Nonlinear propagation of relativistically intense electromagnetic waves in a collisionless plasma

We discuss the nonlinear propagation of relativistically intense electromagnetic waves into collisionless plasmas with special emphasis on one dimensional plane wave solutions of the propagating, standing and modulated types. These solutions exhibit a rich variety of phenomena associated with relativistic electron mass variation and coupling between transverse electromagnetic and longitudinal fields. They have important applications to problems of laser propagation, self-focusing in overdense plasmas, particle and photon acceleration and to electromagnetic radiation around pulsars.     

Experimental study of solitary waves in a nonlinear transmission line

Several properties of solitary waves were measured on a nonlinear transmission line. These include the transition from a linear dispersive response into a solitary wave response as the amplitude of a narrow voltage impulse is increased, and an observation of the recurrence phenomena of solitary waves. Supported in part by the National Science Foundation.     

A Perturbation Method for Complex Root Finding of Nonlinear Electromagnetic Waves

Aspects of the perturbation method are presented and implemented on the analytic function of the complex variable for the propagation of nonlinear electromagnetic surface guided by a thin film. The behavior of nonlinear TE waves guided by asymmetrical dielectric thin film, bounded by a generalizes nonlinear substrate with a permittivity of the form | E | is analyzed. The complex roots, which correspond to the propagation and attenuation coefficient are obtained and discussed.     

Extended Hyperbola Function Method and Its Application to Nonlinear Equations

An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.     

Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation

In this Letter, we present an analytical study of a high-order acoustic wave equation in one dimension, and reformulate a previously given equation in terms of an expansion of the acoustic Mach number. We search for non-trivial traveling wave solutions to this equation, and also discuss the accuracy of acoustic wave equations in terms of the range of Mach numbers for which they are valid.     

Nonlinear interaction of a Gaussian EM beam with an electrostatic upper hybrid wave: Stimulated Raman scattering

Summary In this paper we have studied the nonlinear interaction of a Gaussian electromagnetic beam with an electrostatic upper hybrid wave in a collisionless magnetized plasma. On account of the interaction of the incident Gaussian electromagnetic beam with the plasma, a time-independent component of the ponderomotive force becomes finite and leads to the modification in the background density. This results in the excitation of the upper hybrid mode of the plasma. The excited electrostatic wave leads to the enhanced Raman backscattering. An expression for the scattered power is derived and the effect of the external static magnetic field on the enhancement of the density perturbation and scattered power is discussed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

双面金属包覆介质波导模序数的判别方法

在双面金属包覆介质波导中 ,随着介质层厚度的变化 ,会出现TM0 模与TM1 模的分离和简并两种状态 ,从而影响衰减全反射 (ATR)谱中模序数的确认。通过对金属波导的理论分析和实验研究 ,提出了三种模序数确认方法 :本征角计算法、吸收峰全峰半宽比较法和吸收峰峰间距比较法 ,实现了两种状态下对模序数的准确判断     

Nonlinear three-wave equation for a polydisperse gas-liquid mixture

A new nonlinear three-wave equation of the sixth order for pressure in a polydisperse gas-liquid mixture with bubbles of two sizes is obtained, and its stationary solutions are analyzed. The equation includes two nonlinear quadratic terms of different derivative orders. These terms are of fundamental importance for obtaining good correspondence between the solutions to this equation and the experimentally observed solitary waves in the form of two coupled solitons.     

Nonlinear frequency mixing in a resonant cavity: Numerical simulations in a bubbly liquid

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared. The results show highly efficient generation of the difference frequency at high excitation amplitude. The large acoustic nonlinearity of the bubbly liquid that is responsible for the strong difference-frequency resonance also induces significant enhancement of the parametric frequency mixing effect to generate second harmonic of the difference frequency.     

基于四波混频的光纤非线性系数测量方法

为解决四波混频法测量光纤非线性系数未考虑泵浦消耗而导致结果不准确的问题,提出了一种在简并四波混频情况下测量非线性系数的方法.根据光纤中简并的四波混频理论,推导出了考虑泵浦消耗和光纤损耗的椭圆方程.通过设定数值计算所需的各个参量并利用简单的数学方法分析了计入泵浦消耗、光纤损耗的必要性,得到被测光纤的非线性系数,与Optisystem的仿真结果一致.研究表明,这种改进的测量方法不但适用于小信号情形下的四波混频过程,还可以应用于出现参量饱和现象的场合,为进一步设计光纤2R再生器件提供了重要依据.     

Impedance Characteristics of Closed Elliptic-Groove Waveguide for Millimeter Waves

A characteristic equation and impedance characteristic for the dominant mode of closed elliptic-groove guide have been analyzed and discussed by using the mode-matching method. The reference size of the closed elliptic-groove guide for the good impedance matching with rectangular guide in actual application is given. The obtained conclusions are of important significance in theoretical studies and actual applications of closed elliptic-groove guide for millimeter waves.     

Nonlinear guided waves in plates: A numerical perspective

Harmonic generation from non-cumulative fundamental symmetric (_S0$S_0$) and antisymmetric (_A0$A_0$) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.     

克尔型非线性薄膜波导的TE模

对于芯区为克尔型非线性介质，覆盖层和衬底为线性介质的平板波导，用Ｋｒｙｌｏｖ－Ｂｏｇｏｌｉｕｂｏｖ－Ｍｉｔｒｏｐｏｌｓｋｙ的渐近法导出了色散方程及场分布的二阶近似数学表达式，计算量大为减少且结果精确。给出了对称和非对称情况的典型实例。     

驻波法测超声波衰减系数

用驻波法测量超声波在空气中衰减系数的实验方法。与前人的方法进行比较。新的测量结果更符合实际。只有当换能器反射系数r〈0.619时,用简单波拟合得到的衰减系数才比较可信。同时讨论了该方法的实用意义。     

一种新型非晶态分子材料的非线性光学折射率和吸收特性

用单光束扫描法测量了在532nm处一种新型非晶态分子材料5,5′Bis(dimesitylboryl)2,2′bithiophene的非线性折射率和吸收系数样品非线性透射特性的分析表明,在靠近线性吸收区的532nm处有饱和吸收存在由三能级饱和模型和Zscan法确定了饱和强度、非线性折射率的实部和虚部研究结果表明:这种新型非晶态分子材料具有非常好的光子学应用前景.     

A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation, a new algebraic method, which contains the terms of radical expression of functions f（ξ）, is constructed to explore the new exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to nonlinear Klein-Gordon equation, and some new exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.     

Nonlinear elastic waves in a monatomic chain with nonlinear interactionReceived

Nonlinear wave equation for a one-dimensional anharmonic crystal lattice in terms of its microscopic parameters is obtained by means of a continuum approximation. Using a small time scale transformation, the nonlinear wave equation is reduced to a combine     

Nonlinear elastic waves in a monatomic chain with nonlinear interaction

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Nonlinear Study on FEM Amplifier with a Novel Elliptic-Groove Guide

FEM amplifier with a novel elliptic-groove guide is proposed and three-dimensional nonlinear theory for the elliptic-groove guide FEM amplifier is developed. A set of coupled nonlinear differential equations is derived and the characteristics of this FEM amplifier are numerically analyzed in detail including the evolution of power, efficiency and bandwidth. The effects on saturation efficiency due to electron momentum spread and wiggler taper are also studied.