Photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers

Quantum photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers are studied on the basis of the complex Ginzburg-Landau equation model. We find that, depending on their phase difference, the total photon-number noise of the bound soliton pair can be larger or smaller than that of a single soliton, and the two solitons in the soliton pair have a corresponding positive or negative photon-number correlation. It is predicted for the first time to our knowledge that out-of-phase soliton pairs can exhibit less noise as a result of negative correlation.     

Random evolution and coherence degradation of a high-order optical soliton train in the presence of noise

The intrinsic evolution of a high-order soliton described by the nonlinear Schr?dinger equation is initiated by a self-four-wave mixing effect (or modulational instability) and recurs neatly every soliton period. We show that when there is noise such as amplified spontaneous emission, however, a high-order soliton evolves randomly and independently and is distorted because the evolution is initiated by noise. Thus the time and the frequency coherence of a soliton pulse train are both greatly degraded.     

Numerical investigation of slow solitons in Bragg gratings with a hyperbolic tangent apodization

This paper numerically and analytically investigates the formation and propagation motion of optical soliton in the Bragg grating.We choose the fibre Bragg grating with hyperbolic tangent apodization in the middle section in order to obtain slower solitons.Optical fibre soliton but not Bragg grating soliton is used as input pulse in the discussion,which is much more approximate to the light source for the practical purpose.We discuss in detail the effects of the soliton’s velocity with some parameters in the process of transmission.The results show that by choosing special parameters,one can make the soliton slow-down with a little distortion and energy decay and obtain tunable time-delay on a small scale.     

Dark and bright photovoltaic spatial solitons in photorefractive crystals with positive refractive-index perturbation

We have demonstrated, for what is believed to be the first time, that in a photorefractive crystal with positive refractive-index perturbation a two-dimensional dark or bright photovoltaic spatial soliton can be formed in the same crystal by a signal beam and a background beam of different wavelengths. We discuss the conditions on the effective Glass constants and the absorption coefficients of the background and signal beams in determining the formation of the spatial soliton.     

Long-Time Dynamics of Korteweg–de Vries Solitons Driven by Random Perturbations

This paper deals with the transmission of a soliton in a random medium described by a randomly perturbed Korteweg–de Vries equation. Different kinds of perturbations are addressed, depending on their specific time or position dependences, with or without damping. We derive effective evolution equations for the soliton parameter by applying a perturbation theory of the inverse scattering transform and limit theorems of stochastic calculus. Original results are derived that are very different compared to a randomly perturbed Nonlinear Schrödinger equation. First the emission of a soliton gas is proved to be a very general feature. Second some perturbations are shown to involve a speeding-up of the soliton, instead of the decay that is usually observed in random media.     

饱和对数非线性介质中非相干孤子碰撞对相干性的改善

基于相干密度理论，数值地研究了饱和对数非线性支持的部分非相干亮孤子对的相互作用.研究表明，两个非相干亮孤子碰撞不仅能增大碰撞区的光强，还可以大大改善部分非相干光束的相干性.同时还研究了非相干性对孤子碰撞的影响，非相干性不仅抑制了孤子间的相干作用如吸引、排斥和能量交换，同时还由于非相干叠加作用而引入了弱的相互吸引. 关键词： 非相干性 饱和对数非线性 空间光孤子     

AdS/CFT Correspondence and Dark Soliton

In this paper we use the AdS/CFT correspondence to study dark soliton solutions in a holographic model of a relativistic superfluid. We calculate the length scales corresponding to the condensate and the charge density depletion, and find relation with the chemical potential. We compare our solutions with the quasiparticle excitations above the holographic superfluid and find that the scale of the excitations is comparable to the soliton coherence length scales.     

增益噪声对光孤子通信系统码率距离积的限制

在采用周期性能量补偿的全光孤子通讯系统中,比特率距离积受到孤子脉冲到达时间的Gordon-Haus效应的限制。本文讨论有损光纤中微扰对孤子群速度偏移的影响,分析集中式和分布式能量补偿方式下,增益噪声引起的孤子到达时间抖动,并由此得出系统的极限比特率距离积的大小。分析结果表明:在实际系统中,分布式能量补偿方式下系统极限比特率距离积一般要比集中式能量补偿方式下的高出一倍以上。 关键词：     

Controlling soliton explosions

We investigate the dynamics of solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will show that, in some cases, while some conditions are satisfied, the soliton explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We believe these mechanisms can explain some of the phenomena that recently have been reported to occur in excitable media. We present a method for controlling soliton explosions.     

Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion

Soliton propagation in a cascaded dispersion-managed optical amplifier system with zero net dispersion is examined. We present a qualitative physical explanation for the recently discovered fact that a soliton with finite energy can propagate down a fiber line with zero or normal average dispersion. We describe a specific practical system for the main properties of such a soliton, namely, the dependence of the soliton power on the pulse width at chirp-free points and the soliton average energy and width at chirp-free points as functions of the dispersion-allocation (strength of the map) parameter.     

Soliton assisted control of source to drain electron transport along natural channels – crystallographic axes – in two-dimensional triangular crystal lattices

We present computational evidence of the possibility of fast, supersonic or subsonic,nearly loss-free ballistic-like transport of electrons bound to lattice solitons (a formof electron surfing on acoustic waves) along crystallographic axes in two-dimensionalanharmonic crystal lattices. First we study the structural changes a soliton creates inthe lattice and the time lapse of recovery of the lattice. Then we study the behavior ofone electron in the polarization field of one and two solitons with crossing pathways withsuitably monitored delay. We show how an electron surfing on a lattice soliton may switchto surf on the second soliton and hence changing accordingly the direction of its path.Finally we discuss the possibility to control the way an excess electron proceeds from asource at a border of the lattice to a selected drain at another border by followingappropriate straight pathways on crystallographic axes.     

Ratchet and switching effects in stochastic kink dynamics

We study collective dynamics in a chain of harmonically coupled particles subjected to degenerate but asymmetric on-site double-well potentials and driven by white and exponentially correlated noise. The difference of frequencies of small-amplitude oscillations in the vicinity of the wells appears to be a sufficient condition for the existence of the soliton ratchet effect. We find directed thermally activated soliton motion while at certain critical values of either the correlation time or noise strength, a reversal (switching) of the direction of motion takes place. Furthermore, we observe stochastic soliton transport directed against an applied d.c. field.     

Effective Dynamics of Double Solitons for Perturbed mKdV

We consider the perturbed mKdV equation \({\partial_t u = -\partial_x (\partial_x^2u + 2u^3- b(x,t)u)}\) , where the potential \({b(x,t)=b_0(hx,ht), 0 < h \ll 1 }\) , is slowly varying with a double soliton initial data. On a dynamically interesting time scale the solution is \({ {\mathcal{O}}(h^2) }\) close in H ² to a double soliton whose position and scale parameters follow an effective dynamics, a simple system of ordinary differential equations. These equations are formally obtained as Hamilton’s equations for the restriction of the mKdV Hamiltonian to the submanifold of solitons. The interplay between algebraic aspects of complete integrability of the unperturbed equation and the analytic ideas related to soliton stability is central in the proof.     

Bright matter wave solitons and their collision in Bose–Einstein condensates

We obtain the bright matter wave solitons in Bose–Einstein condensates from a trivial input solution by solving the time dependent Gross–Pitaevskii (GP) equation with quadratic potential and exponentially varying scattering length. We observe that the matter wave density of bright soliton increases with time by virtue of the exponentially increasing scattering length. We also understand that the matter wave densities of bright soliton trains remain finite despite the exchange of atoms during interaction and they travel along different trajectories (diverge) after interaction. We also observe that their amplitudes continue to fluctuate with time. For exponentially decaying scattering lengths, instability sets in the condensates. However, the scattering length can be suitably manipulated without causing the explosion or the collapse of the condensates.     

Propagation of electromagnetic soliton in anisotropic biquadratic ferromagnetic medium

The information storage technology based on anisotropic ferromagnets with sufficiently high magneto-optical effects has received much attention in recent years. The magneto-optical recording combines the merits of magnetic and optical techniques. We investigate the magneto-optical effects on a biquadratic ferromagnet and show that the dynamics of the system is governed by a perturbed nonlinear Schrödinger equation. The evolutions of amplitude and velocity of the soliton are found to be time independent, thereby admitting the lossless propagation of electromagnetic soliton in the medium, which may have potential applications in accordance with the soliton based optical communication systems. We also exploit the role of perturbation, which has a significant impact on the propagation of electromagnetic soliton.     

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.     

Computer simulation and observation of anomalous light emission from nonlinear photonic crystal with various geometry of its elements

Recently, in papers [1, 2] were described the effect of long-time emission of photonic crystal (synthetic opals) under the action of nanosecond laser pulse. The duration of the luminescence is of the order of seconds. Despite on the other phenomena, which were considered in these papers, below we focus our attention on possible explanation of long time emission from nonlinear photonic crystal. The basis of our consideration is papers [3, 4], those deal with soliton formation in several layers of 1D nonlinear photonic crystal. Because of this, the light wave can exist in photonic crystal a long time (in ideal case—infinite time interval). Taking into account a relation between soliton duration and its maximum intensity, the leaving of laser energy from the layer of photonic crystal takes place due not full reflection from boundaries of layer. The time of light emission for this case depends on nonlinear susceptibility of photonic crystal and the intensity of laser pulse. Hence, soliton formation inside the nonlinear elements of photonic crystal can be one of the reasons of long time emission. We got in computer simulation a long time emission of 1D (layered) and 2D (circular or rectangular elements) nonlinear photonic crystal under the action of laser pulse with femtosecond duration under the conditions of soliton formation in some elements of photonic crystal. Input intensity of laser pulse, at which a soliton appears in nonlinear photonic crystal, can be ten times less due to effects of enhancement of optical intensity in periodic structure [4, 5].     

Passive harmonic mode locking of soliton bunches in a fiber ring laser

We report on the experimental observation of passive harmonic mode locking of bunches of single-pulse solitons or twin-pulse solitons in an Erbium-doped fiber ring laser. Experimental investigations on the phenomenon revealed that, although the soliton interaction between the adjacent single-/twin-pulse solitons in a bunch is weaker than that of the pulse interaction in the twin-pulse solitons, a soliton bunch could also function as a unit and form the state of passively harmonic mode-locking. Harmonic mode-locking is one of the intrinsic characteristics of soliton emission in passively mode-locked fiber ring lasers. It can be formed based on the single-pulse soliton, twin-pulse soliton, or bunch of solitons.     

Soliton equations and pseudospherical surfaces

All the soliton equations in 1 + 1 dimensions that can be solved by the AKNS 2 × 2 inverse scattering method (for example, the sine-Gordon, KdV or modified KdV equations) are shown to describe pseudospherical surfaces, i.e., surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws and Bäcklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out.