New representation of the multimode phase shifting operator and its application

Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the multimode coordinate--momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the multimode phase shifting operator.     

Combined spectral estimator for phase velocities of multimode Lamb waves in multilayer plates

A novel combined spectral estimate (CSE) method for differentiation and estimation the phase velocities of multimode Lamb waves whose wave numbers are much close or overlap one another in multiplayer plates is presented in this paper, which based on auto-regressive (AR) model and 2-D FFT. Simulated signals in brass plate were processed by 2-D FFT and CSE. And experiments are performed by using two conventional angle probes as emitter and receiver on the same surface of three-layered aluminum/xpoxy/aluminum plates, which include symmetrical and unsymmetrical plates. The multimode Lamb waves are excited in these laminates, and the received signal is processed by 2-D FFT and CSE, respectively. The results showed that the phase velocities of multimode signals whose wave numbers are much closed cannot be differentiated by 2-D FFT, but CSE has strong spatial resolution. Compared the measured phase velocities with the theoretical values, the error is smaller than 2% on the whole. It promises to be a useful method in experimental signals processing of multimode Lamb waves.     

Separation of multimode Lamb waves overlapped in time and frequency domains by using fractional differential

To separate multimode Lamb wave overlapped both in time and frequency domains,a multimode Lamb wave signal separation method by using fractional differential is proposed.The Tsallis function is used as the model of the amplitude spectrum.The amplitude spectra of Lamb wave signals are divided into fractional order differential.The characteristic parameters of each mode are extracted by using the polynomial between the maximum amplitude and the differential order as well as the polynomial between the peak frequency and the differential order.The corresponding phase spectrum of each mode is derived from the dispersion characteristics.The signal of each mode is constructed through the amplitude spectrum and phase spectrum.The simulated results of S1 and A1 modes in a 1 mm-thick steel plate show that the relative errors of amplitude and bandwidth of both modes are less than 6%,and that the relative errors of central frequency of both modes are less than 0.25%.Therefore,this method could be used to separate the time-frequency overlapped multimode Lamb wave signals.It is helpful for the analysis and recognition of multimode Lamb wave signals.     

用分数阶微分实现时频重叠多模式兰姆波的模式分离

为了分离时频重叠多模式超声兰姆波,提出了一种用分数阶微分理论实现多模式兰姆波模式分离的方法。以时频重叠的S1和A1模式混合信号为例,用赛利斯分布作为幅值谱的模型,首先对信号做频散补偿,由补偿后信号幅值谱分数阶微分推导了幅值谱特征参数的计算式并根据信号模型重建幅值谱,然后结合兰姆波的频散特性推导出对应的相位谱,并通过幅值谱和相位谱重构各模式的信号,实现模式分离。对1 mm钢板中仿真时频重叠的S₁和A₁模式信号分离结果显示分离出信号的幅值和带宽相对误差小于6%,中心频率相对误差小于0.25%。实验结果也证实了方法的可行性。因此当混合信号幅值谱不完全交叠时,本方法可以实现多模式兰姆波信号的分离,有助于多模式兰姆波频散信号的分析和识别。      

Fano resonances in prism-coupled multimode square micropillar resonators

We report Fano resonances in a multimode square glass micropillar resonator; the resonances were obtained by using angle-resolved prism coupling. Our experiments reveal characteristically asymmetric line shapes of high-Q resonances and of detuned low-Q resonances in multimode reflection spectra. The asymmetric resonance line shapes evolve for an approximately pi phase within a 0.5 degree range of reflection angles. We model our observed asymmetric multimode resonances by the far-field interference between a light wave that is evanescently coupled with a high-Q mode orbit and a coherent light wave that is refractively coupled with a detuned low-Q mode orbit.     

基于频散补偿和分数阶微分的多模式兰姆波分离

由于兰姆波的多模和频散特性,实际检测时在同一激发频率下存在多种模式的混合信号,而各模式信号有不同的频散特性,使得在时频混叠的情况下兰姆波的检测变得十分复杂.本文在频散补偿的基础上,通过时延函数建模,依靠不同模式频散趋势的差异性,将时频混叠信号的分离问题转化为部分模式混叠信号的分离问题.基于分数阶微分的理论,用信号幅值谱分数阶微分极大值和对应频率分别与微分阶次拟合多项式实现特征参数的提取并依靠特征参数重建幅值谱.结合相位谱重构时域信号以实现部分混叠信号中频散补偿后的模式的分离.最后恢复频散获得分离后的兰姆波信号.仿真和实验结果表明,本文方法不仅可以实现时频混叠多模式兰姆波信号的分离,更能保证分离精度,有助于复杂多模式频散信号的分离与处理的进一步研究.     

Multidomain spectral method for the helically reduced wave equation

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the “eigenspectral method.” Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.     

回旋行波管多模稳态理论及初步应用

建立了一种回旋行波管的多模稳态理论.利用该理论研究了输入功率和引导中心半径变化对回旋返波振荡的抑制作用,发现两者单独作用都在一定程度上可以减弱返波振荡,但两者的共同作用对改善工作模式输出性能和稳定性更有效.     

Multidomain spectral method for the helically reduced wave equation

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the “eigenspectral method.” Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.     

非对易相空间Dirac oscillator的研究

在极坐标系中研究了非对易相空间中的Dirac oscillator问题.研究显示:系统的波函数可以表示为合流超几何函数,而非对易相空间Dirac oscillator的量子行为类似于朗道问题.最后,对η=0和对易极限两种特殊情况进行了简单讨论.     

Influence of an electromagnetic field on the formation of wet metal foam

Amplitude modulation of a tilted optical lattice can be used to steer the quantum transport of matter wave packets in a very flexible way. This allows the experimental study of the phase sensitivity in a multimode interferometer based on delocalization-enhanced Bloch oscillations and to probe the band structure modified by a constant force.     

Review of photorefractive materials: an application to laser beam cleanup

Nonlinear photorefractive materials are well suited to record dynamic volume holograms using the wave mixing of coherent laser beams. The photo-induced index modulation is due to a space charge field which modulates the crystal refractive index. The basic phenomena and beam interactions are reviewed for different types of materials operating in the visible and near infrared. In particular, we outline their ability to amplify a low intensity signal beam due to the intensity transfer of a spatially multimode pump beam. We apply this interaction to the cleanup of a multimode large core fiber amplifier. This class of nonlinear materials contribute to extending the performances of laser sources for advanced applications of photonics. To cite this article: L. Lombard et al., C. R. Physique 8 (2007).     

基于多模光纤散斑的压缩感知在光学图像加密中的应用

为了安全高效地对图像信息进行传输,提出了一种新颖的基于多模光纤散斑的压缩感知结合双随机相位编码的光学图像加密方法.多模光纤产生的光斑作为压缩感知的测量矩阵,完成对图像的第一次压缩和加密,并且充当第一级密钥;再利用双随机相位编码技术进行第二次加密,实现对图像的完整加密过程,随机相位掩模板充当第二级密钥,解密过程与此相反.通过将光斑测量矩阵与用于压缩感知的常用随机测量矩阵进行对比研究后发现,使用光斑测量矩阵解密后的图像质量更好,而且相比于其他随机测量矩阵在硬件实现上的复杂性与高成本,光斑矩阵可以很容易地通过简单的光学器件来获得,且可以利用工作波长的改变来进行变换,也即第一级密钥非常容易变换.同时经研究表明,本文方法可以有效抵抗统计分析、噪声干扰和剪切等攻击,且对密钥敏感性高,具有良好的鲁棒性和安全性.因此,本文提出的这种基于光斑矩阵的压缩感知与双随机相位编码结合起来的加密方法,可以获得良好的加密效果与极大的密钥空间,并且易于在光学领域整合.     

Model-based analysis of dispersion curves using chirplets

Time-frequency representations, like the spectrogram or the scalogram, are widely used to characterize dispersive waves. The resulting energy distributions, however, suffer from the uncertainty principle, which complicates the allocation of energy to individual propagation modes (especially when the dispersion curves of these modes are close to each other in the time-frequency domain). This research applies the chirplet as a tool to analyze dispersive wave signals based on a dispersion model. The chirplet transform, a generalization of both the wavelet and the short-time Fourier transform, enables the extraction of components of a signal with a particular instantaneous frequency and group delay. An adaptive algorithm identifies frequency regions for which quantitative statements can be made about an individual mode's energy, and employs chirplets (locally adapted to a dispersion curve model) to extract the (proportional) energy distribution of that single mode from a multimode dispersive wave signal. The effectiveness of this algorithm is demonstrated on a multimode synthetic Lamb wave signal for which the ground-truth energy distribution is known for each mode. Finally, the robustness of this algorithm is demonstrated on real, experimentally measured Lamb wave signals by an adaption of a correlation technique developed in previous research.     

Guided wave arrays for high resolution inspection

The paper describes a general approach for processing data from a guided wave transducer array on a plate-like structure. The raw data set from such an array contains time-domain signals from each transmitter-receiver combination. The technique is based on linear superposition of signals in the frequency domain with some amplitude and phase factors and can be applied to any array geometry and any types of array elements. The problem of finding optimal coefficients, which allow the best resolution to be achieved with the minimum number of array elements, is investigated. It is shown that improvements in resolution are obtained at the expense of sensitivity to noise. A method of quantifying this sensitivity is presented. Results are shown that illustrate the application of the technique to a linear array and an array of circular geometry (containing a single ring of elements). Experimental data obtained from a guided wave array containing electromagnetic acoustic transducer elements for exciting and detecting the S0 Lamb wave mode in a 5-mm-thick aluminum plate are processed with different algorithms and the results are discussed. Generalization of the technique for the case of multimode media is suggested.     

Quantum memory for images with feedback

A spatially multimode scheme of the quantum memory for light is presented that can be considered to be a thin hologram, whose long-lived spin subsystem of a multiatomic ensemble stores image peculiarities, such as the multimode superposition and entangled quantum states, which is unattainable for ordinary holography. In the recording process, the measurement of polarization parameters of the transmitted light wave and the feedback are used for the action on an ensemble of fixed atoms (obtained, for example, by means of the laser cooling). The information capacity of a quantum hologram with a feedback will considerably exceed that of a spatially singlemode quantum memory.     

复Ginzburg-Landau方程中模螺旋波的稳定性研究

研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域:在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.     

Phase-resolved second-harmonic imaging with nonideal laser sources

An interferometric imaging setup is described that allows us to map the spatial distribution of the phase of a second-harmonic (SH) wave by using multimode laser sources with achromatic beam imaging of the fundamental and SH waves. Working distances > 1 m and a robust setup allow experiments that were not possible before.     

Complete Polarization Conversion Characteristics of Dielectric Grating Composed of Left-Handed Materials

The TE/TM polarization conversion characteristics of dielectric grating composed of left-handed materials for the case of plane wave oblique incidence are carefully investigated by a method which combines the multimode network theory with the rigorous mode matching method. It is indicated that complete polarization conversion between TE and TM modes can be realized using left-handed gratings. This can hardly achieve in the conventional right-handed gratings. Comparisons of polarization conversion properties between right-handed gratings and left-handed gratings are given with physical explanations. This unique merit of left-handed periodic structure is of important significance for accurate design of new millimeter wave TE/TM polarization converters.     

Quantum phase retrieval of a Rydberg wave packet using a half-cycle pulse

A terahertz half-cycle pulse was used to retrieve information stored as quantum phase in an N-state Rydberg atom data register. The register was prepared as a wave packet with one state phase reversed from the others (the "marked bit"). A half-cycle pulse then drove a significant portion of the electron probability into the flipped state via multimode interference.