Weakly nonparaxial spatial solitons in a medium with Kerr nonlinearity

A version of perturbation theory is developed that intends to determine the field distribution of spatial solitons with a 2D transverse profile in a Kerr medium in the case of small deviations from paraxial conditions. An approximate master equation for transverse components of the electric field in the case of wide solitons is derived. By solving this equation starting from the unperturbed soliton, i.e., Townes mode with linear polarization of radiation, a solution with an axially symmetric field distribution is found. Dependences of the main soliton characteristics on the degree of paraxiality are determined.     

Dissipative Solitons in the Complex Ginzburg-Landau Equation for Femtosecond Lasers

We consider the models of generating femtosecond radiation in solid-state lasers with passive mode locking. An approach in which ultrashort laser pulses (USPs) are associated with the complex Ginzburg-Landau equation (GLE) is developed. The structure of solitons and the range of parameters of their existence are analytically determined and the stability criteria of those solitons are formulated for a number of limiting cases. The scenarios of the cyclic spectral and temporal dynamics of dissipative solitons due to the instability of the background field are studied.     

Structure of Energy Fluxes in Topological Three-Dimensional Dissipative Solitons

The internal structure of dissipative topological solitons has been revealed by example of three-dimensional dissipative optical solitons with one open and one closed dislocation lines of a wavefront. This structure is manifested in the existence of critical points, lines, and surfaces in the field of electromagnetic energy fluxes (Poynting vector). The conservation of the topological characteristics of such solitons, which can be formed in a homogeneous laser medium with saturated amplification and absorption or in lasers with quite large longitudinal and transverse dimensions, provides additional capabilities for information applications.     

Regular and stochastic motion of dissipative optical solitons

Investigations of the motion of dissipative optical solitons and their complexes in wide-aperture nonlinearly optical (with coherent pump radiation) and laser (with incoherent pump radiation) systems have been reviewed. An important characteristic of dissipative solitons is the topology of the energy fluxes, which determines the internal structure of individual solitons and makes it possible to certainly separate the cases of the weak and strong interactions between the solitons. It has been shown that the character of the regular motion of dissipative soliton structures in a homogeneous system is determined by the symmetry of the transverse distributions of the intensity and energy flux; the motion of asymmetric structures is curvilinear. This is also valid for complexes of three-dimensional dissipative optical solitons, “laser bullets.” The extreme possibilities of localization of solitons are determined by quantum noises. The corresponding Brownian motion of the center of the dissipative optical soliton is characterized by a much lower level of the statistic dispersion of the coordinates of its center and velocity than that in the case of conservative solitons.     

Analysis of Nonlinear TE Waves in a Periodic Refractive Index Structure with a Nonlinear Cladding

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First principle theory for cavity solitons in semiconductor microresonators

Cavity solitons are similar to spatial solitons, appearing as localized bright dots in the transverse intensity profile of the electromagnetic field, but they arise in dissipative systems. In this paper we consider a broad-area vertical-cavity semiconductor microresonator, driven by an external coherent field, at room temperature. The active material is constituted by a Multiple Quantum Well GaAs/AlGaAs structure (MQW). We present a set of nonlinear dynamical equations for the electric field and the carrier density valid for both a passive and an active (i.e. with population inversion) configuration. The complex nonlinear susceptibility is derived on the basis of a full many-body theory, with the Coulomb enhancement treated in the Padé approximation. The linear stability analysis of the homogeneous steady states is performed with a generalised approach, and numerical simulations demonstrating the existence of spatial patterns and cavity solitons in experimentally achievable parameter regions are given for the two configurations. Received 18 January 2001     

Large amplitude electromagnetic solitons in intense laser plasma interaction

This paper shows that the standing, backward- and forward-accelerated large amplitude relativistic electromagnetic solitons induced by intense laser pulse in long underdense collisionless homogeneous plasmas can be observed by particle simulations. In addition to the inhomogeneity of the plasma density, the acceleration of the solitons also depends upon not only the laser amplitude but also the plasma length. The electromagnetic frequency of the solitons is between about half and one of the unperturbed electron plasma frequency. The electrostatic field inside the soliton has a one-cycle structure in space, while the transverse electric and magnetic fields have half-cycle and one-cycle structure respectively. Analytical estimates for the existence of the solitons and their electromagnetic frequencies qualitatively coincide with our simulation results.     

圆波导硅探测结构对X波段电磁波模式的响应

采用数值模拟和理论分析方法,研究了圆波导内置n-Si探测结构对X波段几种常用电磁波模式的电场响应。首先基于强电场下的热载流子效应,设计了一种利用n-Si进行高功率脉冲实时测量的圆波导探测结构。接着采用三维并行电磁场时域有限差分方法,模拟研究并分析了TE11(两种极化方向)、TM01和TE01模式作用下圆波导探测结构内的横向电场分布特点。结果表明:不同模式下探测芯片内的横向电场均以径向电场为主,径向和角向电场幅度比约为10,而芯片在圆波导内引入的横向电场驻波比均不大于1.3。最后推导了圆波导探测结构在不同模式电场作用下的灵敏度表达式,理论分析指出了探测结构的最大承受功率与圆波导模式有关,最高可达422MW,响应时间则均为ps量级,初步证实了该探测结构可用于X波段百MW级脉冲波源在线探测的可行性。     

一维光伏空间灰孤子及其稳定性研究

从考虑背景光的光伏作用后的光束在光伏媒质中传播的方程出发,证明了在折射率改变为正的光伏媒质中也可以形成灰孤子。光束以灰孤子状态在光伏晶体中传播时,其横向相位必须具有一个与光强分布有关的形式分布,表达式为φ（s）=v[η-∫y^-2（η）dη],其中v是灰孤子的横向运动速度,η是无量纲化坐标,y（η）是归一化的光场振幅。分别讨论了光束灰度、光强振幅、信号光与背景光的有效Glass系数之比R对一维的光伏空间灰孤子宽度、横向总相移和横向运动速度的影响,并分析了光伏灰孤子的稳定性。当光束的灰度m为0时,这一理论可直接退化为光伏暗孤子的理论。     

A three-soliton structure with strong and weak coupling in a wide-aperture laser with saturable absorption

A soliton complex consisting of three laser solitons is found with the help of numerical simulation of the spatiotemporal structure of the field in a wide-aperture class-A laser with saturable absorption in the mean field approximation with respect to the longitudinal coordinate. Two solitons are strongly coupled and rotate, whereas the third one is weakly coupled with this pair of solitons and revolves around it with a smaller angular velocity. A phase portrait of transverse energy fluxes of radiation that corroborates this type of coupling between the solitons is presented.     

Holographic solitons in photorefractive dissipative systems

A new kind of holographic soliton is proposed for a photorefractive dissipative system consisting of a biased photorefractive crystal and a strong pump beam with a uniform spatial distribution in both transverse dimensions. The self-trapping beam in the system can evolve into a spatial soliton when it couples coherently with the pump beam by two-wave mixing. Unlike the holographic solitons recently proposed by Cohen et al. [Opt. Lett. 27, 2031 (2002)], the most unique features of the present solitons are that they have a fixed amplitude and width that are determined completely by the system parameters and that their existence conditions are independent of the polarity of the bias field. Numerical simulations show that these solitons are stable relative to small perturbations.     

Propagation of vector solitons in a quasi-resonant medium with stark deformation of quantum states

The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces ?? transitions, while the extraordinary component induces the ?? transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.     

局域单PT对称势中多级孤子的传输特性研究

具有Parity-Time(PT)对称性的光学系统是近年提出的一种新型光学结构,在光开关、光子信息处理器件等方面具有潜在的应用。研究了局域单PT对称光学系统中双级孤子和三级孤子的存在范围与稳定特性。研究结果表明:多级孤子存在一临界传播常数,传播常数对应了线性模下的本征值。双级孤子和三级孤子仅能在较深的PT对称势中才能稳定地传输。多级孤子的稳定性的范围随着PT对称势的深度增加而扩大;孤子的能量随着传播常数的增大而增加,但随着PT对称势的调制深度的增加而减少。     

Soliton dynamic structure factors in a planar ferromagnetic chain

For a planar ferromagnetic chain in a transverse magnetic field we present calculations for the soliton contribution to the longitudinal and transverse dynamic structure factors. We treat the solitons as a dilute relativistic ideal gas. Criteria for the breakdown of the continuum sine-Gordon model are discussed.     

Beat excitation of terahertz radiation in a semiconductor slab in a magnetic field

Two infrared lasers of frequencies ω₁ and ω₂ propagating in the TM/TE mode along $\stackrel{?}{z}$ direction in a rippled density semiconductor waveguide are shown to resonantly excite terahertz radiation at the beat frequency when ripple wave number is suitably chosen to satisfy the phase matching. The wave vector of the density ripple is along the direction of laser propagation while a static magnetic field is applied transverse to it. The lasers exert a ponderomotive force on the electrons at the beat frequency. This force, in the presence of density ripple and transverse magnetic field, produces a nonlinear current at the terahertz frequency. The magnetic field enhances the amplitude of the terahertz wave. However terahertz yield is significantly higher in the TM mode laser beating than in the TE mode laser beating.     

Generation of high order multi-bound solitons and propagation in optical fibers

We demonstrate experimental generation of multi-bound solitons of up to sextuple in an active FM mode-locked fiber ring laser operating under power saturation in the locking state. The ring laser consists of two booster optical amplifiers operating in saturation regime, an electro-optic phase modulator driven by a sinusoidal electrical wave and a length of dispersive fiber. The periodic phase modulation generates phase chirp of the generated lightwaves in the ring laser. The chirped phase state plays an important role in the phase matching condition for mode-locking as well as the stabilization and the determination of the bound states of multi-solitons. The formation of such high order multi-bound solitons is explained based on the chirping of the phase and the behavior of the optical pulse sequence in the near field region of the dispersive fiber. The propagation of these multi-bound solitons through single mode optical fibers is observed. Experimental and simulation results of bound solitons have been shown to follow similar trends.The propagation of these multi-bound solitons through single mode optical fibers is described. Their mutual interaction through such quadratic phase media shows the influence of the quadratic phase property on the differential phase of individual solitons of the bound group. Simulated results confirm the evolution of the bound solitons over dispersive single mode optical fibers.     

Ince-Gaussian solitons in strongly nonlocal nonlinear media

We have introduced a novel class of higher-order spatial optical Ince-Gaussian solitons (IGSs) that constitute the third complete family of exact and orthogonal soliton solutions of the Snyder-Mitchell model. The transverse structure of the IGSs is characterized by the Ince polynomials and has an inherent elliptical symmetry. The IGSs form the exact and continuous transition modes between Hermite-Gaussian solitons and Laguerre-Gaussian solitons.     

Quasi-solitonic propagation modes of two-component acoustic video pulses in a paramagnetic crystal

Nonlinear propagation of longitudinal-transverse acoustic pulses down to a length of one cycle (video pulses) in a low-temperature paramagnetic crystal in the direction parallel to an external magnetic field is investigated theoretically. The case of a crystal with paramagnetic impurity ions with effective S=1/2 spin is considered. It is shown that, due to spin-phonon interaction, two-component acoustic pulses can propagate in the form of high-power quasi-solitons. Conditions are determined for the formation of exponentially localized subsonic rational solitons which propagate with a velocity higher than the velocity of transverse sound and which have a transverse component with a rotating plane of polarization.     

Optical vortex solitons in parametric wave mixing

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a "halo-vortex," consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a "ring-vortex" soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.     

Solitons in PT-symmetric potential with competing nonlinearity

We investigate the effect of competing nonlinearities on beam dynamics in PT-symmetric potentials. In particular, we consider the stationary nonlinear Schrödinger equation (NLSE) in one dimension with competing cubic and generalized nonlinearity in the presence of a PT-symmetric potential. Closed form solutions for localized states are obtained. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow associated with these complex solitons is also examined.