Lamb waves in phononic crystal slabs: truncated plane parallels to the axis of periodicity

A theoretical study is presented on the propagation properties of Lamb wave modes in phononic crystal slabs consisting of a row or more of parallel square cylinders placed periodically in the host material. The surfaces of the slabs are parallel to the axis of periodicity. The dispersion curves of Lamb wave modes are calculated based on the supercell method. The finite element method is employed to calculate the band structures and the transmission power spectra, which are in good agreement with the results by the supercell method. We also have found that the dispersion curves of Lamb waves are strongly dependent on the crystal termination, which is the position of the cut plane through the square cylinders. There exist complete or incomplete (truncated) layers of square cylinders with the change of the crystal termination. The influence of the crystal termination on the band gaps of Lamb wave modes is analyzed by numerical simulations. The variation of the crystal termination leads to obvious changes in the dispersion curves of the Lamb waves and the widths of the band gaps.     

Bloch定理与散射平面波的干涉

从波动学的角度分析空晶格模型中的自由电子在周期性晶体势微扰作用下转变为晶体中Bloch电子的过程,揭示出了这一过程的物理实质,结果表明,在晶体势微扰作用下,代表空晶格模型中自由电子定态波函数的行进平面波在晶体内各点处产生了各种许可波矢的散射平面波,Bloch定理是晶体微观结构的平移对称性（即周期性）使得这些散射平面波产生干涉的结果。     

Modelling and simulation of acoustic wave propagation in locally resonant sonic materials

Sonic crystals are artificial structures consisting of a periodic array of acoustic scatterers embedded in a homogeneous matrix material, with a usually large impedance mismatch between the two materials. They exhibit strong sound attenuation at selective frequency bands due to the interference of multiply reflected waves. However, sound attenuation bands in the audible range are only achieved by unfunctionally large sonic crystals. If local resonators are used instead of simple scatterers, the frequencies of the attenuation bands can be reduced by about two orders of magnitude. In the present paper we perform numerical simulations of acoustic wave propagation through sonic crystals consisting of local resonators using the local interaction simulation approach (LISA). Three strong attenuation bands are found at frequencies between 0.3 and 6.0 kHz, which do not depend on the periodicity of the crystal. The results are in good qualitative agreement with experimental data. We analyze the dependence of the resonance frequencies on the structural parameters of the local resonators in order to create a tool for design and optimization of any kind of sonic crystal.     

Widely tunable broadband terahertz radiation generation using a configurationally locked polyene 2-[3-(4-hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene] malononitrile crystal via difference frequency generation

Widely tunable terahertz (THz) waves were successfully generated from 0.5 to 10 THz via difference frequency generation (DFG) in a configurationally locked polyene 2-[3-(4-hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene] malononitrile (OH1) crystal. Potassium titanium oxide phosphate optical parametric oscillator pumped by nanosecond Q-switched Nd:YAG laser was used to generate two waves, which were then used to irradiate OH1 crystal. The maximum energy of the generated THz wave was about 461 pJ/pulse. We investigated the dependency of generated THz energy to the excitation pump power density and OH1 crystal thickness. In addition, we compared the THz energy generated by OH1 crystal to 4-N,N-dimethylamino-4′-N′-methyl-4-stilbazolium tosylate (DAST) crystal using DFG, and we achieved 560 times higher energy using OH1 crystal than DAST crystal at around 1.1 THz.     

Vibrational properties of thin films adsorbed on crystals with strong spatial dispersion

The effect of strong spatial dispersion of the substrate crystal onto the dynamics of thin epitaxially adsorbed films is described in a simple model through the following quantities: i) phonon reflection coefficients ii) depth-dependent local densities of states (LDOS) and iii) finite-lifetime surface states called leaky waves. The correspondence of these three types of characteristics accessible in different experimental methods is established. The bulk band of the substrate crystal consists of two distinct frequency ranges separated by an edge singularity: above the singularity the substrate supports two different waves for a given frequency, whereas only one wave can exist for each frequency in the low-frequency range. The resonances in the low-frequency range are found to correspond to maxima in the LDOS, to maxima in the amplitude of a near field arising in phonon reflection and to leaky waves involving a single leakage wave packet. The antiresonances in the same frequency range are characterised by minima in LDOS and in the near field, whereas the corresponding leaky waves involve two leakage wave packets. The only leaky waves found in the high-frequency range involve two leakage wave packets and are related to resonances. The antiresonances then are characterised by an anomalous increase in the extraordinary reflected wave. The edge singularity manifests itself in an additional quasi resonance, whose features depend on the coupling between the substrate and the thin film.     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

Visualization of surface acoustic wave scattering by dislocations

Stroboscopic X-ray topography at the synchrotron beam line was used to visualize the propagation of a 580 MHz surface acoustic waves (SAW) in LiNbO3 crystals. For this purpose, the X-ray bursts coming from the synchrotron storage ring with periodicity of 5.68 MHz were synchronized with the SAW frequency in a phase-locked mode. This method allowed us to "stop" the SAW in time and to observe the X-ray diffraction contrast caused by the dynamic deformation field of SAW. The X-ray topographic images showed well-resolved individual acoustic wave fronts of 6 microm SAW as well as their distortions due to SAW scattering by linear dislocations. Some of the images revealed an exceptional contrast of the concentric rings about the dislocation line, which is caused by coherent interaction of the secondary elastic waves. This contrast is similar to the Fresnel zones in optics, and this conclusion is confirmed by direct summation of secondary waves emitted by local elements of a vibrating dislocation string.     

Excitation of surface polaritons by nondegenerate four-wave mixing of evanescent waves

We propose a method for exciting a surface polariton wave by nonlinear mixing of three evanescent waves. The nonlinear polarization and phase matching conditions are analyzed for diatomic cubic crystals and a numerical example is given for GaP showing that this scheme is possible. Furthermore, by consideration of the energy balance in the crystal, the gain coefficient for the surface wave and the intensity of the wave coupled to the vacuum are also calculated.     

Bidirectional vectorial light amplification in cubic crystals with unshifted photorefractive gratings

We present a new method of light amplification based on vectorial two-wave mixing in cubic crystal via an unshifted photorefractive grating. The energy transfer between interacting waves is achieved in an experimental configuration that provides the amplitudes of modulation of refractive indices of opposite signs, Dn(1)=-Dn(2), for two orthogonal polarization modes of the interacting waves. The configuration demonstrates bidirectional amplification; i.e., the weak wave is always amplified, independent of its direction with respect to the strong pump beam. We present the results of numerical analysis along with the experimental results for a Bi(12)TiO(20) crystal with a dc applied electric field.     

Coherent CW image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal

A BaTiO₃ crystal was used to amplify an image illuminated by an Ar-laser. The amplification mechanism is two-wave mixing in an electrooptic crystal, usually called dynamic holography. We achieved gain factors of 4000 with pump powers of 150 mW and holographic resolution. As the interaction between signal and pump wave is not effected through excited states of the crystal, the amplification process is virtually noise free. This has to be traded in with slow response, 0.1-1 s. To demonstrate the high optical quality of the amplifier, it was incorporated in a ring resonator as gain medium. It was possible to excite pure discrete transversal modes of higher order. That reveals the high optical homogeneity of the crystal over the mode cross-section of > 1 mm. The coupling process of the pump with the two counter-propagating waves forming the standing resonator wave is not symmetric. Consequently a travelling wave develops in the resonator.     

Upconversion of whistler waves by gyrating ion beams in a plasma

A gyrating ion beam, with a ring-shaped distribution in velocity, supports negative energy beam modes near the harmonics of beam gyro-frequency. An investigation of the non-linear interaction of high-frequency whistler waves with the negative energy beam cyclotron mode is made. A non-linear dispersion relation is derived for the coupled modes. It is shown that a gyrating ion-beam frequency upconverts the whistler waves separated by harmonics of beam gyro-frequency. The expression for the growth rate of whistler mode waves has been derived. In Case 1, a high-amplitude whistler wave decays into two lower frequency waves, called a low-frequency mode and a side band of frequency lower than that of pump wave. In Case 2 a high-amplitude whistler wave decays into two lower frequency daughter waves, called the low-frequency mode and whistler waves. Generation mechanism of these waves has application in space and laboratory plasmas.     

Study of superluminal-pulse propagation in one-dimensional photonic crystals by the FDTD method

We study the pulse propagation in a one-dimensional photonic crystal using the finite-difference time-domain method. The wave propagation inside the crystal is the result of superposition of forward and backward waves. We observed the superluminal phenomena and negative values of the velocity of the energy-density maximum. The energy velocities within the crystal never exceed the speed of light in vacuum. We hope that our study contributes to a further understanding of the superluminal phenomena.     

THz wave generation by repeated and continuous frequency conversions from pump wave to high-order Stokes waves

We propose a novel scheme for THz wave generation by repeated and continuous frequency conversions from pump wave to high-order Stokes waves (HSWs). The repeated frequency conversions are accomplished by oscillations of Stoke waves in resonant cavity (RC) where low-order Stokes waves (LSWs) are converted to high-order Stokes waves again and again. The continuous frequency conversions are accomplished by optimized cascaded difference frequency generation (OCDFG) where the poling periods of the optical crystal are aperiodic leading to the frequency conversions from low-order Stokes waves to high-order Stokes waves uninterruptedly and unidirectionally. Combined with the repeated and continuous frequency conversions, the optical-to-THz energy conversion efficiency (OTECE) exceeds 26% at 300 K and 43% at 100 K with pump intensities of 300 MW/cm².     

平行光子晶体波导的传输特性及应用

采用时域有限差分法研究两平行光子晶体波导的传输特性及模场分布,利用耦合模理论计算光子晶体波导的耦合系数。计算结果表明,在不同的频率范围内两平行光子晶体波导之间表现出不同的耦合特性:在高频段(0.32~0.44)(ωa/2πc)的范围内两直波导表现出相互的能量交换,实现光耦合,耦合系数随入射波 频率增加而减小;而在低频段(0.29~0.32)(ωa/2πc)的范围内,两波导的传输谱图几乎重合。最后,提出一种采用固定波导耦合长度同时实现光分束及光均分器的方案,当耦合长度取34a时,可将频率为0.333 (ωa/2πc)和 0.357(ωa/2πc)的两入射波分束传播,同时将低频段中的任意频率波进行能量均分。     

Frequency Selective Properties of Two-Dimensional Dielectric Gratings: TE- and TM-Polarizations

This work analyzes the propagation characteristics of electromagnetic waves and the frequency selectivity of dielectric gratings with periodicity in two dimensions, having in mind their application as dichroic surfaces in the millimeter wave band. The moment method and the Green's functions, along with the volume equivalence theorem are used. Particular cases were analyzed to compare with results available in the specialized literature and agreement was observed. This work gives evidence that the inclusion of the periodicity along a second dimension allows an additional adjusting parameter of the frequency selective characteristics for the design requirements of dielectric gratings.     

Dielectric matrices with air cavities as a waveguide photonic crystal

Frequency dependences of the transmission coefficient of a microwave photonic crystal that represents a structure containing alternating layers of ceramic material (Al₂O₃) with a relatively large number of cavities and foam plastic are studied in the presence and absence of distortions of the periodicity of a photonic structure. The frequency dependences of the transmission coefficient can be analyzed using a model of effective medium that makes it possible to consider the interaction of electromagnetic wave and photonic crystal using a transfer matrix of a 1D photonic crystal. The band character of the frequency dependence of the transmission coefficient of the photonic crystal related to the periodicity of the photonic crystal in the transverse plane for the waveguide with a standard cross section is not manifested in a certain range of material permittivities.     

Experimental and numerical study of the propagation of focused wave groups in the nearshore zone

The propagation of focused wave groups in intermediate water depth and the shoaling zone is experimentally and numerically considered in this paper. The experiments are carried out in a two-dimensional wave flume and wave trains derived from Pierson-Moskowitz and JONSWAP spectrum are generated. The peak frequency does not change during the wave train propagation for Pierson-Moskowitz waves; however, a downshift of this peak is observed for JONSWAP waves. An energy partitioning is performed in order to track the spatial evolution of energy. Four energy regions are defined for each spectrum type. A nonlinear energy transfer between different spectral regions as the wave train propagates is demonstrated and quantified. Numerical simulations are conducted using a modified Boussinesq model for long waves in shallow waters of varying depth. Experimental results are in satisfactory agreement with numerical predictions, especially in the case of wave trains derived from JONSWAP spectrum.     

Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system

We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.     

Nearly backward reflection of bulk acoustic waves at grazing incidence in a TeO2 crystal

Reflection of bulk acoustic waves in a TeO₂ acoustooptic single crystal is studied for the case of a grazing incidence on the free crystal-vacuum boundary. The propagation and reflection of elastic waves is considered in the XOY plane of the material cut out in the form of a rectangular prism. An extraordinary case of reflection at the grazing incidence, when the energy flow of one of the two reflected waves in the crystal is directed opposite to that of the incident wave, is studied. It is shown that the transformation of the incident elastic energy into the energy of the backward-reflected wave can occur with an efficiency close to 100% and can be observed in a wide range of crystal cut angles. An abrupt change of the reflection coefficients in the vicinity of the critical angle is predicted.