Theorie der parametrischen Vier-Photonen-Wechselwirkung. II., Verstärkung und Oszillation in der Näherung des vorgegebenen Pumpfeldes)

The processes of parametric amplification and oscillation in a medium with cubic polarization is investigated in parametric approximation. For the case of amplification the threshold power of the pump wave is calculated. The influence of a finite phase mismatching and of the initial phases on the amplification process is discussed. For larger values of mismatching a periodical change between amplification and depletion may appear. For the cases of a single resonant oscillator (for the signal wave only), a double resonant oscillator (for both signal and idler wave) and a double resonant oscillator with the pump wave reflected at the second mirror the threshold power of the pump wave and the rise time are calculated. Characteristic differences between four-photon and three-photon parametric oscillators are discussed. A numerical estimation of the threshold power for some media with nonlinear susceptibilities known from literature leads to the conclusion that the realization of a four-photon parametric oscillator should be possible. In the appendix we discuss the influence of diffraction, focussing, birefrigence, nonstationarity and depletion of the pump wave on the studied process as well as the conditions under which these effects can be neglected.     

Wave dispersion in viscoelastic single walled carbon nanotubes based on the nonlocal strain gradient Timoshenko beam model

Based on the nonlocal strain gradient theory and Timoshenko beam model, the properties of wave propagation in a viscoelastic single-walled carbon nanotube (SWCNT) are investigated. The characteristic equations for flexural and shear waves in visco-SWCNTs are established. The influence of the tube size on the wave dispersion is clarified. For a low damping coefficient, threshold diameter for shear wave (SW) is observed, below which the phase velocity of SW is equal to zero, whilst flexural wave (FW) always exists. For a high damping coefficient, SW is absolutely constrained, and blocking diameter for FW is observed, above which the wave propagation is blocked. The effects of the wave number, nonlocal and strain gradient length scale parameters on the threshold and blocking diameters are discussed in detail.     

共振条件下载波包络相位效应对阈上电离谱的影响

本文通过求解三维含时薛定谔方程, 从理论上研究了共振条件下氢原子的光电子能谱与角分布随着激光脉冲载波包络相位(CEP)的变化规律. 研究结果表明: 在共振位置附近, 光电子能谱的强度与CEP有强烈的依赖关系; 进一步对各个分波的分析, 可以确定共振电离初态的角量子数. 此外, 利用光电子的角分布信息, 可以对多周期激光脉冲的初始相位信息进行高精度探测. 关键词： 阈上电离 超短脉冲 载波包络相位     

原子核的单粒子共振态

采用基于相对论平均场的耦合常数解析延拓方法研究球形核的单粒子共振态.具体计算了Zr同位素链中巨晕核的核芯核122Zr阈值附近的中子共振态的能量、宽度和波函数,其结果同相应的散射相移法的结果一致. Using analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory, the energies, widths and wave functions for single-particle resonant states close to the continuum threshold are evaluated. Predictions are also compared with corresponding results obtained by the scattering phase shift method.     

The Spectrum of Squeezing in Degenerate Four-Wave Mixing

We analyze a simple model for degenerate four wave mixing, introduced by Savage and Walls. In the resonant case, the system exhibits a phase instability when the pump intensity is increased well beyond the threshold for generation of the signal mode. Still in the resonant configuration, we calculate the amplitude and phase squeezing spectra both for the signal and the pump mode. In the signal (pump) mode, the squeezing becomes especially large when the signal (pump) mode is much more damped than the pump (signal) mode. The signal field can exhibit both phase and amplitude squeezing, in distinct domains of the parameter space. On the other hand, the pump field can show squeezing only in the amplitude quadrature component. In general, the model exhibits sizable squeezing over very extended regions of the parameter space.     

Spontaneous hole-clump pair creation in weakly unstable plasmas

A numerical simulation of a kinetic instability near threshold shows how a hole and clump spontaneously appear in the particle distribution function. The hole and clump support a pair of Bernstein, Greene, Kruskal (BGK) nonlinear waves that last much longer than the inverse linear damping rate while they are upshifting and downshifting in frequency. The frequency shifting allows a balance between the power nonlinearly extracted from the resonant particles and the power dissipated into the background plasma. These waves eventually decay due to phase space gradient smoothing caused by collisionality.     

On the design of structural junctions for the purpose of hybrid passive-active vibration control

A theoretical investigation of wave scattering and the active modification of wave scattering at structural junctions is presented. A resonant and a non-resonant Euler-Bernoulli beam are coupled, and an external force is introduced at the junction. The external force is intended for feedforward control in order to manipulate the scattering properties at the junction. The purpose of the investigated control law is to make the junction non-reflective in the case of an incident bending wave. The control effort and the resulting power flow are investigated for different properties of the beams. By introducing damping in the resonant beam all incidence wave power is absorbed either passively, in the resonant beam, or actively, by the force. The results form the basis for a discussion of the possible benefits of using such a configuration for hybrid passive-active vibration control. The results show that for certain ratios of bending stiffness and mass the presented hybrid passive-active solution may offer advantages compared to purely passive or purely active solutions.     

Nonlinear conductivity and narrow band noise in NbSe3

A charge density wave system near commensurability and with strong damping is considered, as a model for NbSe₃. The observed threshold field is associated with depinning of a commensurate part of the charge density, while the excess charge, in form of phase kinks, contributes just to the ohmic conductivity. The characteristic length associated with the frequency generation is one lattice constant.     

Ion-acoustic soliton-like waves undergoing Landau damping

Effects of Landau damping on ion-acoustic soliton-like waves are investigated experimentally and numerically. Landau damping is enhanced by increasing the ion temperature in the experiments. A ramp which is composed of resonant ions is observed in front of a soliton-like wave. The ramp is also seen in numerical simulations of an extended Korteweg–de Vries equation with a term of Landau damping. Experimental results of the height of the ramp are found to agree with numerical ones.     

Threshold analysis for a THz-wave parametric oscillator with a quasi-phase-matching scheme in lithium niobate

The analytical expressions of the parametric gain for the terahertz wave (THz-wave) and the Stokes wave of THz-wave parametric oscillator (TPO) with a quasi-phase-matching scheme in periodically poled LiNbO₃ (PPLN) are deduced. The pump threshold expression of the TPO with a quasi-phase-matching scheme in PPLN is derived based on the gain expression of the Stokes wave. The expression is theoretically analyzed to find the relationship between the pump threshold and the parameters of the resonant cavity.     

Conservation of Resonant Periodic Solutions for the One-Dimensional Nonlinear Schrödinger Equation

We consider the one-dimensional nonlinear Schrödinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the mass term). We investigate conservation of small amplitude periodic solutions for a large measure set of frequencies. In particular we show that there are infinitely many periodic solutions which continue the linear ones involving an arbitrary number of resonant modes, provided the corresponding frequencies are large enough, say greater than a certain threshold value depending on the number of resonant modes. If the frequencies of the latter are close enough to such a threshold, then they can not be too distant from each other. Hence we can interpret such solutions as perturbations of wave packets with large wave number.     

Theorie der parametrischen Vier-Photonen-Wechselwirkung. III. Verstärkung und Oszillation bei Berücksichtigung der Rückwirkung auf die Pumpwelle

The processes of parametric amplification and oscillation in a medium with cubic polarization are investigated theoretically taking into consideration the depletion of the pump wave. We suppose that phase-matching is realized exactly (a possible nonlinear detuning of the exact phase-matching should be compensated by a suitable subsequent adjustment of the frequencies). A consequence of linear losses is the appearance of a threshold for the parametric amplification. There exist a maximum length, a minimum length and an optimum length of the nonlinear medium for the process of parametric amplification. The threshold intensity, the optimum length of the nonlinear medium and the optimum reflection coefficient for outcoupling are determined for two arrangements of the double resonant parametric four-photon oscillator (ring resonator, FABRY -PEROT resonator). It is shown that for the above mentioned arrangements of the single resonant and the double resonant four-photon oscillator the efficiency is a monotonous function of the threshold excess. On the contrary in case of the three-photon oscillator there exists an optimum value of the threshold excess.     

Existence of metastable kinetic modes

The nonlinear evolution of resonantly driven systems, such as suprathermal particle driven modes in magnetically confined plasmas, is shown to strongly depend on the existence and nature of an underlying damping mechanism. When background resonant damping is present, subcritical states can take place. In particular, purely nonlinear steady-state regimes are found, whose destabilization threshold and saturation levels are calculated and validated using numerical simulations. This nonlinear behavior can be of relevance for acoustic modes in magnetically confined plasmas.     

随机驱动等离子体电流

本文探索波驱动等离子体电流的一种新机制,称之为随机驱动效应。在相干波与磁化等离子体相互作用的系统中,当波的强度超过某个阈值时,速度空间中的一些共振区将互相重迭。共振区的重迭可导致粒子的随机运动,引起速度空间中的扩散现象。如果在电子平行于磁场方向的速度分布中,这种重迭区是不对称的,这样,就可驱动纵向等离子体电流。 关键词：     

Threshold characteristic of intracavity optical parametric oscillator pumped by all-solid-state Q-switched laser

We derive the threshold pump intensity for a singly resonant intracavity optical parametric oscillator (IOPO)based on a temporal coupled field model.Particular attention is Paid to the dependence of the intracavity singly resonant OPO(SRO)threshold intensity on the signal wave output coupling.Meanwhile,a Nd:YAG laser pumped KTiOPO4(KTP)IOPO for eye-safe laser output is studied experimentally.The experiment is performed with four signal wave output reflectivities of 60%,70%,80%,and 90%,respectively.The measured values are in good agreement with the theoretical results.With an output coupler reflectivity of 80%,a peak power of 70 kW at 1572 nm has been obtained at a repetition rate of 3.5 kHz.The pulse width is 4.9 ns.Such investigation is helpful to identifying suitable operational regime of low pump intensity.     

气泡线性振动时近海面气泡群的声散射

海洋中的不同成因的气泡群是常见的水下声学目标及声呐混响源,因此对水下气泡群进行声学建模意义重大。利用有效媒质理论描述气泡群内部的相速度及声衰减变化,并考虑到海洋中气泡群往往产生于不同界面附近,进一步利用球面波叠加原理描述海面对气泡群散射声波的再辐射,导出了平海面作用下气泡群声散射截面的一般表达式,建立了其声散射模型,研究了单一尺寸及混合尺寸气泡群的声学特性。数值分析表明,气泡群的谐振频率会随其半径或孔隙率增加而降低;由于海面的存在,气泡群声散射截面会随频率进行周期性变化,且随气泡群远离海面,这一变化逐渐加剧。此外,若气泡的黏滞阻尼项在全部阻尼项中占比较高,气泡群声散射强度会在谐振频率附近存在起伏振荡。该模型可为近海面鱼群、气泡羽流及海底泄漏的甲烷气体的声学建模提供一定的理论基础。     

Negative effective gravity in water waves by periodic resonator arrays

Based on analytic derivations and numerical simulations, we show that near a low resonant frequency water waves cannot propagate through a periodic array of resonators (bottom-mounted split tubes) as if water has a negative effective gravitational acceleration g(e) and positive effective depth h(e). This gives rise to a low-frequency resonant band gap in which water waves can be strongly reflected by the resonator array. For a damping resonator array, the resonant gap can also dramatically modify the absorption efficiency of water waves. The results provide a mechanism to block water waves and should find applications in ocean wave energy extraction.     

Resonant response of a thermalized ensemble of nonlinear oscillators

The analysis is carried out of the response of the center of gravity (dipole moment) of the distribution of noninteracting thermalized nonlinear oscillators to a sinusoidal driving force. Heat bath coupling is modeled by damping and noise. The driving is weak, but the frequency is resonant, so that there is a nonlinear resonance in the phase space. The response has a linear part that can be obtained from the perturbation analysis and a small nonlinear correction that is specific for the resonant structure.     

微探针纳米尺度振动测试的实验研究

微探针是扫描探针显微镜(SPM)的重要组成部件,其共振频率等振动特性直接影响系统的性能。给出了系统微探针共振频率的测试方法,对微探针在压电陶瓷驱动力作用下的受迫振动进行了有限元分析。提出了相位变化0.1°所对应的0.1nm位移分辨率的双频激光外差干涉光学测量系统,对微探针纳米尺度振动特性进行了测试对比实验,并对SPM标定样块进行了比对分析。实验结果验证了双频激光外差干涉测量方法的可行性和其应用价值。