Interaction of two dark solitons in nonlinear left-handed materials

A system of coupled nonlinear Schrödinger equations (CNLS) has dark soliton solutions. In nonlinear left-handed materials, the interaction of two of these dark solitons with the same parameter κ can generate new electromagnetic envelops that are quite different from a single soliton, even including a ‘bright’ envelop. But the new-generated envelops can also propagate steadily in the materials, we call them quasi-soliton. Numerical calculations demonstrate that varying either the parameter κ or the distance between the two solitons will change the envelop shape of the quasi-soliton remarkably. And an analysis of the phenomena is presented.     

Frequency characteristics of the dark and bright surface solitons at a nonlinear metamaterial interface

We investigate the generation and properties of dark and bright surface waves at the interface of a conventional medium and a metamaterial. It is shown that the stable dark and bright surface solitons can coexist even when the nonlinear Kerr coefficients of the two media are negative, completely different from those at the interface between two conventional media. Most importantly, both the dark and bright surface solitons exist only within a certain range of the effective refractive index of the metamaterial, greatly depending on the frequency of the electromagnetic wave propagating in it. Therefore, the generation conditions for surface solitons, and the properties of the generated surface solitons such as the peak positions and the intensity of the dark and bright surface solitons, can be controlled by adjusting the structure parameters of the metamaterial and/or the frequency of the electromagnetic wave.     

New Exact Jacobi Elliptic Function Solutions of Three—Dimensional Nonlinear Helmholtz Equation in a Nonlinear Kerr—Type Medium

In this letter the three-dimensional nonlinear Helmholtz equation is investigated.which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained,by using our extended Jacobian elliptic function expansion method.When the modulus m-→1 or 0,the corresponding solitary waves including bright solitons,dark solitons and new line solitons and singly periodic solutions can be also found.     

Interacting signal packets in a lossless nonlinear transmission network with linear dispersion

In the small amplitude limit, we use the reductive perturbation method and the continuum limit approximation to derive a coupled nonlinear Schrö dinger (CNLS) equation describing the dynamics of two interacting signal packets in a discrete nonlinear electrical transmission line (NLTL) with linear dispersion. With the help of the derived CNLS equations, we present and analyze explicit expressions for the instability growth rate of a purely growing modulational instability (MI). We establish that the phenomenon of the MI can be observed only for “small” nonzero modulation wavenumbers. Also, we point out the effects of the linear dispersive element, as well as of the frequencies of the signal packets, on the instability growth rate. It is shown that the linear dispersion and the frequencies of signal packets can be well used to control the instability domain. Through the CNLS equations, we analytically investigate the propagation of solitary waves in the network. Our analytical studies show four types of interaction of signal packets propagating in the network: bright–bright, dark–dark, bright–dark and dark–bright soliton interactions.     

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.     

F-函数扩展法求解超介质中的亮孤子和暗孤子

利用F-函数扩展法求解超介质中的超短脉冲传输方程, 探讨了超介质中的反常自陡效应和特有的二阶非线性色散效应所导致的新的孤子现象和规律. 结果表明, 正折射区的二阶非线性色散效应可以代替线性色散效应形成亮孤子; 正、负折射区的反常自陡效应由于其符号可改变, 从而可在特定条件下分别在反常色散和正常色散区形成有别于常规介质的亮、暗孤子; 反常自陡效应的符号或者反常自陡效应和三阶线性色散效应的相互比较关系能够控制亮、暗孤子中心的漂移方向. 关键词： 孤子 超介质 F-函数扩展法     

Two-component coupled photovoltaic soliton pair in two-photon photorefractive materials under open circuit conditions

The existence and nonlinear dynamics of two-component incoherently coupled composite solitons in two-photon photorefractive materials under open circuit conditions have been investigated. In the steady-state regime, these incoherently coupled solitons can propagate in bright–dark, bright–bright and dark–dark configurations. These photovoltaic soliton families can be established provided that the carrier beams share the same polarization and wavelength. The influence of the gating beam on the dynamics of stable solitons is discussed. Numerical simulations show that these solitons are stable for small perturbation on amplitude.     

Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing,defocusing and mixed type nonlinearities

Bright and bright-dark type multisoliton solutions of the integrable N-coupled nonlinear Schrödinger (CNLS) equations with focusing, defocusing and mixed type nonlinearities are obtained by using Hirota’s bilinearization method. Particularly, for the bright soliton case, we present the Gram type determinant form of the n-soliton solution (n:arbitrary) for both focusing and mixed type nonlinearities and explicitly prove that the determinant form indeed satisfies the corresponding bilinear equations. Based on this, we also write down the multisoliton form for the mixed (bright-dark) type solitons. For the focusing and mixed type nonlinearities with vanishing boundary conditions the pure bright solitons exhibit different kinds of nontrivial shape changing/energy sharing collisions characterized by intensity redistribution, amplitude dependent phase-shift and change in relative separation distances. Due to nonvanishing boundary conditions the mixed N-CNLS system can admit coupled bright-dark solitons. Here we show that the bright solitons exhibit nontrivial energy sharing collision only if they are spread up in two or more components, while the dark solitons appearing in the remaining components undergo mere standard elastic collisions. Energy sharing collisions lead to exciting applications such as collision based optical computing and soliton amplification. Finally, we briefly discuss the energy sharing collision properties of the solitons of the (2+1) dimensional long wave-short wave resonance interaction (LSRI) system.     

Photons trapping within a nano-ring resonator controlled by light

We propose the interesting results that a bright and dark soliton pulse can be localized within a nonlinear nano-waveguide. The system consists of nonlinear micro- and nano-ring resonators, whereas the soliton pulse can be input into the system and trapped within the nano-waveguide. A soliton input is chopped by the nonlinear effects known as chaos into smaller pulses. The required pulse is filtered and amplified, which can be controlled and localized within the nano-waveguide. The localized bright and dark solitons are trapped within a nano-waveguide by controlling the nano-waveguide input power, which means that the photons trapping is controlled by light.     

拉曼增益对双折射光纤中孤子传输特性的影响

本文采用考虑拉曼增益的耦合非线性薛定谔方程,利用分步傅里叶方法求解并仿真模拟了光孤子脉冲在不同性质的双折射光纤中传输时的演化过程.结果表明,拉曼增益可以有效抑制非线性耦合导致的孤子漂移,同时会导致光孤子脉冲峰值在传输时不断增大,产生拉曼放大效应.拉曼增益也可以有效抑制双折射光纤中传输的相邻光孤子之间的相互作用.     

高阶效应影响下高阶孤子在超常介质中的传输特性研究

基于描述超短脉冲在超常介质中传输的非线性薛定谔方程,本文数值研究了高阶效应影响下高阶亮、暗孤子在超常介质中的传输情况。数值模拟表明,三阶色散和自陡峭效应都会引起高阶孤子的分裂和辐射,破坏高阶亮孤子周期性演化特性,导致高阶暗孤子分裂出的灰孤子不对称;孤子的阶数越高,三阶色散和自陡峭的影响越大。利用超常介质可控的色散和非线性特性,通过调节三阶色散和自陡峭效应的系数,发现超常介质中可以基本支持二阶亮孤子、二阶暗孤子和三阶暗孤子的稳定演化。本文的研究结果为将来进一步研究超常介质中高阶亮、暗孤子的存在及传输特性提供了一定的参考价值。     

A novel temporal dark-bright solitons conversion system via an add/drop filter for signal security use

We propose a new design of a security scheme by using the nonlinear behaviors of temporal dark and bright solitons within a micro-ring resonator system for signal security application. When a dark soliton pulse is input into the proposed system, the chaotic signal is generated, where the required bright soliton pulse can be retrieved and detected by the add/drop filtering device. The chaotic wave form can be cancelled by using an add/drop device, which can be connected and used in the communication link. By using the appropriate ring parameters, simulation results obtained have shown that the soliton conversion can be performed. The ring radii used are within the ranges from 5 to 10 μms and A_eff=0.10-0.50 μm². In application, the chaotic signal is generated and formed by the dark soliton within a nonlinear micro-ring device. This can be seen by using the add/drop device, where the bright soliton is formed and detected, which is available to use in communication link. The different temporal soliton response time is seen, the response times of 169 and 84 ns are noted for temporal dark and bright solitons, respectively, which can also be used to form the security key.     

飞秒暗孤子间相互作用的数值研究

通过数值模拟对飞秒暗孤子间的相互作用进行了研究，并且同飞秒亮孤子和皮秒暗孤子分别进行了比较，结果表明：同飞秒亮孤子相比，飞秒暗孤子间的相互作用比较小，前者表现为相互吸引、碰撞、合二为一，然后相互排斥，不具有周期性；而后者从一开始就相互排斥，且这种排斥作用较亮孤子来说相当微弱，同样也不具有周期性。此外，数值模拟的结果还表明，飞秒暗孤子间的相互作用同皮秒尺度下暗孤子间的相互作用基本一致，并且通过计算表明，飞秒暗孤子间的相互作用在一定范围内仍可利用皮秒尺度下暗孤子间相互作用的经验公式。但是，数值模拟结果显示，两孤子的初始间距越小，由经验公式计算结果所带来的误差就越大。     

New Exact Jacobi Elliptic Function Solutions of Three-Dimensional Nonlinear Helmholtz Equation in a Nonlinear Kerr-Type Medium

In this letter the three-dimensional nonlinear Helmholtz equation is investigated, which describes electro-magnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic functionsolutions are obtained, by using our extended Jacobian elliptic function expansion method. When the modulus m → 1or0, the corresponding solitary waves including bright solitons, dark solitons and new line solitons and singly periodicsolutions can be also found.     

Backward-wave propagation and discrete solitons in a left-handed electrical lattice

We study experimentally, analytically and numerically the backward-wave propagation, and formation of discrete bright and dark solitons in a nonlinear electrical lattice. We observe experimentally that a focusing (defocusing) effect occurs above (below) a certain carrier frequency threshold, and backward-propagating bright (dark) discrete solitons are formed. We develop a discrete model emulating the relevant circuit and benchmark its linear properties against the experimental dispersion relation. Using a perturbation method, we derive a nonlinear Schrödinger equation, that predicts accurately the carrier frequency threshold. Finally, we use numerical simulations to corroborate our findings and monitor the space-time evolution of the discrete solitons.     

The linear and nonlinear optical effects of white light

An overview of our research group’s experimental and theoretical developments is provided on the linear and nonlinear optical effects of white light since 2003. Their work includes the experimental researches on the white light one-dimensional photovoltaic dark spatial solitons and the waveguides and directional couplers induced by them, the circular and elliptic white-light dark spatial solitons and the white-light photorefractive phase masks, two-dimensional white-light photonic lattices and the applicati...     

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg-Landau equation with variable coefficients

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.     

Matching group velocity of bright and/or dark solitons via double-dark resonances

We propose a scheme which can generate group velocity matching bright and/or dark solitons in a four-level tripod configuration atomic system via double-dark resonances. It is shown that the linear absorption properties can be controlled by the controlling fields. For the nonlinear case, the optical soliton can form in the first and second electromagnetically induced transparency windows and their group velocities can be matched under the condition of equal half Rabi frequencies of the two controlling fields. We also show that adjusting the amplitude and group velocity of the soliton as well as the bright and dark solitons conversion can be realized.     

一种基于非线性光纤环镜开关特性的超短光孤子产生方法

提出了一种利用非线性光纤环镜的开关特性将连续波同时转化为亮孤子和暗孤子的新方法 ,即让连续波和另一波长的调制脉冲串共同耦合入光纤环镜 ,交叉相位调制使得一部分连续波被环镜透射 ,其余部分被反射 ;再让透射波和反射波分别在反常色散光纤和正常色散光纤中传输 ,自相位调制和群速度色散之间的相互作用使得透射波和反射波分别演化为亮、暗孤子。数值计算表明 ,该方法不仅可产生脉宽比调制脉冲窄、重复频率比调制脉冲高的亮孤子和暗孤子 ,而且几乎可将全部的连续波能量转化为孤子能量。     

Soliton Properties of Light Pulses on the Surface of Ionic Crystals Generated by Strong Nonlinear Effects

In this paper, we theoretically discuss the soliton properties of light pulse transportation on the surface of an ionic crystal having strong nonlinear interactions between ions of unit cells. We analyze in detail the dark solitons when the nonlinear coefficient g is positive and negative, respectively. It is found that whether the nonlinear coefficient g is positive or negative, the dark solitons can be formed over the whole dispersion relation area of surface polaritons considering nonlinear effects. Attention should be paid to the fact that around ωTO, the light pulse can form advanced dark solitons, and there is a switching area from advanced dark soliton to retarded dark soliton near ωTO. We also discuss the effects of higher nonlinear dispersion on the solitons.