Self-action of laser radiation in cluster plasma

We have analytically and numerically studied the self-action dynamics of laser radiation in a plasma with ionized gas clusters. Based on the simplified model of a cluster in the form of a superposition of two charged (electron and ion) bunches, we analyze the nonlinearity mechanisms. We refine the electrodynamic cluster model by the molecular dynamics method. The polarization behavior of the plasma bunch in the main part of the laser pulse is shown to be the same as that in the simplified model. We investigate the self-action dynamics of laser radiation under conditions when the nonlinearity of the stratified medium is determined by the anharmonicity of the electron motion in the cluster, while the group velocity dispersion is determined by both the background plasma and the ionized clusters. Since the characteristic field for the electron nonlinearity depends strongly on the cluster size, the peculiarities of the self-action dynamics result from plasma bunch expansion. The spatiotemporal evolution of the wave field is shown to be accompanied by pulse self-compression near the trailing edge.     

Structural features of self-action of laser radiation in the electromagnetic induced transparency mode

Structural features of the laser radiation self-focusing dynamics in the electromagnetic induced transparency (EIT) band are studied for an atomic system with a Λ-type energy level diagram. Effective nonlinearity of an EIT medium is manifested primarily as nonlinear dispersion (dependence of the group velocity on the wave amplitude). Qualitative analysis of the dynamics of self-action of laser pulses, which is confirmed by numerical simulation, shows that nonlinear evolution of a 3D wave packet follows the scenario of self-focusing, which serves as the background on which the envelope profile turnover and the formation of a shock wave occur at an advanced rate.     

Self-focusing of wave packets and envelope shock formation in nonlinear dispersive media

The self-action of three-dimensional wave packets is analyzed analytically and numerically under the conditions of competing diffraction, cubic nonlinearity, and nonlinear dispersion (dependence of group velocity on wave amplitude). A qualitative analysis of pulse evolution is performed by the moment method to find a sufficient condition for self-focusing. Self-action effects in an electromagnetically induced transparency medium (without cubic nonlinearity) are analyzed numerically. It is shown that the self-focusing of a wave packet is accompanied by self-steepening of the longitudinal profile and envelope shock formation. The possibility of envelope shock formation is also demonstrated for self-focusing wave packets propagating in a normally dispersive medium.     

The structural features of wave collapse in medium with normal group velocity dispersion

The dynamic characteristics of self-action in three-dimensional wave packets described by the nonlinear Schrödinger equation with a hyperbolic space operator were studied analytically and numerically. The class of the initial wave field distributions for which self-focusing effects predominated over dispersion spreading and caused the arising of wave collapses was considered. The collapse of tubular wave packets was shown to be accompanied by packet shape changes during its contraction to the axis of the system. The nonlinear stabilization of collapses resulted in wave field fragmentation in the longitudinal direction followed by the expansion of the bunches thus formed along the axis. The dynamics of collapses was numerically studied taking into account medium nonlinearity saturation and nonlinear dissipation.     

Regime of wave-packet self-action in a medium with normal dispersion of the group velocity

Peculiar features of the self-action of non-one-dimensional wave packets described by the nonlinear Schrodinger equation with a hyperbolic spatial operator were studied analytically and numerically. It was shown that the self-action dynamics is determined by the consequence of the processes of transverse self-focusing filamentation and longitudinal splitting. Splitting scenarios were classified. It is shown that the strongest inhomogeneities are excited along "hyperbolas" in the self-similar collapse process.     

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%.     

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.     

Nonlinear effects of self-action of waves in 2D coupled ferromagnetic structures

Magnetostatic wave self-action effects in a 2D structure consisting of two ferromagnetic films have been studied using a numerical solution to the system of two-dimensional nonlinear Schrödinger equations. Main features of these effects have been analyzed in comparison with similar effects in a 2D structure based on a single film. The applicability of coupled structures to control the formation of 2D nonlinear wave beams and magnetostatic wave packets has been considered.     

Self-action of electromagnetic wave in plasma under parametric instability

The self-action of a strong electromagnetic wave in an inhomogeneous plasma is considered near the plasma resonance.     

Self-Action of Nonparaxial Few-Cycle Optical Waves in Dielectric Media

A mathematical model of evolution of the space–time spectra of nonparaxial few-cycle optical waves in isotropic dielectric media with an arbitrary dispersion of the refractive index and the inertialess third-order nonlinearity has been discussed. It has been shown that, at the self-focusing of a wave single-cycle at the input to a nonlinear medium into an optical filament with transverse dimensions comparable with the central radiation wavelength, the strength of the increased longitudinal component of its electric field can become larger than the initial longitudinal component by a factor of 7 and can be 18% of the transverse component of the input wave field. Errors of the calculations of the self-action of radiation with superwide time and spatial spectra within simplified mathematical models have been estimated.     

Lattice Boltzmann simulation for the energy and entropy of excitable systems

The internal energy and the spatiotemporal entropy of excitable systems are investigated with the lattice Boltzmann method.The numerical results show that the breakup of spiral wave is attributed to the inadequate supply of energy,i.e.,the internal energy of system is smaller than the energy of self-sustained spiral wave.It is observed that the average internal energy of a regular wave state reduces with its spatiotemporal entropy decreasing.Interestingly,although the energy difference between two regular wave states is very small,the different states can be distinguished obviously due to the large difference between their spatiotemporal entropies.In addition,when the unstable spiral wave converts into the spatiotemporal chaos,the internal energy of system decreases,while the spatiotemporal entropy increases,which behaves as the thermodynamic entropy in an isolated system.     

Quasi-Potential Equations for a Complex Two-Particle System in the Context of Scalar Theories with Self-Action

Within the framework of the covariant simultaneous approach of quantum field theory, a complex system of two identical scalar particles with third- and fourth-order self-action is examined. Explicit forms of the retarded component of the Green's two-time function and of the energy-dependent interaction operator of the system are obtained in the lowest orders of perturbation theory. Three-dimensional quasi-potential equations for the relativistic wave function of a bound state are derived. Based on the results obtained, a complex system of two Higgs bosons is examined.     

Wave processes in microinhomogeneous elastic media with hysteretic nonlinearity and relaxation

The nonlinear propagation of an initially harmonic acoustic wave in a microinhomogeneous medium containing defects with quadratic hysteretic nonlinearity and relaxation is studied by the perturbation method. The frequency dependences of the effective nonlinearity parameters are determined for the self-action of the quasi-harmonic acoustic wave and the higher harmonic generation processes.     

Peculiarities of the Self-Action of Inclined Wave Beams Incident on a Discrete System of Optical Fibers

Based on a discrete nonlinear Schrödinger equation (DNSE), we studied analytically and numerically the peculiarities of the self-action of one-dimensional quasi-optic wave beams injected into a spatially inhomogeneous medium consisting of a set of equidistant mutually coupled optical fibers. A variational approach allowing the prediction of the global evolution of localized fields with the initially plane phase front was developed. The self-consistent equations are obtained for the main parameters of such beams (the position of the center of mass, the effective width, and linear and quadratic phase-front corrections) in the aberrationless approximation. The case of radiation incident on a periodic system of nonlinear optical fibers at an angle to the axis oriented along them is analyzed in detail. It is shown that for the radiation power exceeding a critical value, the self-focusing of the wave field is observed, which is accompanied by the shift of the intensity maximum followed by the concentration of the main part of radiation only in one of the structural elements of the array under study. In this case, the beams propagate along paths considerably different from linear and the direction of their propagation changes compared to the initial direction. Asymptotic expressions are found that allow us to estimate the self-focusing length and to determine quite accurately the final position of a point with the maximum field amplitude after radiation trapping a channel. The results of the qualitative study of the possible self-channeling regimes for wave beams in a system of weakly coupled optical fibers in the aberrationless approximation are compared with the results of direct numerical simulations within the DNSE framework.     

CO2激光器对相位共轭波时空混沌系统控制和同步的研究

以一维耦合映象格子为对象,研究了相位共轭波时空混沌系统特性. 基于Lyapunov稳定性定理,通过选取耦合参数,实现了CO₂激光器对相位共轭波时空混沌系统的控制,以及驱动多个相位共轭波时空系统达到并行同步. 数值模拟结果显示,耦合参数对相位共轭波时空混沌系统的控制和同步速度有影响,即耦合参数越大同步时间越短. 关键词： 2激光器')" href="#">CO₂激光器 相位共轭波 时空混沌 控制和同步     

On self-focusing of an ultrashort intense relativistic laser pulse in a plasma

The development of the spatiotemporal (filamentation) instability of a laser pulse upon excitation of a plasma wave is studied numerically and analytically. It is shown that first, as in a medium with inertialless cubic nonlinearity, the filamentation of radiation occurs and then filaments are attracted to each other. The following evolution differs weakly from the evolution of a smoothed wave beam in a medium with inertial nonlinear response.     

Transverse instability of optical spatiotemporal solitons in quadratic media

We present experimental and numerical observations of transverse instability in quadratic media under conditions that emphasize the inherently spatiotemporal and multidimensional nature of the wave propagation. Intensity-dependent beam filamentation is shown to be closely connected to the periodic evolution of quadratic solitons, and implications for the generation of three-dimensional spatiotemporal solitons are discussed.     

Self-action of seismic acoustic waves in the moist sandy soil

The effect of phase self-action of the longitudinal seismic acoustic wave observed in moist sandy soil is studied theoretically in framework of the phenomenological equation of state.     

FitzHugh-Nagumo系统中螺旋波的控制

采用FitzHugh-Nagumo方程,研究了二维时空系统中螺旋波的控制问题,利用相空间压缩方法对部分系统变量的振幅进行限制从而影响螺旋波的稳定性.研究表明,控制过程可分为三个不同的阶段:在较小压缩限条件下螺旋波可以被完全消除,系统进入均匀定态;在较大的压缩限条件下螺旋波能够稳定存在,而且其振荡频率不随控制参数的改变而发生变化;当压缩限介于上述两者之间时,系统表现为时空混沌态.对上述控制过程进行了进一步的讨论,研究了不同控制参数条件下的系统斑图、变量的演化、相空间轨道等性质,并且对振幅函数和振荡频率特征进 关键词： 螺旋波 相空间压缩 FitzHugh-Nagumo方程