Self-constriction of a wave packet in a non-linear medium

The possibility of a controlled deformation of a wave packet in the non-linear medium is discussed. The exact analytical solutions, describing, in the bounds of non-linear geometrical optics, the pulse envelope evolution and the non-linear modulation of such a packet, are found.     

New Cnoidal and Solitary Wave Solutions of Coupled Higher-Order Nonlinear SchrSdinger System in Nonlinear Optics

The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.     

The non-linear Schrödinger equation and the non-stationary evolution of the intense localized wave field

The possibility of the origin of the high intensity localized region near the wave pulse maximum is illustrated by means of exact solutions of the non-linear Schrödinger equation. The critical and supercritical regimes of wave pulse non-stationary evolution are illustrated. The tendencies of evolution depend essentially upon the initial profile of the pulse.     

The self-action of the electromagnetic field in a medium with considerable nonlinearity

The propagation of the electromagnetic wave field in a nonlinear medium is discussed in the framework of generalized nonlinear geometrical optics. In this approach the nonlinearity of the medium and the angles between the rays and the general orientation of the wave's beam are not assumed to be small. The exact analytical solutions of the equations of this generalized nonlinear geometrical optics are constructed. These solutions show the possibility of a peculiar mechanism of space stratification of the field.     

The controlled non-linear evolution of TE and TH ps-pulses in Selfoc fibre

The threshold amplitude values for fundamental and higher TE and TH modes of intense ps-pulses in Selfoc optical fibres responsible for non-linear self-constriction of these pulses are determined. The non-linear stabilization of TH pulses in the vicinity of these thresholds may be associated with smaller amplitudes than for TE ones. The characteristic scales of non-linear evolution, calculated for higher modes are longer than for fundamental modes. The asymmetric evolution of initially symmetric ps-pulses due to the relaxation of non-linearity is analysed both for self-constriction and self-spreading of such pulses. The exact analytical solutions described the intense ps-pulse rebuilding in the framework of the inverse scattering method and non-linear geometric optics are obtained.     

Study of Exact Solutions to Cubic-Quintic Nonlinear Schrödinger Equation in Optical Soliton Communication

A systematic method which is based on the classical Lie group reduction is used to find the novel exact solution of the cubic-quintic nonlinear Schrödinger equation (CQNLS) with varying dispersion, nonlinearity, and gain or absorption. Algebraic solitary-wave as well as kink-type solutions in three kinds of optical fibers represented by coefficient varying CQNLS equations are studied in detail. Some new exact solutions of optical solitary wave with a simple analytic form in these models are presented. Appropriate solitary wave solutions are applied to discuss soliton propagation in optical fibres, and the amplification and compression of pulses in optical fibre amplifiers.     

Theory of the statistical properties of ultra-short pulses generated by a passively mode-locked solid-state laser

The evolution of ultra-short pulses from noise in a passively mode-locked solid-state laser is treated. The statistical properties of the laser field, such as correlation functions, the mean pulse shape and its fluctuations, are investigated. The maximum intensity and the width of the pulse train are estimated taking account of the amplification saturation. As an example of the application of the results to non-linear optics, TPF traces are calculated.     

The stratification of a wave packet in a nonlinear medium

The possibility of controlled large-scale stratification of the wave impulse in the nonlinear medium is discussed. The wide class of exact analytical solutions, describing, in the bounds of the nonlinear geometrical optics, the formation of the new intensity maxima, are found. The characteristics dimensions of the oscillations of the packet are much greater than the wave length.     

Parametric amplification of chirped optical pulses under pump depletion

We present simple analytical solutions of coupled wave equations describing chirped pulse parametric amplification under pump depletion. The evolution of the duration and spectrum of amplified pulses in OPA pumped by Gaussian and supergaussian pulses has been investigated both numerically and analytically. Also, the dependence of the energy conversion efficiency from pump to signal was determined for a range of parameter values, and an optimum ratio of signal and pump pulse durations was evaluated.     

Complex geometrical optics of Kerr type nonlinear media

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.     

Localized nonlinear waves in combined time-dependent magnetic–optical potentials with spatiotemporally modulated nonlinearities

We construct explicit novel solutions of the nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. By using a modified similarity transformation we explore some localized nonlinearities and combined time-dependent magnetic–optical potentials in the form of linear-lattice ones and harmonic-lattice ones. Several families of exact localized nonlinear wave solutions in terms of Mathieu and elliptic functions corresponding to these potentials are then studied, such as snakelike solitons and breathing solitons. The stability of the obtained localized nonlinear wave solutions is investigated numerically such that some stable solutions are found.     

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.     

Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift

We solve the higher order nonlinear Schr?dinger equation describing the propagation of ultrashort pulses in optical fibers. By means of the coupled amplitude-phase formulation fundamental (solitary wave) dark soliton solutions are found.     

用错位相位光栅产生的可调光学双阱

提出了用相位型错位光栅产生光学双阱的新方案.用平面光波(或TEM₀₀模式高斯光波)照射、正透镜聚焦,在透镜焦平面上产生的适用于冷原子或冷分子囚禁的多对可调光学双阱.计算和推导了双阱的光强分布、强度梯度以及光阱的几何参数与光学系统参数间的解析关系,研究了双阱到单阱三种不同的演化过程.同时还计算了光学双阱囚禁冷原子的光学偶极势和光子散射速率.研究发现,该方案不仅简单可行、操作方便,而且在原子物理、原子光学、分子光学和量子光学领域中有着广阔的应用前景. 关键词： 原子光学 相位光栅 光学双阱 冷原子囚禁     

Stability Analysis of Solitary Wave Solutions for Coupled and(2+1)-Dimensional Cubic Klein-Gordon Equations and Their Applications

The searching exact solutions in the solitary wave form of non-linear partial differential equations(PDEs play a significant role to understand the internal mechanism of complex physical phenomena. In this paper, we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the(2+1)-dimensional cubic Klein-Gordon(K-G) equation. The Klein-Gordon equation are relativistic version of Schr¨odinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which severa solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions o PDEs arise in mathematical physics.     

Space- and time-resolved Brillouin light scattering from nonlinear spin-wave packets

We have constructed a new Brillouin light scattering apparatus, based on the Sandercock multipass tandem interferometer design, for space- and time-resolved investigations of nonlinear wave packets in thin films. We have applied the method to studies of nonlinear spin-wave pulse propagation in yttrium iron garnet (YIG) films. Spatial resolution is achieved by scanning the laser spot across the YIG film surface, and temporal resolution is obtained by measuring the elapsed time between the launch of spin-wave pulses by an applied microwave pulse and the arrival of the respective inelastically scattered photons at the detector. We report the observation of nonlinear self-focusing of wave beams and pulses in one and two dimensions, the formation of one-dimensional envelope solitons, and of strongly localized, two-dimensional wave packets, 'spin-wave bullets', analogous to 'light bullets' predicted in nonlinear optics. By generating two counter-propagating wave pulses, pulse collision experiments were performed. We show that quasi-one-dimensional envelope solitons formed in narrow film stripes ('waveguides') retain their shapes after collision, while two-dimensional spin-wave packets formed in wide YIG films are destroyed in collision.