Matryoshka locally resonant sonic crystal

The results of numerical modeling of sonic crystals with resonant array elements are reported. The investigated resonant elements include plain slotted cylinders as well as their various combinations, in particular, Russian doll or Matryoshka configurations. The acoustic band structure and transmission characteristics of such systems have been computed with the use of finite element methods. The general concept of a locally resonant sonic crystal is proposed that utilizes acoustic resonances to form additional band gaps that are decoupled from Bragg gaps. An existence of a separate attenuation mechanism associated with the resonant elements that increases performance in the lower frequency regime has been identified. The results show a formation of broad band gaps positioned significantly below the first Bragg frequency. For low frequency broadband attenuation, a most optimal configuration is the Matryoshka sonic crystal, where each scattering unit is composed of multiple concentric slotted cylinders. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for noise barrier technology. The finding opens alternative perspectives for the construction of sound barriers in the low frequency range usually inaccessible by traditional means including conventional sonic crystals.     

A sonic crystal diode implementation with a triangular scatterer matrix

This paper investigates a nonreciprocal sound transmission effect provided by a triangular lattice two-dimensional sonic crystal made of rods in a triangular cross-section. This sonic crystal (SC) device works as a frequency selective acoustic diode operating at a frequency of 8950 Hz. The scatterer matrix of the sonic crystal diode prototype was composed of triangular shaped wood rods that break the symmetry of the spatial inversion and provide nonreciprocal wave transmission with a contrast rate of 89% in experiments. This acoustic diode device can provide a high contrast, narrow band, one-way sound transmission for acoustic wave control applications.     

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.     

径向声子晶体隔声特性*

该文构造了由两种匀质材料交替分布的径向声子晶体柱壳模型。首先,针对声波在其中的轴对称传播情况进行了理论分析,建立了声波由内向外传播的传递矩阵,进而导出了声压透射系数和隔声量表达式。采用数值分析的方法系统地讨论了径向声子晶体柱壳的隔声特性,并与单一材质柱壳的传播规律进行对比分析,其次,借助有限元仿真分析的手段对数值结果进行了验证。最后,详细分析了内外流体的特性阻抗对径向声子晶体柱壳隔声特性的影响,得到了相应的参数影响规律。研究表明,径向声子晶体柱壳存在声波带隙,导致其在带隙范围内的隔声效果远远优于单材质柱壳,并且该结构的固有特性突破了质量定律的限制;声波带隙内表面局域态现象出现与否由内外声场和结构场共同决定。     

Band structures of two dimensional solid/air hierarchical phononic crystals

The hierarchical phononic crystals to be considered show a two-order “hierarchical” feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.     

Transmission and radiation of acoustic oblique incident through tube arrays based on phononic crystals theory

In a utility boiler, the heat exchanger’s structure is similar to a two-dimensional phononic crystal. Based on the phononic crystal theory, this paper studies sound propagation through tube arrays as a function of the incident sound direction and the surroundings temperature. We carried out both the computational and experimental work for particular values of the pitch and diameters in the tube arrays and studied the band-gap diagram and insertion loss spectra for different angles of incidence. The first band gap is found to correspond to Bragg’s Law while the second band gap moves to lower frequencies as the angle increases. Simulations indicate also that the uneven temperature field influences the insertion loss spectrum. Results of experiments and calculations confirm that, for a particular tube array, the most important factors influencing sound propagation are incidence angle and the surrounding temperature. For the acoustic source in tube arrays, the acoustic radiation have relation with the frequency whether in the acoustic bang gap or not. The results should provide a basis for further work: both on sound source localization and low frequency sonic cleaning in large tube arrays.     

Propagation of acoustic waves in the woodpile sonic crystal with a defect

Acoustic wave propagation in a woodpile sonic crystal with a defect is studied theoretically and experimentally. The woodpile sonic crystal is composed of polymethyl methacrylate square rods which orthogonally stacked together, and it is embedded in air background. Defects are created by varying the width and positions of the middle rods in the periodic structure. Defect bands and transmission spectra are calculated by using the finite element method with the periodic boundary condition and the Bloch–Floquet theorem. Frequencies of defect bands are strongly dependent on the width and positions of the middle rods in the periodic structure. The experimental transmission spectra of the woodpile sonic crystals with a defect are also presented and compared with the numerical results. The defect mode properties of the woodpile sonic crystal with a defect can be applied to design novel acoustic devices for filtering sound and trapping sound in defects.     

一维光子晶体禁带的展宽

作为一维光子晶体的应用基础，一维光子晶体的禁带是研究的重点。通过传输矩阵的方法分析了一维光子晶体禁带的特性，讨论了影响带宽的因素。说明了相对带宽对光子晶体设计的重要性。在这个基础上讨论了扩展一维光子晶体带宽的方法，提出了在角域范围内对光子晶体进行叠加的方法，为设计制造一维光子晶体提供了一种行之有效的方法。分别对2个、3个和4个晶体的叠加进行了分析，最后计算了所设计的合成晶体的反射率。其中4个晶体的叠加，相对带宽达到57．52％，极大地展宽了一维光子晶体的禁带，从而证明利用角域的叠加来展宽一维光子晶体的禁带是非常有效的。     

声波在二维固/流声子晶体中的禁带特性研究

采用时域有限差分法(FDTD),分析了声波在二维四方点阵铝/空气组合声子晶体中的禁带特性,并利用实验测试验证了理论分析的正确性.在此基础上研究了两种不同声阻抗率比固(实心圆柱和空心圆管)/流系统声子晶体的禁带特性.对于实心圆柱体,分析了有限尺寸结构声子晶体在传播方向上的层数对声波传播特性的影响,得到了这两种系统在不同填充率下取得最大声波禁带宽度所需的最少层数.同时指出,在低声阻抗率比条件下,对于空心圆管填充物,通过选取适当的半径比,可以获得比实心柱体更宽的方向带隙.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

Standardised acoustic characterisation of sonic crystals noise barriers: Sound insulation and reflection properties

This work presents sound insulation and sound reflection measurements conducted over sonic crystal noise barriers according to the European standards EN 1793-2, EN 1793-5 and EN 1793-6. In most of the reference literature, sound insulation and reflection properties of sonic crystals are measured or a diffuse sound field or in a direct sound field including the top and side edge diffraction effects together with the transmitted (or reflected) components. The aim of this work is to perform free-field measurements over a real-sized sample in order to window out all diffraction components and to verify the points of strength and weakness of the application of standardised measurements to sonic crystals. Diffuse field measurements in laboratory are also done for comparison purposes. Since the target frequency range for traffic noise spectrum is centred at around 1000 Hz, a finite element based parametric investigation is performed to design unit cells capable of generating band gaps in the one-third octave bands ranging from 800 Hz to 1250 Hz. Then, 3 × 3 m sonic crystal noise barriers are installed in the Laboratory of the University of Bologna and sound insulation and sound reflection measurements are performed according to the mentioned active standards for normal incidence. Sound insulation is measured for diffuse incidence too. The two methods give different results. The method more directly comparable to calculations is the free-field one. However, if on the one hand the application of a time window allows to compute the transmitted or reflected component only, on the other hand the time window itself limits the maximum width of the sample for which all reflections of the n-th order having a significant spectral content are included, and thus results critical in the analysis of this kind of noise barriers. Nevertheless, the standardised measurements allow a direct comparison between the performance of sonic crystals and common noise barriers.     

Fusion in prospect

In the first part of this introductory review we outline the developments in photonic band gap materials from the physics of photonic band gap formation to the fabrication and potential applications of photonic crystals. We briefly describe the analogies between electron and photon localization, present a simple model of a band structure calculation and describe some of the techniques used for fabricating photonic crystals. Also some applications in the field of photonics and optical circuitry are briefly presented. In the second part, we discuss the consequences for the interaction between an atom and the light field when the former is embedded in photonic crystals of a specific type, exhibiting a specific form of a gap in the density of states. We first briefly review the standard treatment (Weisskopf?–?Wigner theory) in describing the dynamics of spontaneous emission in free space from first principles, and then proceed by explaining the alterations needed to properly treat the case of a two-level atom embedded in a photonic band gap material.     

基于手性声子晶体的谷拓扑声输运

研究手性风车形散射体构建的谷拓扑声波导。具有右手与左手手性风车形散射体的声子晶体具有截然不同的声谷拓扑特性。当两种手性风车形散射体从-60°旋转到60°时,其所构建的声子晶体均出现2次偶然简并的狄拉克点与谷霍尔相变。基于两种具有相反谷霍尔相的手性声子晶体构建的谷拓扑声波导,在其重叠体带隙内存在一对局域在波导分界面处的谷态边缘态。实验研究表明,该边缘态可以很好的支持谷拓扑声输运,且对弯曲与无序两种缺陷具有一定的鲁棒性.      

Higher-Order Topological Spin Hall Effect of Sound

We theoretically propose a reconfigurable two-dimensional(2 D) hexagonal sonic crystal with higher-order topology protected by the six-fold,C_6,rotation symmetry.The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit cell.In the nontrivial phase,the sonic crystal realizes the topological spin Hall effect in a higher-order fashion:(i) the edge states emerging in the bulk band gap exhibit partial spin-momentum correlation and are gapped due to the reduced spatial symmetry at the edges.(ii) The gapped edge states,on the other hand,stabilize the topological corner states emerging in the edge band gap.The partial spin-momentum correlation is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta,where the pseudospin is emulated by the acoustic orbital angular momentum.We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.     

广义Fibonacci准周期结构声子晶体透射性质的研究

提出了一维广义Fibonacci准周期结构的声子晶体模型. 对弹性波通过该一维准周期结构声子晶体的透射系数进行数值计算,并与周期结构和标准Fibonacci准周期结构声子晶体的透射系数进行比较. 结果表明,利用一维广义Fibonacci准周期结构的声子晶体可获得比周期结构和标准Fibonacci准周期结构声子晶体更大的带隙范围,同时在带隙内有更丰富的局域模式存在. 对局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 广义Fibonacci准周期结构 声子晶体 局域化     

Oblique incidence properties of locally resonant sonic materials with resonance and Bragg scattering effects

A locally resonant sonic material (LRSM) is an elastic matrix containing a periodic arrangement of identical local resonators (LRs), which can reflect strongly near their natural frequencies, where the wavelength in the matrix is still much larger than the structural periodicity. Due to the periodic arrangement, an LRSM can also display a Bragg scattering effect, which is a characteristic of phononic crystals. A specific LRSM which possesses both local resonance and Bragg scattering effects is presented. Via the layered-multiple-scattering theory, the complex band structure and the transmittance of such LRSM are discussed in detail. Through the analysis of the refraction behavior at the boundary of the composite, we find that the transmittance performance of an LRSM for oblique incidence depends on the refraction of its boundary and the transmission behaviors of different wave modes inside the composite. As a result, it is better to use some low-speed materials (compared with the speed of waves in surrounding medium) as the LRSM matrix for designing sound blocking materials in underwater applications, since their acoustic properties are more robust to the incident angle. Finally, a gap-coupled LRSM with a broad sub-wavelength transmission gap is studied, whose acoustic performance is insensitive to the angle of incidence.     

Impacts of uniaxial elongation on the bandstructures of two-dimensional sonic crystals and associated applications

Influences of uniaxial elongation along the [11] direction of triangular and [10] direction of square sonic crystals under the constraint of conserved unit cell area are investigated by examining band structures and equi-frequency contours. Lowest-lying band gap of the triangular lattice observed at high filling fractions diminishes for negative elongation (compression), whereas another band gap develops at lower frequencies whose width reaches appreciable values for moderate elongation. The band gap of the square lattice, which appears at high filling fractions, is modified slightly with elongation. Frequency ranges of the bands, and thus the group velocities along the high-symmetry directions, vary with elongation which may be useful in applications like slow sound propagation. Elongation is observed to modify the equi-frequency contours significantly through reducing the lattice symmetry. The most prominent impact is the transformation of closed contours into open ones, whereas the rest are stretched either along or normal to the elongation axis of the 1st Brillouin Zone. This observation is utilized to implement wide-band all-angle self-collimation and superprism effect, which are demonstrated through Finite-Element computations.     

An Analysis of Structural-Acoustic Coupling Band Gaps in a Fluid-Filled Periodic Pipe

A periodic pipe system composed of steel pipes and rubber hoses with the same inner radius is designed based on the theory of phononic crystals. Using the transfer matrix method, the band structure of the periodic pipe is calculated considering the structural-acoustic coupling. The results show that longitudinal vibration band gaps and acoustic band gaps can coexist in the fluid-filled periodic pipe. The formation of the band gap mechanism is further analyzed. The band gaps are validated by the sound transmission loss and vibration-frequency response functions calculated using the finite element method. The effect of the damp on the band gap is analyzed by calculating the complex band structure. The periodic pipe system can be used not only in the field of vibration reduction but also for noise elimination.     

Applications of the finite difference mode solution method to photonic crystal structures

The finite difference waveguide mode solution method, which has been popularly employed in the study of waveguide modes on various optical and dielectric waveguides, is utilized to calculate the modal characteristics of photonic crystal fibers (PCFs) and planar photonic crystal waveguides and the band diagrams of two-dimensional photonic crystals. Vector guided modes on both PCFs based on the total internal reflection guiding mechanism ('holey fibers') and those resulting from photonic band gap effect are accurately computed, with their effective indexes and field distributions compared with other methods. Calculated dispersion of a single-core holey fiber and coupled-power behavior of a two-core holey fiber are found to agree with measured results. For applications to band diagram calculation and planar photonic crystal waveguide analysis, the finite difference scheme is modified simply by imposing suitable periodic boundary condition. Numerical results for air-column crystals and dielectric-rod crystals are both found to agree well with calculations using other methods.     

Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode

Nonreciprocal wave propagation typically requires strong nonlinear materials to break time reversal symmetry. Here, we utilized a sonic-crystal-based acoustic diode that had broken spatial inversion symmetry and experimentally realized sound unidirectional transmission in this acoustic diode. These novel phenomena are attributed to different mode transitions as well as their associated different energy conversion efficiencies among different diffraction orders at two sides of the diode. This nonreciprocal sound transmission could be systematically controlled by simply mechanically rotating the square rods of the sonic crystal. Different from nonreciprocity due to the nonlinear acoustic effect and broken time reversal symmetry, this new model leads to a one-way effect with higher efficiency, broader bandwidth, and much less power consumption, showing promising applications in various sound devices.