at well-defined velocities which correspond to quasi-steady states, while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations. When a small external driving force is applied to the system, the same velocities appear as plateus in the strongly nonlinear mobility of the kink. The energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system, and the preferential velocities for the kink are obtained to good accuracy. Similar results may be expected to be valid for other discrete systems manifesting topological solitons. The numerical simulations reveal also new stable “multiple-kink” excitations which can propagate almost freely in extremely discrete systems where “ordinary” simple kinks are pinned to the lattice by discreteness. The stability of the “multiple-kinks” is discussed.     

Soliton complexes and flat-top nonlinear modes in optical lattices

We describe a continuous analog of the quasirectangular flat-top nonlinear modes earlier found for discrete nonlinear models. We show that these novel nonlinear modes can be understood as multi-soliton complexes with either in-phase or out-of-phase neighboring solitons trapped by the periodic potential of the lattice. We demonstrate a link between the flat-top states and the truncated nonlinear Bloch waves, and discuss how these nonlinear localized modes can be monitored experimentally in photonics and Bose–Einstein condensates. PACS 42.65.Tg; 42.65.Jx; 03.75.Lm     

Dynamic stability and manipulation of bright matter-wave solitons by optical lattices in Bose-Einstein condensates

An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a time-space periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.     

(1+1)维光折变亮屏蔽孤子相互作用的数值分析

利用束传播法对（1+1）维光折变亮屏蔽孤子间的相互作用进行了详细地数值模拟研究.结果表明：两同相孤子相互吸引,并伴有孤子融合现象,且孤子融合发生时的作用距离随着孤子初始间距的增大而增大;两反相孤子相互排斥,且排斥作用随着孤子初始间距的减小而增强;当两孤子的相位差位于区间（0,π）和（－π,0）中时,其相互作用过程将伴有能量转移,但两区间内能量转移的方向相反,并表现出反转对称性;由于孤子间的距离和相对相位对孤子间的相互作用均有很大的影响,因此多个孤子间的相互作用过程非常复杂,但可以通过分析相邻孤子间的相互作用对其进行定性的预测.     

Dynamical structure functions,collective modes,and energy gap in charged-particle bilayers

The dynamical properties of strongly coupled charged-particle bilayers are investigated by molecular dynamics (MD) simulation and theoretical analysis. The spectra of the current correlation functions show the existence of two (in-phase and out-of-phase) longitudinal and two (in-phase and out-of-phase) transverse collective modes. The out-of-phase modes possess finite frequencies at wave numbers k-->0, confirming the existence of the predicted long-wavelength energy gap in the bilayer system. A theoretical model based on an extended Feynman ansatz for the dynamical structure functions provides predictions on the strength of the collective modes that are verified by the MD experiment.     

Demonstration of surface soliton arrays at the edge of a two-dimensional photonic lattice

We demonstrate surface soliton arrays at the interface between a homogeneous medium and an optically induced two-dimensional semi-infinite photonic lattice. These are nonlinear Tamm-like surface states localized in one but extended periodically in the other transverse dimension. Both in-phase and staggered out-of-phase soliton arrays are observed, and the experimental results are corroborated by numerical simulations.     

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.     

光诱导平面波导阵列中离散空间光孤子的相干相互作用

采用Petviashvili迭代法对光诱导平面波导阵列中的一维离散空间光孤子进行求解,利用分步束传播法对离散空间光孤子间的相干相互作用进行了详细的数值模拟.探讨了离散孤子间的相位差、孤子光强、波导阵列写入光的强度和周期以及外加电场对相互作用过程的影响.结果表明：离散孤子间的相位差对相互作用的影响与连续介质中的情况类似,不同相位差情况下的相互作用也表现为吸引、排斥以及能量转移等现象.同时,离散孤子间的相干相互作用过程(如融合距离和排斥间距等)均会受到孤子光强、波导阵列写入光的强度和周期以及外加电场大小的影响 关键词： 光诱导平面波导阵列 离散空间光孤子 相干相互作用     

Phonon anomalies due to collective stripe modes in high T(c) cuprates

Phonon anomalies observed in various high T(c) cuprates by neutron experiments are analyzed theoretically in terms of the stripe concept. The phonon self-energy correction is evaluated by taking into account the charge collective modes of stripes, giving rise to dispersion gap, or kink and shadow phonon modes at twice the wave number of spin stripe. These features coincide precisely with observations. The gapped branches of the phonon are found to be in-phase and out-of-phase oscillations relative to the charge collective mode.     

Lagrangian approach for dark soliton in nonlocal nonlinear media

We theoretically investigate the dynamics of dark solitons as well as their interaction in nonlocal media. Approximate equations describing the evolution of the beams are obtained via suitable trial functions of amplitude u and refractive index n in an averaged Lagrangian. Our results reveal that out-of-phase dark solitons can evolve into stable bound states in nonlocal materials. Moreover, it is found that the separations in the bound state monotonically increase with the degree of nonlocality in nonlocal limit. These results are in excellent agreement with the numerical simulations.     

Asymmetrical surface soliton trains

We elucidate the existence, stability and propagation dynamics of multi-spot soliton packets in focusing saturable media. Such solitons are supported by an interface beside which two harmonically photonic lattices with different modulation depths are imprinted. We show that the surface model can support stable higher-order structures in the form of asymmetrical surface soliton trains, which is in sharp contrast to homogeneous media or uniform harmonic lattice modulations where stable asymmetrical multi-peaked solitons do not exist. Surface trains can be viewed as higher-order soliton states bound together by several different lowest order solitons with appropriate relative phases. Their existence as stable objects enriches the concept of compact manipulation of several different solitons as a single entity and offers additional freedom to control the shape of solitons by adjusting the modulation depths beside the interface.