(1+2)维强非局域空间光孤子的相互作用

强非局域空间光孤子是指满足强非局域条件的空间孤子.在Snyder和Mitchell工作的基础上，获得了不共面对称斜入射(1+2)维强非局域空间光孤子对相互作用问题的精确解析解.结果表明，光束初始中心距离在大范围尺度内变化时，双孤子的演化都能形成类似DNA结构的稳定缠绕，这种稳定缠绕的结构与双孤子的初始相位差无关；光束中心在横截面上的投影轨迹一般是一个斜椭圆，通过改变两光束的初始中心距离和倾斜度可以控制该椭圆轨迹的变化.指出了利用(1+2)维强非局域空间光孤子的相互作用特性实现平面全光开关和全光互联的潜在可能性. 关键词： (1+2)维非局域非线性介质 空间光孤子的相互作用 全光开关 全光互联     

强非局域光晶格中空间孤子的脉动传播

根据强非局域结构中空间孤子的演化方程——非局域非线性薛定谔方程,采用分步傅里叶方法,对一维强非局域光晶格结构中空间孤子的脉动传播进行数值研究.分析了孤子的初始光束能量、非局域程度、光晶格调制强度、光晶格周期以及线性折射率的纵向调制率与空间孤子的脉动传播周期之间的关系,并对影响脉动传播的内在物理机制进行了讨论.同时,还研究了在线性折射率纵向调制情况下强非局域光晶格结构中空间孤子传输的开关行为. 关键词： 非局域非线性薛定谔方程 光晶格 空间孤子 光开关     

椭圆强非局域空间光孤子

对傍轴椭圆高斯光束在具有椭圆对称响应特性的强非局域非线性介质中的演化规律进行研究，得到了光束各参量演化的精确解析解，分析了单向空间光孤子和强非局域椭圆空间光孤子的形成条件，发现了椭圆光孤子的相移与介质响应函数的椭圆率有关. 关键词： 椭圆对称强非局域响应介质 椭圆强非局域空间光孤子 相移     

基于强非局域空间光孤子特性的光子开关和光子逻辑门

利用(1+1)维Snyder-Mitchell模型讨论了由强非局域介质构成的平面介质波导中同频率和同极化的双光束和三光束同向共同传输的相互作用过程，得到了任意斜入射双光束和三光束相互作用的精确解析解.强非局域空间光孤子的相互作用过程是其特殊情况.基于强非局域空间光孤子的相互作用原理， 提出了实现光子开关、光子“同”(XNOR)和“或非”(NOR)逻辑的新理论方案，并讨论这些基本光子信息处理器件的优化设计问题. 关键词： 强非局域非线性介质 空间光孤子的相互作用 光子开关和光子逻辑     

强非局域非线性介质中的旋转涡旋光孤子

利用变分方法,得到了Snyder-Mitchell模型的旋转空间调制涡旋光孤子的近似解析解.在传输过程中,这种光孤子具有可观察的旋转特性.在一定的条件下,旋转的空间调制涡旋光孤子将退化为圆对称的涡旋光孤子. 关键词： 非局域非线性介质 强非局域性 空间调制涡旋光孤子 变分法     

非局域克尔介质中空间光孤子的相互作用

研究了强非局域克尔介质中光束的演化规律，通过相位分析得到了空间孤子相互作用所满足 的非局域非线性薛定谔方程的简化近似模型，并获得了双光束传输的解析解.结果表明在传 输过程中相互作用的高斯光束的相位决定于它们的输入总功率.以振幅一强一弱共同传输的 高斯光束为例进行了具体研究，得到了强光和弱光的解析式，相位分析显示弱光在相当短的 传输距离之内能产生大的相移，可以通过对强光能量的调控来实现对弱光的相位调制. 关键词： 非局域克尔介质 空间光孤子 孤子相互作用 相位调制     

光谱重置法在非局域空间光孤子研究中的应用

利用光谱重置法在数值上求解非局域非线性薛定谔方程,快速准确地计算出非局域非线性介质中空间光孤子的波形,并得到在不同非局域程度下形成孤子的临界功率和临界束宽的关系.研究结果表明,在任意非局域程度条件下都可以形成稳定的空间光孤子.在响应函数不同时分别与解析解进行对比,发现数值解和解析解只有在强非局域和弱非局域这两种极限条件下是一致的,并给出了对应解析解的有效范围.     

不同非局域程度条件下空间光孤子的传输特性

光束在非局域非线性介质中传输由非局域非线性薛定谔方程描述.讨论了在不同非局域程度 条件下，空间光孤子的传输特性.提出了一个基于分步傅里叶算法数值求解孤子波形和分布 的迭代算法.假定介质的非线性响应函数为高斯型，得出了在不同非局域程度条件下空间光 孤子的数值解，并数值证明了它们的稳定性.结果表明，不论非局域程度如何，光束都能以 光孤子态在介质中稳定传输.光孤子的波形是从强非局域时的高斯型过渡到局域时的双曲正 割型，形成孤子的临界功率随非局域程度的减弱而减小，光孤子相位随距离线性增大，相位 的变化率随非局域程度的减弱而减小. 关键词： 非局域非线性薛定谔方程 空间光孤子 临界功率 相位     

强非局域非线性介质中光束传输的厄米高斯解

利用强非局域非线性介质中空间对称实响应函数的泰勒展开简化了非局域非线性薛定谔方程 ，文章基于强非局域非线性空间中的线性模型得到了矩空间1+D(D=1，2)维的厄米高斯 型解，得到了高阶孤子波的解析式，高斯解是最低阶孤子，即基模光孤子，并得到了入射光 束的临界功率．图示展现了几个低阶光孤子解，并发现了强非局域非线性介质中存在非对称 光孤子． 关键词： 高阶孤子 强非局域介质 厄米高斯     

非局域空间光孤子相互作用的相关影响因素

非局域空间光孤子相互作用受到很多因素的影响,通过数值模拟和实验方法讨论了相位和外置偏压对向列相液晶中空间光孤子相互作用的影响。基于向列相液晶中的非局域非线性薛定谔方程,利用分步傅里叶变换算法进行数值求解,分析了相位对非局域空间光孤子相互作用的影响;另外,实验上在不同的入射条件下,研究了向列相液晶中双孤子的相互作用性质,得到了向列相液晶中两束光交叉点的位置与偏置电压的关系。     

Matter wave interferometry for measuring a molecular transition dipole moment

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ ₁) is less than that of the LOL (V ₀) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ ₁ > V ₀, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ ₁ < V ₀. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.     

Coupled matter-wave solitons in optical lattices

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (V_eff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well V_eff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of V_eff(LOL) increases as k increases and that of V_eff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution they exhibit decay and revival.     

Long range interactions between some charged solitons

A procedure is offered for evaluating the forces between classical, charged solitons at large distances. This is employed for the solitons of a complex, scalar two-dimensional field theory with a U(1) symmetry, that leads to a conserved chargeQ. These forces are the analogues of the strong interaction forces. The potential,U(Q, R), is found to be attractive, of long range, and strong when the coupling constants in the theory are small. The dependence ofU(Q, R) onQ, the sum of the charges of the two interacting solitons (Q will refer to isospin in the SU(2) generalisation of the U(1) symmetric theory) is of importance in the theory of strong interactions; group theoretical considerations do not give such information. The interaction obtained here will be the leading term in the corresponding quantum field theory when the coupling-constants are small.     

Solitons and coreless defects in icosahedral quasicrystals

New types of spatially non-uniform excitations in icosahedral quasicrystalline lattices — solitons and coreless defects — are studied by the projection and topology techniques. The topological charges of particle-like solitons are revealed, each represents the set (z ₁,z ₂) of integers. The coreless defects are found to be topologically unstable excitations.     

Rational solutions to Q3δ in the Adler-Bobenko-Suris list and degenerations

We derive rational solutions in Casoratian form for the Nijhoff-Quispel-Capel (NQC) equation by using the lattice potential Korteweg-de Vries (lpKdV) equation and two Miura transformations between the lpKdV and the lattice potential modified KdV (lpmKdV) and the NQC equation. This allows us to present rational solutions for the whole Adler-Bobenko-Suris (ABS) list except Q4. The known Miura transformation for soliton solutions between the NQC equation and Q3_δ and the known degenerations for solitons from Q3_δ to Q2, Q1_δ, H3_δ, H2 and H1 in the ABS list are used. We show that the Miura transformation and degenerations are valid as well for rational solutions which are usually considered as “long-wave-limit” of solitons. All the rational solutions can be expressed in terms of {z _j} which are linear functions of (n, m).     

Spatiotemporal optical solitons in planar waveguide with periodically modulated cubic-quintic nonlinearity

The propagation and stability of spatiotemporal optical solitons (or optical bullets) in a planar waveguide with periodically modulated cubic-quintic nonlinearity is studied numerically as a function of the amplitudes of modulation (A _m ), the frequency of modulation (ω _m ) and the propagation distance z. The optical spatiotemporal solitons are the result of the balance between the nonlinear parameters, of dispersion (dispersion length, L _D ) and diffraction (diffraction length, L _d ) with temporal and spatial auto-focusing behavior respectively. With the objective of ensure the stability and preventing the collapse or the spreading of pulses, in this study we explore the cubic-quintic nonlinearity with the optical fields coupled by XPM and take into account several values for the non linear parameter α and for amplitudes (A _m ) and frequency (ω _m ) of modulation as a function of the propagation distance z and we cause the collisions of two pulses (envelope of the optical field) to ensure that the optical pulse are solitons. After numerical analysis of parameter settings selected four conditions and for all we get stable solitons and this paper shown that, for a fixed amplitude and frequency of modulation we have stable spatiotemporal solitons.     

Generation of bound solitons in actively phase modulation mode-locked fiber ring resonators

Bound solitons generated in actively mode-locked lasers enable new forms of pulse pairs and multiple pairs or groups of solitons in optical transmission or logics. In this paper, we present the generation of stable bound states of multiple solitons in an active mode-locked fiber laser using continuous phase modulation for wideband phase matching. Not only that dual-soliton bound states but also the triple- and quadruple-soliton pulses can be established. Simulation of the generated solitons are demonstrated. We have also prove by simulation that experimental relative phase difference and chirping caused by phase modulation of LiNbO₃ modulator in the fiber loop significantly influences the interaction between the solitons and hence their stability as they circulate in the anomalous path-averaged dispersion fiber loop.     

On stationary topological solitons in a two-dimensional anisotropic Heisenberg model

We study stationary two-dimensional solitons in an easy-axis Heisenberg magnet with the Hamiltonian density wherei=1, 2,a=1, 2, 3, and (x _i ) is the angle between unit vector s(x _i ) and the easy axis, 0<p<. Stable solitons with a topological chargeQ=1 and localized distributionss ^a (x _i ) withQ=2 are found. The existence of the bound states of two solitons withQ=1 is shown numerically for 0<p<.     

Thermal diffusion of envelope solitons on anharmonic atomic chains

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[x _s ] which predicts a stronger than linear time dependence of Var[x _s ] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.Received: 28 June 2004, Published online: 26 November 2004PACS: 05.10.Gg Stochastic analysis methods - 05.45.Yv Solitons - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics     

Incoherent interaction between bright–bright photovoltaic soliton in an unbiased series two-photon photorefractive crystal circuit

We have investigated incoherent interaction between photovoltaic bright–bright soliton pairs in photorefractive crystals under steady-state condition in an unbiased series two-photon photorefractive crystal circuit in one dimension. The numerical scheme according to the Crank-Nicholson and Runge-kutta methods are applied to simulate the propagation of incoherent interaction for different normalized separation distances and different E₀. Results show that in the case of one-dimensional interaction between these photovoltaic solitons, attraction occurs and width of beams decreases with increasing biased field E₀ and two soliton interact in longer distance for smaller E₀. The result can be used for design optical switches that controlled by biased field.