Propagation of nonlinear longitudinal waves in a solid with regard to the interaction between the strain field and the field of defects

A model of nonlinear longitudinal wave propagation in a solid with quadratic nonlinearity of an elastic continuum exposed to laser impulses is developed in view of the interaction between the strain field and the field of point defects. The influence of the generation and recombination of laser-induced defects on the propagation of an elastic strain wave is analyzed. The existence of a nonlinear elastic shock wave of low intensity is revealed in the system and its structure is studied. The estimations of the depth and velocity of the wave front are performed. The contributions due to the interaction of the strain field and the field of defects to both a linear elastic modulus and the dispersion parameters of a lattice are found.     

Stationary thermomagnetic waves in superconductors

The propagation of a nonlinear stationary thermomagnetic wave in superconducting media is qualitatively analyzed in view of the effect of an external magnetic field. The velocity and the thickness of the wave front are estimated. It is demonstrated that the inclusion of an external magnetic field affects the thermomagnetic wave profile only slightly.     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

Localization in the model of contacting media with specific nonlinearity and interface interaction

In this paper, we consider the new model of nonlinear contacting media based on nonlinear Schrodinger equation with point potential and term, which is depended stepwise on field amplitude. Such a model theoretically describes a change in properties of the boundary regions along the interface between a Kerr-type crystal with cubic nonlinearity and a nonlinear medium characterized by abruptly change in dielectric constant depending on field amplitude. The short-range local interaction between wave and interface is taken into account by point potential in nonlinear Schrodinger equation. We obtain two new types of localized states characterized by composite structure consisting of three parts of the field distributions. We find exact and approximate solutions of dispersion equations. We described new properties of the spectrum of localized states arising as a result of the interaction of the wave with the interface and the presence of threshold field of the switching between the medium constants. All results are obtained in an analytical form. The proposed theory can be used to describe the propagation features of intense light beams localized along media interfaces in nonlinear optics, and to describe Bose-Einstein condensates with cubic nonlinearity.     

圆管结构中周向导波非线性效应的模式展开分析

在二阶微扰近似条件下, 采用导波模式展开分析方法研究了圆管结构中周向导波的非线性效应. 伴随基频周向导波传播所发生的二次谐波, 可视为由一系列二倍频周向导波模式叠加而成. 从动量定理出发, 结合柱坐标系下非线性应力张量及其散度的数学表达式, 针对圆管中某一基频周向导波模式, 推导出相应的二倍频应力张量及二倍频彻体驱动力的数学表达式, 建立了确定二倍频周向导波模式展开系数的控制方程, 得到了伴随基频周向导波传播所发生的二次谐波声场的形式解. 理论分析和数值计算表明, 当构成二次谐波声场的某一二倍频周向导波模式与基频周向导波的相速度匹配时, 该二倍频周向导波模式的位移振幅表现出随传播周向角积累增长的性质; 当两者的相速度失配时, 二倍频周向导波的振幅随传播周向角表现出“拍”效应.     

Spontaneously generated walking X-shaped light bullets

In quadratic nonlinear media with normal dispersion and nonvanishing group velocity mismatch between fundamental wave and second-harmonic pulses, the wave packets of two harmonics can be locked together in propagation in the form of walking X-shaped light bullets. The output wave packets are developed into X-shaped light bullets with significant group delay time due to mutual dragging and significant shifting in spatiotemporal spectrum due to delayed nonlinear phase shift. We also show that spontaneously generated phase-front tilting can balance the dragging force induced by group velocity mismatch and lead to zero-velocity walking X-shaped light bullets.     

Nonlinear propagation and control of acoustic waves in phononic superlattices

The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.     

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.     

光纤光栅非线性对色散特性的影响

通过在能量较高、考虑非线性时,求解光纤光栅非线性耦合模方程连续波条件下的解,得到光纤光栅失谐量δ与光脉冲传播常量q的非线性色散关系和光栅致群速度色散系数βg2与δ的关系.用MATLAB绘图,得到非线性参量γ和光脉冲能量P0的乘积γP0对色散和βg2的影响.结果表明:随着βg2的增加,非线性色散曲线的上、下两支向δ的负值区移动,当超过某一临界值时,曲线上支开始形成环,这时光纤光栅引起的群速度色散中的反常色散区消失,全部变成正常色散.     

Second Harmonic Generation of Lamb Wave in Numerical Perspective

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective.Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching,with and without group velocity matching,respectively.The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance.The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity.The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective,while group velocity matching is demonstrated to not be a necessary condition.     

有偏压中心对称光折变晶体中的屏蔽孤子

给出了中心对称光折变晶体中屏蔽孤子的高阶空间电荷场.当高阶项可以忽略时,这个电荷场就变为早前在中心对称光折变晶体中研究的屏蔽孤子的空间电荷场.研究了中心对称光折变晶体中屏蔽孤子的高阶非线性波动方程.在适当的条件下,这个非线性波动方程能够展示明暗空间光孤子.这类晶体不同于非中心对称晶体,其非线性折射率的改变来源于二次电光效应,而不是一般的线性电光效应.应用光束传播的方法,对这些孤子的稳定性进行了讨论.表明在小的微扰下这类孤子是稳定的,不会发生分裂.     

Self-action dynamics of ultrashort electromagnetic pulses

The self-action dynamics of three-dimensional wave packets whose width is on the order of the carrier frequency is studied under fairly general assumptions concerning the dispersion properties of the medium. The condition for the wave field collapse is determined. Self-action regimes in a dispersion-free medium and in media with predominance of anomalous or normal group velocity dispersions are numerically investigated. It is shown that, for extremely short pulses, nonlinearity leads not only to the self-compression of the wave field but also to a “turn-over” of the longitudinal profile. In a dispersionless medium, the formation of a shock front within the pulse leads to the nonlinear dissipation of linearly polarized radiation and to self-focusing stabilization. For circularly polarized radiation, the wave collapse is accompanied by the formation of an envelope shock wave.     

Nonlinear Stability of Weak Detonation Waves¶for a Combustion Model

We show that the weak detonation waves for a combustion model of Rosales–Majda are nonlinearly stable. Because of the strongly nonlinear nature of the wave, usual stability analysis of weakly nonlinear nature does not apply. The chemical switch on-off is the main feature of nonlinearity. In particular, the propagation of the wave depends sensitively on the tail behaviour of the flow in front of it. Unlike the strong detonation waves, a weak detonation is supersonic and there is the separation of the gas waves from the reacting front. As a consequence, the reacting front needs to be traced. Received: 6 October 1998 / Accepted: 2 February 1999     

Wave packet dynamics in a nonlinear tunnel-coupled structure of right- and left-handed media

The dynamics of a wave packet formed by tunnel-coupled forward and backward waves in a waveguide structure consisting of media with different signs of real parts of their refractive indices is investigated. Expressions for coupled-wave amplitude and reflection and transmission coefficients that are corrected for absorption are derived in the linear approximation. The expressions governing the wave-packet duration and propagation velocity of its envelope maximum are derived, taking into account the second-order dispersion, cubic nonlinearity, and dispersion of the nonlinearity. The possibility of efficient control of the forward wave velocity by applying an external magnetic field is demonstrated.     

Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

A multiscale model for the two-dimensional nonlinear wave propagation in a locally microdamaged medium is presented, and numerical simulations are analyzed in view of nondestructive testing applications. The multiscale model uses a statistical distribution of hysterons and upscales their microscopic stress-strain relations to a mesoscopic level. Macroscopic observations are then predicted by finite integration techniques. The influence of a small region with hysteretic nonlinearity on the generation of harmonics is investigated, and numerical results for different amplitudes of the input signal and different analysis techniques of the response signal are presented. Second, a study is conducted on the interaction of a Rayleigh wave with a microdamaged zone with hysteretic nonlinearity at the surface of an otherwise linear body, and the influence of the microdamaged zone on the surface wave velocity and on the generation of harmonics is examined. It is found that the effect of hysteresis on the Rayleigh wave propagation can be barely seen in the surface wave velocity measurement, but shows up nicely in the wave spectrum. The potential of a nonlinearity based depth profiling technique is explored by evaluating the nonlinear responses at different frequencies for a vertically stratified medium with spatially varying hysteresis properties.     

Nonlinear propagation of spark-generated N-waves in air: modeling and measurements using acoustical and optical methods

The propagation of nonlinear spherically diverging N-waves in homogeneous air is studied experimentally and theoretically. A spark source is used to generate high amplitude (1.4 kPa) short duration (40 μs) N-waves; acoustic measurements are performed using microphones (3 mm diameter, 150 kHz bandwidth). Numerical modeling with the generalized Burgers equation is used to reveal the relative effects of acoustic nonlinearity, thermoviscous absorption, and oxygen and nitrogen relaxation on the wave propagation. The results of modeling are in a good agreement with the measurements in respect to the wave amplitude and duration. However, the measured rise time of the front shock is ten times longer than the calculated one, which is attributed to the limited bandwidth of the microphone. To better resolve the shock thickness, a focused shadowgraphy technique is used. The recorded optical shadowgrams are compared with shadow patterns predicted by geometrical optics and scalar diffraction model of light propagation. It is shown that the geometrical optics approximation results in overestimation of the shock rise time, while the diffraction model allows to correctly resolve the shock width. A combination of microphone measurements and focused optical shadowgraphy is therefore a reliable way of studying evolution of spark-generated shock waves in air.     

Stability of self-similar plane shocks with Hertzian nonlinearity

The nonlinear progressive wave equation [McDonald and Kuperman, J. Acoust. Soc. Am. 81, 1406-1417 (1987)] is expressed in a form to accommodate Hertzian nonlinearity of order n=3/2 typical of granular media. Stability of self-similar plane weak shocks against perturbations in three dimensions is demonstrated for arbitrary order nonlinearity with 1 相似文献   

On the Traversal Time of Barriers

Fifty years ago Hartman studied the barrier transmission time of wave packets (J Appl Phys 33:3427–3433, 1962). He was inspired by the tunneling experiments across thin insulating layers at that time. For opaque barriers he calculated faster than light propagation and a transmission time independent of barrier length, which is called the Hartman effect. A faster than light (FTL or superluminal) wave packet velocity was deduced in analog tunneling experiments with microwaves and with infrared light thirty years later. Recently, the conjectured zero time of electron tunneling was claimed to have been observed in ionizing helium inside the barrier. The calculated and measured short tunneling time arises at the barrier front. This tunneling time was found to be universal for elastic fields as well as for electromagnetic fields. Remarkable is that the delay time is the same for the reflected and the transmitted waves in the case of symmetric barriers. Several theoretical physicists predicted this strange nature of the tunneling process. However, even with this background many members of the physics community do not accept a FTL signal velocity interpretation of the experimental tunneling results. Instead a luminal front velocity was calculated to explain the FTL experimental results frequently. However, Brillouin stated in his book on wave propagation and group velocity that the front velocity is given by the group velocity of wave packets in the case of physical signals, which have only finite frequency bandwidths. Some studies assumed barriers to be cavities and the observed tunneling time does represent the cavity lifetime. We are going to discus these continuing misleading interpretations, which are found in journals and in textbooks till today.