Generalized Theory of One-Dimensional Steady-State Optical Spatial Solitons

We present a generalized soliton theory based on the one-dimensional generalized nonlinear Schroedinger equation,from which one can easily obtain the bright, dark, and grey soliton waveforms, and their existence curves. We show that the forming conditions of spatial solitons are directly dependent on the relationship between the index perturbation and the intensity, no matter whether the index perturbation is positive or negative. Some relevant examples are presented when the solitons are supported by the photoisomerization nonlinearity.     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.     

Optical spatial solitons supported by photoisomerization nonlinearity in a polymer

We present a theory for a new type of optical spatial soliton that is based on the angle hole burning mechanism of photoisomerization in some polymers. We predict that the photoisomerization nonlinearity can support steady-state dark and bright spatial solitons in the polymer. We also discuss the dependence of the FWHM of the spatial soliton on wavelengths of the background beams and on the ratio of the intensity of the background beam to that of the signal beam.     

Dark Solitons for the Defocusing Cubic Nonlinear Schrödinger Equation with the Spatially Periodic Potential and Nonlinearity

We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.     

Subwavelength spatial solitons

We analyze the effects of additional terms in the nonlinear Schr?dinger equation for spatial solitons, directly derived from the Maxwell's equations with the Kerr nonlinearity, on the shapes of bright and dark solitons with a fixed polarization. Combining analytical and numerical methods, we find that the additional terms always render the solitons broader. The most essential result is a fundamental limitation on the width of the subwavelength soliton: The ratio of the FWHM of the bright soliton to the wavelength cannot be smaller than 1/2, and the same ratio for the FWHM of the dark soliton cannot be smaller than 1/4.     

Counterpropagating spatial Kerr soliton in reflection gratings

We analytically predict the existence of both spatial bright and dark counterpropagating solitons in a reflection grating in the presence of the Kerr nonlinearity. The basic trapping mechanism consists of a twofold balance where diffraction is compensated by self-focusing and reflection is altered by the nonlinear-induced interferometric grating. We find that, whenever the spectral soliton profile lies within the grating stop band, bright and dark solitons exist only if the mutual phase of the counterpropagating solitons is pi or 0, respectively.     

Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction

Exact unified rational solutions describing a family of Peregrine solitons as well as related algebraic soliton pairs in either self-focusing or self-defocusing Kerr media are presented, with distinct defining regimes and an explicit relationship for those of opposite nonlinearity. The active role of the space–time correction effect that plays in these soliton species is highlighted, leading to unique dynamics such as the persistence of Peregrine solitons in a defocusing Kerr medium, the availability of giant peak amplitude for the bright–bright soliton pair, and the existence of so-called bright–dark soliton pair. The evolution dynamics of the algebraic two-soliton state toward a spliced single soliton is also discussed.     

What types of spatial soliton can be formed based on two-photon-isomerisation?

In this paper we answer the question: “what types of spatial soliton can be formed based on two-photon-isomerisation (TPI)”. The conclusion that anti-dark solitons are not supported by monotonic nonlinearity should cast light on the notion of fundamental spatial solitons. The idea to obtain a bright TPI soliton with the joining of a background light or with the coupling of a dark soliton offers new schemes of light-controlling-light.     

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.     

Localization of solitons: linear response of the mean-field ground state to weak external potentials

Two aspects of bright matter?Cwave solitons in weak external potentials are discussed. First, we briefly review recent results on the Anderson localization of an entire soliton in disordered potentials, as a paradigmatic showcase of genuine quantum dynamics beyond simple perturbation theory. Second, we calculate the linear response of the mean-field soliton shape to a weak, but otherwise arbitrary, external potential, with a detailed application to lattice potentials.     

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.     

闭路光伏光折变聚合物中非相干耦合亮-暗空间孤子对

为了得到闭路光折变有机聚合物中存在非相干耦合亮-暗光伏空间孤子对,采用数值模拟的方法,对稳态情况下两束互不相干的光束,在闭路光伏光折变有机聚合物中的传播进行了研究。结果表明,具有相同偏振和相同波长的两束互不相干的光束,可在光伏光折变有机聚合物中形成非相干耦合亮-暗光伏孤子对。在给定适当参量或扰动不太大的情况下,孤子对中的亮孤子和暗孤子都能在光伏光折变有机聚合物中稳定传播。研究结果可为光折变有机聚合物空间孤子理论的发展提供理论依据。     

Controlling the collision between two solitons in the condensates by a double-barrier potential

We present an analytical solution of two solitons of Bose-Einstein condensates trapped in a double-barrier potential by using a multiple-scale method.In the linear case,we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence.For weak nonlinearity,it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties.Especially,in the case of regarding a double-barrier potential as the output source of the solitons,the collision spots between two dark solitons can be controlled by the height of the barrier potential.     

Non-autonomous bright matter wave solitons in spinor Bose–Einstein condensates

We investigate the dynamics of bright matter wave solitons in spin-1 Bose–Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross–Pitaevskii (3-GP) equations using Hirota?s method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite–Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.     

Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates

We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length.     

An exact (2 + 1)-dimensional optical soliton with spatially modulated nonlinearity and an external potential

An exact (2 + 1)-dimensional spatial optical soliton of the nonlinear Schrödinger equation with a spatially modulated nonlinearity and a special external potential is discovered in an inhomogeneous nonlinear medium, by utilizing the similarity transformation. Exact analytical solutions are constructed by the products of Whittaker functions and the bright and dark soliton solutions of the standard stationary nonlinear Schrödinger equation. Some examples of such composed solutions are given, in which these spatial solitons display different localized structures. Numerical calculation shows that the soliton is stable in propagating over long distances, thus also confirming the validity of the exact solution.     

光折变介质中空间光孤子自弯曲现象研究

光折变非线性介质在外加直流电压时会引起介质内部电荷移动,而移动后的电荷又会导致空间电荷的扩散效应,从而产生非局域非线性现象。从理论上研究了具有流动和扩散非局域非线性的光折变晶体中所支持的空间光学孤子的传播行为。应用等效粒子近似方法分析了这类介质中(1 1)维空间光学孤子动力学行为,得出孤子运动"加速度"显式解。孤子的有效"加速度"决定于孤子参量和光折变非局域参量。所得的解析结果可在一定参量范围内直接用来计算孤子的传播轨迹。对孤子在光折变非局域非线性作用下的传播动力学行为做了仿真模拟,数值模拟结果与理论分析结论符合得很好。     

Modulation instability of bright photovoltaic solitons on a partially incoherent background

We present the observation of incoherent anti-dark photovoltaic solitons in LiNbO₃:Fe crystal. This new class of soliton states involves bright photovoltaic solitons on a background beam meeting ?? > 1, where ?? is the ratio of background illumination photovoltaic constant to that of soliton beam. For ?? < 1, dark photovoltaic solitons are generated. Furthermore, this novel type solitons are investigated experimentally by injecting coherent light and partially coherent background of infinite extent. In case of spatial coherence of the background lower than the threshold of incoherent modulation instability, these results indicate that bright photovoltaic solitons can propagate in a stable fashion.     

Effect of temperature on the evolution of bright and dark screening—photovoltaic spatial solitons

We investigate theoretically the temperature effects on the evolution of both bright and dark screening-photovoltaic optical spatial solitons in biased photovoltaic-photocefractive crystals in the case of neglecting the diffusion process.For a stable bright or dark screening-photovoltaic soliton originally formed in a crystal at a given temperature,when the crystal temperature changes,it will evolve into another stable screening-photovoltaic soliton if the change is quite small,whereas it will become unstable or break down if the temperature change is large enough.The spatial shape of a stable screening-photovoltaic soliton can be reshaped by appropriately adjusting the crystal temperature.