杂质中心吸收宽带的电声子耦合问题(Ⅱ)

在这篇文章中,我们用一维晶格模型讨论了杂质中心中电声子耦合强度的问题。用场论方法严格地解得了含杂质晶格之运动方程的本征函数。由此得到了电声子耦合强度的解析表示式,它是用声子的波数k、表示相互作用范围的参量λ以及杂质参量P=γ′/γ解析地表示出来的。其中γ′和γ分别为杂质与近邻之间和一般近邻之间的力常数。对结果的分析表明,只改变质量的杂质不影响电声子耦合;导致力常数变化的杂质对电声子耦合有显著的影响。当有奇的局域模出现时,在离子晶体中它对带宽的贡献可以比带内模的贡献大很多。尤其是在离子晶体中有可能出现所谓“临界散射”,这时带内模的贡献可能变得很小,而主要的贡献几乎全来自于局域模。相反地,在非极化晶体中,局域模的贡献一般是很小的。文中最后讨论了由一维模型得到的结论对于三维晶体可能有的意义。     

Approximations for modal coupling in scattered fields from orifices

Previous investigations have used Hankel transforms to establish the velocity potentials of the wave fields resulting from arbitrary angle plane wave impingement on a circular orifice in a rigid, thick wall. The scattered field from the orifice is examined, in particular the modal contributions to the amplitude of its velocity potential. For each m,n mode the amplitude is dependent upon the amplitude of the in-orifice waves and a driving term unique to each m,n mode. In establishing the amplitudes of the in-orifice waves, the effects of modal coupling are also considered. In this work these two components of the scattered wave amplitude are investigated on a modal basis and approximations given for coupling effects. These approximations are then used to calculate the scattered field and the results compared with conventional solutions that use full modal coupling.     

Wave chaos and mode-medium resonances at long-range sound propagation in the ocean

We study how the chaotic ray motion manifests itself at a finite wavelength at long-range sound propagation in the ocean. The problem is investigated using a model of an underwater acoustic waveguide with a periodic range dependence. It is assumed that the sound propagation is governed by the parabolic equation, similar to the Schrodinger equation. When investigating the sound energy distribution in the time-depth plane, it has been found that the coexistence of chaotic and regular rays can cause a "focusing" of acoustic energy within a small temporal interval. It has been shown that this effect is a manifestation of the so-called stickiness, that is, the presence of such parts of the chaotic trajectory where the latter exhibit an almost regular behavior. Another issue considered in this paper is the range variation of the modal structure of the wave field. In a numerical simulation, it has been shown that the energy distribution over normal modes exhibits surprising periodicity. This occurs even for a mode formed by contributions from predominantly chaotic rays. The phenomenon is interpreted from the viewpoint of mode-medium resonance. For some modes, the following effect has been observed. Although an initially excited mode due to scattering at the inhomogeneity breaks up into a group of modes its amplitude at some range points almost restores the starting value. At these ranges, almost all acoustic energy gathers again in the initial mode and the coarse-grained Wigner function concentrates within a comparatively small area of the phase plane.     

Horizontal array beamforming in an azimuthally anisotropic internal wave field

A numerical study of beamforming on a horizontal array is performed in a shallow water waveguide where a summer thermocline is perturbed by a time evolving realization of an internal wave field. The components of the internal wave field consist of a horizontally (azimuthally) isotropic, spatially homogeneous contribution, and a horizontally anisotropic, spatially inhomogeneous component. These terms represent a diffuse ("background") internal wave field and a localized solitary wave packet, respectively. Conventional beamforming is performed as a function of time while the internal wave field evolves throughout a computational volume containing the source-receiver paths. Source-receiver orientation with respect to the azimuthally anisotropic component has a significant effect on the beamformed output. When the source-receiver configuration is oriented approximately parallel to the solitary wave crests, beam wander, fading, beam splitting and coherence length degradation occurs in a time-dependent manner as the solitary wave packet passes through the environment. Both horizontal refraction of energy and a time-dependent modal source excitation distribution are responsible for these beamforming effects. In cases where source-receiver orientation is not approximately parallel to the wave crests, these effects are substantially reduced or eliminated, indicating that an azimuthally selective perturbation of the acoustic field can be attributed to the wave packet. Modal decomposition of the acoustic field and single mode starting fields are used to infer that, for the source-receiver orientation along the wave crests and troughs, acoustic propagation is predominantly adiabatic. A modal phase speed analysis explains several features associated with the beamformed power.     

Broadband modeling of downslope propagation in a penetrable wedge

Sound propagation in a wedge-shaped environment with a penetrable bottom is simulated with broadband adiabatic mode, coupled mode, and parabolic equation model computations. Simulated results are compared to measured data taken in a tank experiment by Tindle et al. The coupled mode formalism is shown to predict, in agreement with that experiment, that modal wave fronts in penetrable wedges are approximately circular arcs centered at the apex of the wedge for a source near the apex. It is also shown that for wedge angles up to 6 degrees, the received waveforms are well approximated by the adiabatic waveforms time-shifted by a depth-dependent interval to account for the curvature of the modal wave fronts. A small deviation from circularity in the modal wave fronts is possibly observed in the 6 degrees case.     

On the width of a ray

Consistent with earlier work by Kravtsov and Orlov, a simple general expression for the width of a Fresnel zone deltar(F) in a smooth inhomogeneous environment is derived; this is the diffractive contribution to the width of a ray. In a stratified environment at long range, the general Fresnel zone width expression is shown to reduce approximately to one that is proportional to [equation in text] where alpha is the ray stability parameter, sigma is the acoustic frequency, r is the range from the source to the field point of interest, and R is the source to receiver range. In a stratified environment on which a weak small-scale perturbation is superimposed, deterministic rays in the background environment that connect fixed end points break up into bundles of micromultipaths at moderate to long range and a second, scattering-induced, contribution deltar(s) to the width of a ray must be considered. It is shown that deltar(s) is proportional to /alpha/r(R-r) and argued that in a micromultipathing environment the total effective width of a background ray is deltar(tot)= [equation in text] . Theoretical predictions are shown to agree well with travel-time sensitivity kernel calculations.     

On the acoustic field in a Pekeris waveguide with attenuation in the bottom half-space

The acoustic field in a Pekeris channel with an attenuating basement is critically examined, based on contour integrations of the wave number integrals for the two domains. In both regions, the field consists of a finite sum of proper (square integrable) normal modes plus a branch line integral around a hyperbolic cut. For low bottom attenuation, only "trapped" modes exist but as the loss increases additional "dissipation" modes contribute to the mode sum. A Newton-Raphson iterative procedure is introduced for finding the complex eigenvalues of the modes and a new expression is derived which shows that the total number of proper (trapped plus dissipation) modes supported by the waveguide increases essentially linearly with rising bottom attenuation. Approximations for the complex shape functions of the modes in the water column and the basement are developed and compared with the exact shape functions determined from the Newton-Raphson procedure. An expression derived for the modal attenuation coefficient scales in proportion to the square of the mode number and inversely with the square of the frequency. Stationary-phase approximations for the branch line integrals for both domains are developed, which serve to illustrate the asymptotic range dependence of the lateral wave but otherwise have little utility.     

Comparison of hybrid three-dimensional modeling with measurements on the continental shelf

During the CALOPS 2007 experiment, off the coast of Fort Lauderdale, Florida, three-dimensional (3D) multipath was observed using a bottom mounted horizontal line array during source tows along the 200 m isobath [Kevin D. Heaney and James J. Murray, J. Acoust. Soc. Am. 125(4), 1394-1402 (2008)]. In this paper a hybrid modeling approach is presented to model the 3D sound on the Florida shelf, nearly shaped like the canonical wedge. The hybrid approach combines vertical acoustic normal modes with the parabolic equation solution (in range/cross-range). The approach is shown to satisfy the 3D Cartesian-coordinate wave equation in the limit of adiabatic mode propagation. In the adiabatic mode parabolic equation (AMPE) approach modal phase speeds vs position are used as the input to the parabolic equation computation with dimensions of easting (km) and northing (km). Vertical adiabatic modes and horizontal rays are also computed to illustrate the 3D multipath arrival. The AMPE field is computed for all the modes for each element of the horizontal array. Beamforming vs source range is then conducted and excellent agreement with data is achieved.     

Spectral and modal formulations for the Doppler-shifted field scattered by an object moving in a stratified medium

Spectral and normal mode formulations for the three-dimensional field scattered by an object moving in a stratified medium are derived using full-field wave theory. The derivations are based on Green's theorem for the time-domain scalar wave equation and account for Doppler effects induced by target motion as well as source and receiver motion. The formulations are valid when multiple scattering between the object and waveguide boundaries can be neglected, and the scattered field can be expressed as a linear function of the object's plane wave scattering function. The advantage of the spectral formulation is that it incorporates the entire wave number spectrum, including evanescent waves, and therefore can potentially be used at much closer ranges to the target than the modal formulation. The normal mode formulation is more computationally efficient but is limited to longer ranges. For a monochromatic source that excites N incident modes in the waveguide, there will be roughly N2 distinct harmonic components in the scattered field. The Doppler shifts in the scattered field are highly dependent upon the waveguide environment, target shape, and measurement geometry. The Doppler effects are illustrated through a number of canonical examples.     

Manifestation of ray stochastic behavior in a modal structure of the wave field

A ray-based mathematical formalism is described to analyze modal structure variations in a range-dependent wave guide. In the scope of this formalism mode amplitudes are expressed through parameters of ray trajectories. Therefore, the approach under consideration provides a convenient tool to study how chaotic ray motion manifests itself in an irregular range dependence of the modal structure. The phenomenon of nonlinear ray-medium resonance playing a crucial role in the emergence of ray chaos has been interpreted from the viewpoint of normal modes. It has been shown that in terms of modes the coexistence of regular and chaotic rays means the presence of regular and irregular constituents of mode amplitudes. An analog to incoherent summation of rays has been proposed to evaluate mode intensities (squared mode amplitudes) smoothed over the mode number. Numerical calculations have shown that it gives correct results for smoothed mode intensities at surprisingly long ranges.     

Pair production and optical lasers

Electron-positron pair creation in a standing wave is explored using a parameter-free quantum kinetic equation. Field strengths and frequencies corresponding to modern optical lasers induce a material polarization of the QED vacuum, which may be characterized as a plasma of e+e- quasiparticle pairs with a density of approximately 10(20) cm-3. The plasma vanishes almost completely when the laser field is zero, leaving a very small residual pair density n(r) which is the true manifestation of vacuum decay. The average pair density per period is proportional to the laser intensity but independent of the frequency nu. The density of residual pairs also grows with laser intensity but n(r) proportional to nu(2). With optical lasers at the forefront of the current generation, these dynamical QED vacuum effects can plausibly generate 5-10 observable two-photon annihilation events per laser pulse.     

高功率光纤中传输光模式与其波长相关性研究

针对高功率光纤激光模式诊断和光谱诊断的需求,研究了光纤中传输模式的波长相关性,数值计算了光纤中各个模式的模场分布随波长的变化曲线及相应的光束质量,采用双傅里叶变换F~2法实际测量了光纤模式成分与波长的关系曲线.结果表明,光纤中各个模式的模场分布随波长变化,波长越长,模场面积越大;模式的光束质量随波长变化不大,但在截止频率附近明显变差;光纤中各个模式的功率占比与波长有关.     

ON THE RELATION BETWEEN COMPLEX MODES AND WAVE PROPAGATION PHENOMENA

This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic structures. It shows how complex modes can be interpreted in terms of wave propagation phenomena caused by either localized damping or propagation to the surrounding media. Numerical simulation results are presented for different kinds of structures exhibiting modal and wave propagation characteristics: straight beams, an L-shaped beam, and a three-dimensional frame structure. The input/output transfer relations of these structures are obtained using a spectral formulation known as the spectral element method (SEM). With this method, it is straightforward to use infinite elements, usually known as throw-off elements, to represent the propagation to infinity, which is a possible cause of modal complexity. With the SEM model, the exact dynamic behavior of structures can be investigated. The mode complexity of these structures is investigated. It is shown that mode complexity characterizes a behavior that is half-way between purely modal and purely propagative. A coefficient for quantifying mode complexity is introduced. The mode complexity coefficient consists of the correlation coefficient between the real and imaginary parts of the eigenvector, or of the operational deflection shape (ODS). It is shown that, far from discontinuities, this coefficient is zero in the case of pure wave propagation in which case the plot of the ODS in the complex plane is a perfect circle. In the other extreme situation, a finite structure without damping (or with proportional damping), where the mode shape (or the ODS) is a straight line on the complex plane, has a unitary complexity coefficient. For simple beam structures, it is shown that the mode complexity factor can also be calculated by curve-fitting the mode to an ellipse and computing the ratio of its radii.     

Letter: Brane Cosmology with a van der Waals Equation of State

The evolution of a Universe confined onto a 3-brane embedded in a five-dimensional space-time is investigated where the cosmological fluid on the brane is modeled by the van der Waals equation of state. It is shown that the Universe on the brane evolves in such a manner that three distinct periods concerning its acceleration field are attained: (a) an initial accelerated epoch where the van der Waals fluid behaves like a scalar field with a negative pressure; (b) a past decelerated period which has two contributions, one of them is related to the van der Waals fluid which behaves like a matter field with a positive pressure, whereas the other contribution comes from a term of the Friedmann equation on the brane which is inversely proportional to the scale factor to the fourth power and can be interpreted as a radiation field, and (c) a present accelerated phase due to a cosmological constant on the brane.     

等离子体填充耦合腔链特性研究

 用严格的场匹配方法分析了填充等离子体的耦合腔链，研究了等离子体 腔混合模的形成以及“冷带宽”和“热带宽”的展宽效应。等离子体填充周期性耦合腔链后，形成周期性的截止频率为0的等离子体TG模式。当填充的等离子体密度较大，且腔模和TG模式发生部分重叠时，两者相互耦合，形成等离子体 腔混合模式。工作在混合模式下，其“冷带宽”和“热带宽”大大增宽，且耦合阻抗比真空时提高了近5倍，因此在填充等离子体后，耦合腔链的慢波特性得到了显著的改善。     

Dispersion characteristics of surface magnetostatic waves with dissipation

It is shown that unlike undamped waves, the dispersion characteristics of spin surface waves with dissipation have a maximum wave number at which there is a downward reversal in the dispersion curve of a wave number. This forms the upper branch of a dispersion curve with inverse dispersion and high attenuation, leading to an unclear frequency dependence of the wave vector. The lower primary dispersion branch corresponds to waves with forward dispersion, and attenuation is proportional to the small parameter of dissipation. However, the coefficient of wave attenuation grows sharply near the maximum wave number. Some angular and frequency limits of surface wave propagation change as well.     

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.     

周期极化非线性晶体中太赫兹波辐射研究

 从理论上详细研究了飞秒激光在周期极化非线性晶体中由光整流效应产生的太赫兹（THz）波辐射。利用天线辐射原理和光栅衍射理论，着重研究THz波辐射的频域场和时域场的分布。讨论和分析了THz波辐射的中心频率、频谱宽度和电场随辐射角的变化。研究表明，THz波的带宽反比于晶体的长度或光栅数，电场随辐射角呈准谐波变化。     

Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures.

The properties of the single flow-line Doppler spectrum using pulsed wave (PW) ultrasound is studied on the basis of previously developed spectral theory for transducers with apodized apertures. It has been shown previously that the spectral width of Doppler signals from a sample volume in low velocity-shear flow is independent of the sample volume depth but that is not true for the spectra from the individual streamlines. The work presented here on the Doppler flow-line spectrum shows that its width should be invariant with flow-line location, if the sample volume depth is fixed. At the same time, for a transducer operating in PW mode not only the Doppler spectral width depends on the sample volume depth, but also the modal Doppler frequency shift changes with flow-line displacement in the illuminating field except if the sample volume centre and the beam focus coincide. The variation of modal Doppler frequency shift is the more explicit manifestation of the effect of wavefront curvature increasing for lines and sounding depths distant from the focal point. The values of the Doppler shift and spectral bandwidth are reported taking account of beam diffraction and variations in its geometry due to focusing.