MULTIDIMENSIONAL COUPLED VIBRATIONS OF PIEZOELECTRIC VIBRATORS——PURE PIEZOELECTRIC VIBRATORS

In this paper,the fundamental modes of two- and three-dimensional coupled vibrations ofvarious piezoelectric ceramic vibrators,including the rectangular cross-sectional bar,the rectangularplate,the finite solid cylinder and hollow cylinder,are analyzed by using the apparent elasticitymethod,and some quite simple analytic formulae for the resonant frequencies of the above-men-tioned various piezoelectric vibrators are obtained,These formulae have been used to calculatethe variations of frequency constants with the geometric size of the vibrators,and the calculatedresults are in satisfactory agreement with the published experimental results and results calculatedby using various other methods,including the finite difference method,finite element method andRitz variational method.These formulae are quite simple,and the resonant frequencies or the geo-metric size of the vibrators can be rapidly calculated by using a scientific calculator instead of acomputer,so this method is more convenient for engineering     

Order Parameter of a Nanometre-Scale S-Wave Superconducting Grain in Quantum Tunnelling Process： Frequency Space Analysis

A nano-scale s-wave superconducting grain, coupled to a normal metallic contact through a tunnelling junction, is placed in an external magnetic field. We suppose that effect of this quantum tunnelling on the Fourier transform of the order parameter is in the form of a small additive correction to the BCS order parameter. At the first order approximation in terms of this correction term and by using an instanton method, the related Green functions （in frequency space） are obtained. By establishing a self-consistent configuration an analytic formula for the order parameter is also found. We also show that a departure from superconductivity can be captured by this formula. This change of state is indeed a manifestation of a quantum transition induced by quantum fluctuations. In this sense, this is an advantage of our simple method which, like other more elaborate methods, can detect a quantum transition in the state of the grain.     

ACOUSTICAL PROPERTIES OF QING

The qing was an important percussion musical instrument in ancient China.Qing is a stone plate withspecial form.The vibration of qing is studied both theoretically and experimentally in this paper.Thevibrational modes of a qing have been calculated by using finite element method in accordance with the ex-perimental results.As compared with a rectangular plate,the frequency relations between the overtones arevaried with the changes of shape of the qing.From the analysis,it is possible to speculate upon the idea ofdesign of the qing in ancient time.In order to confirm the idea,the sound of qing has been simulated bycomputer and judged subjectively.An empirical formula for the calculation of the pitch frequency of qingsound is given.     

A theoretical study of harmonic generation in a short period AlGaN/GaN superlattice induced by a terahertz field

Based on an improved energy dispersion relation, the terahertz field induced nonlinear transport of miniband electrons in a short period AlGaN/GaN superlattice is theoretically studied in this paper with a semiclassical theory. To a short period superlattice, it is not precise enough to calculate the energy dispersion relation by just using the nearest wells in tight binding method: the next to nearest wells should be considered. The results show that the electron drift velocity is 30% lower under a dc field but 10% higher under an ac field than the traditional simple cosine model obtained from the tight binding method. The influence of the terahertz field strength and frequency on the harmonic amplitude, phase and power efficiency is calculated. The relative power efficiency of the third harmonic reaches the peak value when the dc field strength equals about three times the critical field strength and the ac field strength equals about four times the critical field strength. These results show that the AlGaN/GaN superlattice is a promising candidate to convert radiation of frequency ω to radiation of frequency 3ω or even higher.     

Controllable optical multi-well trap and its optical lattices using compounded cosine patterns

This paper proposes a flexible scheme to form various optical multi-well traps for cold atoms or molecules by using a simple optical system composed of an compounded amplitude cosine-only grating and a single lens illuminated by a plane light wave or a Gaussian beam.Dynamic manipulation and evolution of multi-well trap can be easily implemented by controlling the modulation frequency of the cosine patterns.It also discusses how to expand this multi-well trap to two-dimensional lattices with single-or multi-well trap by using an orthogonally or non-orthogonally modulated grating,as well as using incoherent multi-beam illumination,and these results show that all the symmetric structures of two-dimensional Bravais lattices can be obtained facilely by using proposed scheme.     

Density-dependent potential for multi-neutron halo nuclei

We apply a simple density-dependent potential model to the three-body calculation of the groundstate structure of drip-line nuclei with a weakly bound core. The hyperspherical harmonics method is used to solve the Faddeev equations. There are no undetermined potential parameters in this calculation. We find that for the halo nuclei with a weakly-bound core, the calculated properties of the ground-state structure are in better agreement with experimental data than the results calculated from the standard Woods-Saxon and Gauss type potentials. We also successfully reproduce the experimental cross sections by using the density calculated from this method. This may be explained by the fact that the simple Fermi or Gaussian function can not exactly describe the density distribution of the drip-line nuclei.     

Mechanical properties of silicon nanobeams with an undercut evaluated by combining the dynamic resonance test and finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications.A numerical experimental method of determining resonant frequencies and Young’s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper.Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process,which inevitably generates the undercut of the nanobeam clamping.In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut,dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L,which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data.By using a least-square fit expression including △L,we finally extract Young’s modulus from the measured resonance frequency versus effective length dependency and find that Young’s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon.This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.     

Mechanical properties an undercut evaluated resonance test and of silicon nanobeams with by combining the dynamic finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young＇s modulus from the measured resonance frequency versus effective length dependency and find that Young＇s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.     

Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.     

A time domain correction method for Doppler-distortion signal from acoustic moving source

Doppler effect widely exists in the signal from the moving acoustic source. In order to solve such problems as frequency shift and frequency band expansion, a time domain cor- rection method is presented in this paper. First, the discrete time vector for interpolation and the amplitude restoration formula is derived based on the moving relationship and the Morse acoustic theory, then the amplitude weights are corrected and the distortion signal is interpolated. Every point of the discrete signal is operated separately in time domain. Compared with the existing frequency domain methods, this method does not need to know the characteristic frequency beforehand and would not be influenced by the blending of the frequency band. Hence, this method can be employed to correct multiple frequency signals and it is also a simple and effective Doppler effect reduction method.     

Azimuthal correlations of hadrons and fragments in nucleus-nucleus collisions

Two-particle (two-fragment) azimuthal correlation functions are studied by using a simple formula which describes uniformly azimuthal distributions of final-state charged particles and nuclear fragments. This formula is obtained in the framework of a multi-source thermal model (or multi-source ideal gas model). The calculated results are compared and found to be in agreement with the experimental data of charged hadrons and nuclear fragments in nucleus-nucleus collisions at intermediate and high energies.     

Guided-mode resonant Brewster filter consisting of two homogenous layers and a single grating with an equal refractive index

In this paper,a new type of resonant Brewster filter(RBF) consisting of two homogenous layers and a single grating with an equal refractive index is presented.The properties are studied by using the plane waveguide method(PWM) and rigorous coupled-wave analysis(RCWA).It is found that the variation of the grating thickness does not effectively change the position of the resonant wavelength,however it has a remarkable effect on the line width,and the resonant peak can be adjusted back to its original position by slightly tuning the grating period.Moreover,by simultaneously tuning the thicknesses of the homogeneous layers above and beneath the grating structure,multiple channels can also be obtained when the RBF is illuminated at the Brewster angle calculated with the effective medium theory(EMT) of subwavelength grating.The adjacent optical thickness for acquiring the multiple channels is about three-quarters of the resonant wavelength.Furthermore,it is demonstrated that the line width at the operating resonant wavelength can be appreciably narrowed by tuning the thickness of the homogenous layer to its corresponding thickness without fine tuning the grating period or the thickness.Therefore,it is very useful for designing filters with different line widths at the desired wavelength.In addition,it is shown from our calculations that the symmetrical line feather can be obtained if the total optical thickness for the homogeneous layer meets the special condition.     

A robust method for frequency stabilization of 556-nm laser operating at the intercombination transition of ytterbium

A frequency-stabilized 556-nm laser is an essential tool for experimental studies associated with 1 S 0-3 P 1 intercombination transition of ytterbium (Yb) atoms.A 556-nm laser light using a single-pass second harmonic generation (SHG) is obtained in a periodically poled MgO:LiNbO 3 (PPLN) crystal pumped by a fiber laser at 1111.6 nm.A robust frequency stabilization method which facilitates the control of laser frequency with an accuracy better than the natural linewidth (187 kHz) of the intercombination line is developed.The short-term frequency jitter is reduced to less than 100 kHz by locking the laser to a home-made reference cavity.A slow frequency drift is sensed by the 556-nm fluorescence signal of an Yb atomic beam excited by one probe beam and is reduced to less than 50-kHz by a computer-controlled servo system.The laser can be stably locked for more than 5 h.This frequency stabilization method can be extended to other alkaline-earth-like atoms with similar weak intercombination lines.     

A NEW METHOD OF ADAPTIVE ARRAY PROCESSING FOR SIGNALS OF UNKNOWN CHARACTERISTICS

This paper describes a new method of adaptive array processing for signals of unknown frequencycharacteristics.Under practical circumstances,it is easier to obtain the estimation of the power spec-trum in the observed direction than to obtain that of the frequency characteristics.Thus the maximumentropy spectral analysis can be used to incorporate with the adaptive array processing. In this paper the autocorrelation function is calculated from the power spectrum and the predictedcoefficients of MEM(maximum entropy method)can be obtained by solving the normal equation of thecorrelation matrix,and the predicted coefficients are used as the constrained conditions of the algorithmfor adaptive array processing. The above method is further extended and an adaptive array processor is presented for the moregeneral cases,in which the signal characteristics in the observed direction are completely unknown.Firstly the space filtering of the adaptive array is performed by the all-pass constrained conditions inthe fr     

Mechanical properties of silicon nanobeams with undercut evaluated by combining dynamic resonance test and finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young's modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by laser Doppler vibrometer is presented in this paper. Silicon nanobeams test structures are fabricated from silicon-on-insulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value Δ L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including Δ L, we finally extract Young's modulus from the measured resonance frequency versus effective length dependency and find that Young's modulus of silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to surface effect does not play a role in mechanical elastic behaviour of silicon nanobeams with the thickness larger than 200 nm.     

DYNAMIC SPECTRAL ANALYSIS OF INFRASONIC SIGNAL WITH HILBERT TRANSFORM

In the past we analyzde the dynamic spectrum of infrasonic waves with FFT,but that isnot suitable to this analysis in any case.In this paper another method is proposed to analyzeinfrasonic waves.This method is that,after digital filtering of the signal and Hilbert transform,this paper the computation of the envelope with Hilbert transform and 1/12-octave filter are dis-cussed.Then a synthetic infrasonic signal generated by a large nuclear explosion is analyzed withthe two methods,and their results are compared.It is shown that,in the dynamic spectrum,usingHilbert transform,not only higher resolution is obtained,the main frequency range of separatedmodes can be achieved,but also their waveform can be obtained preliminarily for some modes.Thus it seems that in some cases this method is more efficient for discovering the characteristicsof an infrasonic signal.     

Noise Shielding Using Acoustic Metamaterials

We exploit theoretically a class of rectangular cylindrical devices for noise shielding by using acoustic metamateriais. The function of noise shielding is justified by both the far-field and near-field full-wave simulations based on the finite element method. The enlargement of equivalent acoustic scattering cross sections is revealed to be the physical mechanism for this function. This work makes it possible to design a window with both noise shielding and air flow.     

Modeling of Fano Resonance in High-Contrast Resonant Grating Structures

A new model is presented for Fano resonance in resonant grating structure based on the temporal coupled mode theory. By using this model, the reflection spectrum can be reproduced with the information of eigenmode of the structure, which can be numerically calculated by the finite element method. Therefore, the eigenmode plays a key role in determining the profile of the line shape of the Fano resonance in the resonant grating structure. When the space of two grating modulations is decreased, the line shape experiences a significant change. Such a drastic change can be attributed to the increase of quality factor of the eigenmodes. Thus, our model not only provides a simple and intuitive understanding on the mechanism of Fano resonance, but it also offers a convenient way to engineer the line shape of the Fano resonance. The proposed model can be used in many applications, such as biosensors, optical filters, and optical switchers.     

Investigation of a wideband folded double-ridged waveguide slow-wave system

The folded double-ridged waveguide structure is presented and its properties used for wide-band traveling-wave tube are investigated.Expressions of dispersion characteristics,normalized phase velocity and interaction impedance of this structure are derived and numerically calculated.The calculated results using our theory agree well with those obtained by using the 3D electromagnetic simulation software HFSS.Influences of the ridge-loaded area and broad-wall dimensions on the high frequency characteristics of the novel slow-wave structure are discussed.It is shown that the folded double-ridged waveguide structure has a much wider relative passband than the folded waveguide slow-wave structure and a relative passband of 67% could be obtained,indicating that this structure can operate in broad-band frequency ranges of beam-wave interaction.The small signal gain property is investigated for ensuring the improvement of bandwidth.Meanwhile,with comparable dispersion characteristics,the transverse section dimension of this novel structure is much smaller than that of conventional one,which indicates an available way to reduce the weight of traveling-wave tube.     

Efficient Dual-LBO Second-Harmonic Generation by Using a Polarization Modulation Configuration

We analyse the relationship of conversion efficiency with the inter-crystal phase shift by the heuristic theory and propose a novel configuration of two cascaded nonlinear crystals for the second-harmonic generation with the polarization modulation. With this configuration, 70% external doubling efficiency is obtained, which is, to the best of our knowledge, the highest conversion efficiency with LBO crystal externM frequency doubling. This configuration provides a simple and effective method to improve the second harmonic conversion efficiency.