Photonic band gap of one-dimensional periodic structure containing dispersive left-handed metamaterials

Band structures of one-dimensional(1D)photonic crystals(PCs)containing dispersive left-handed metamaterials are studied theoretically.The results show that the structure possesses a type of photonic band gap originating from total internal reflection(TIR).In contrast to photonic band gaps corresponding to zero average refractive index and zero phase.the TIR gap exhibits sharp angular effect and has no polarization effect.It should also be noted that band structures of transverse electric(TE) and transverse magnetic(TM) mode waves are exactly the same in the PCs we studied.     

Positive-negative birefraction phenomenon for TM polarization in annular photonic crystal

We propose a two-dimensional (2D) annular photonic crystal (APC) with dual equi-frequency contours (EFCs) in one band. The refractive behaviors of a Gaussian beam incident from air to the APC are analyzed by the EFC analysis and finite-diflerence time-domain (FDTD) method. The results show the positive-negative birefraction phenomenon for the transverse magnetic (TM) polarization in the same band occurs at the interface between air and the APC, and the surface termination of the APC has a large effect on the strength of the negatively refracted beam.     

Localisation of elastic waves in two-dimensional randomly disordered solid phononic crystals

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional solid–solid phononic crystals with the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the disorder degree on the band structures for both anti-plane and in-plane wave modes are investigated. It is found that, with increase of the disorder degree, the band gaps become narrower with more flat bands appearing in the gaps. Both displacement distribution and response spectra show that at the flat bands, elastic waves are localised due to the presence of the disorder. Wave localisation is more pronounced at the flat bands near the lower/upper edge for the radius/location disorder. Wave propagation and localisation in a randomly disordered system with a point defect is also studied. The influence of the disorder on the point-defect state is discussed. The results show that the disorder can tune the frequencies of the defect states. It is particularly noticed that the double degenerate mode appearing within the gap of the mixed in-plane waves is split up into two separated ones when the random disorder is introduced into the system. Generally, the influence of the disorder is more pronounced for the mixed in-plane modes than the anti-plane modes. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on wave behaviours in phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into periodic systems.     

Enhancement of phononic band gaps in ternary/binary structure

Based on the transfer matrix method (TMM) and Bloch theory, the interaction of elastic waves (normal incidence) with 1D phononic crystal had been studied. The transfer matrix method was obtained for both longitudinal and transverse waves by applying the continuity conditions between the consecutive unit cells. Dispersion relations are calculated and plotted for both binary and ternary structures. Also we have investigated the corresponding effects on the band gaps values for the two types of phononic crystals. Furthermore, it can be observed that the complete band gaps are located in the common frequency stop-band regions. Numerical simulations are performed to investigate the effect of different thickness ratios inside each unit cell on the band gap values, as well as unit cells thickness on the central band gap frequency. These phononic band gap materials can be used as a filter for elastic waves at different frequencies values.     

Transverse wave band gaps and longitudinal wave band gaps in solid phononic crystals

Based on the properties of transverse (divergenceless) waves and longitudinal (irrotational) waves, we divided the transverse wave modes and longitudinal wave modes from the mixed eigen modes in solid phononic crystals. By investigating the transverse wave and longitudinal wave band structures at low frequency, we found that transverse bands and longitudinal bands exhibit different behaviors in solid systems including spherical scatterers. Phononic crystal with a large density ratio of solid spheres to the background can guarantee both the large longitudinal and large transverse band gap, but solid spheres with a small ratio of longitudinal wave velocity to transverse wave velocity can only help to enlarge the longitudinal band gap, and do not help to enlarge the transverse band gap.     

Backscattering enhancements from Rayleigh waves on the flat face of a tilted solid cylinder in water

When the face of a finite solid elastic cylinder is ensonified by an acoustic wave, a variety of backscattering contributions associated with acoustic wave coupling into elastic waves are observed. A significant backscattering enhancement is observed for tilts such that the acoustic wave is incident on the face of the cylinder in the vicinity of the coupling angle for launching Rayleigh waves across the face. The observed backscattering indicates that the Rayleigh waves are reflected at the edge of the face and subsequently radiate acoustic waves in the backscattering direction. The measured backscattering is compared to an approximate theoretical prediction. Approximating the focusing of the Rayleigh wave after reflection at the (circular) edge by a Gaussian beam pressure distribution on the cylinder's face yields simple expressions for the amplitude which are consistent with the measurements. In the vicinity of end-on incidence, other backscattering contributions due to the reflection of waves traveling down the length of the cylinder are observed. There is also evidence of a face-traversing longitudinal wave for slightly tilted cylinders.     

The layer multiple-scattering method for calculating transmission coefficients of 2D phononic crystals

We extend the layer multiple-scattering theory (LMST) to elastic waves propagating in two-dimensional (2D) periodical composites. The formalism to calculate the reflection and transmission coefficients for elastic waves through finite slabs is presented. In this spirit, the crystal is viewed as a sequence of identical monolayer which has one-dimensional (1D) periodicity along a given direction. The reflection and transmission coefficients for a multilayer slab can be obtained by a double-layer scheme through the calculation of the scattering matrix of a monolayer. To demonstrate the application of this formalism, we calculate transmission coefficients for systems consisting of pure solid components or mixing (solid and fluid) components. The validity of this method is checked by both band structure calculations and transmission measurement of ultrasonic experiment.     

Investigating the dispersive properties of the three-dimensional photonic crystals with face-centered-cubic lattices containing epsilon-negative materials

In this paper, dispersive properties of three-dimensional (3D) photonic crystals (PCs) with face-centered-cubic (fcc) lattices composed of the isotropic positive-index materials and epsilon-negative materials are theoretically investigated based on a modified plane wave expansion (PWE) method. The eigenvalue equations of such structure (spheres with epsilon-negative materials inserted in the dielectric background) are deduced. The band structures can be obtained by solving such nonlinear eigenvalue equations. It can be obviously seen that a photonic band gap (PBG), a flat band region, and two stop band gaps (SBGs) in the Г-X and Г-L directions appear, respectively. The results show that the upper edges of flat band region cannot be tuned by any parameters except for the electronic plasma frequency. The first PBG and the first SBGs above the flat band region in the Г-X and Г-L directions for the 3D PCs can be modulated by the filling factor, relative dielectric constant and electronic plasma frequency, respectively. However, the damping factor has no effect on the locations of the first PBG and the first SBGs above the flat band region in the Г-X and Г-L directions. These results may provide theoretical instructions to design the future optoelectronic and communication devices containing epsilon-negative materials.     

Imaging properties of triangular lattice photonic crystal at multi-bands

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction in the second and the eighth band. A flat superlen formed from such a PC has been designed and its imaging properties have been investigated systematically. Both in band 2 and band 8, a quite high quality image in the opposite side of the slab can be found.     

Simultaneous complete elastic and electromagnetic band gaps in periodic structures

We study elastic and electromagnetic properties in periodic structures and present “deaf and blind” structures, i.e. materials having simultaneous complete phononic and photonic band gaps, that is, transverse electric (TE) and transverse magnetic (TM) electromagnetic waves, pure shear elastic waves, and mixed shear and dilatation elastic waves, cannot propagate within these structures. These composite materials can control the flow of light and sound at the same time. The existence of complete gaps for electromagnetic and elastic waves can lead to the simultaneous localization of light and sound, a novel phenomena that can have strong influence on photon–phonon interactions. We study the dependence of the simultaneous and complete gaps on material parameters to provide design guidelines on how to create these photonic–phononic crystals. PACS 78.66.Sq; 78.20.Bh; 63.20.-e     

Low band gap frequencies and multiplexing properties in 1D and 2D mass spring structures

This study reports on the propagation of elastic waves in 1D and 2D mass spring structures.An analytical and computation model is presented for the 1D and 2D mass spring systems with different examples.An enhancement in the band gap values was obtained by modeling the structures to obtain low frequency band gaps at small dimensions.Additionally,the evolution of the band gap as a function of mass value is discussed.Special attention is devoted to the local resonance property in frequency ranges within the gaps in the band structure for the corresponding infinite periodic lattice in the 1D and 2D mass spring system.A linear defect formed of a row of specific masses produces an elastic waveguide that transmits at the narrow pass band frequency.The frequency of the waveguides can be selected by adjusting the mass and stiffness coefficients of the materials constituting the waveguide.Moreover,we pay more attention to analyze the wave multiplexer and DE-multiplexer in the 2D mass spring system.We show that two of these tunable waveguides with alternating materials can be employed to filter and separate specific frequencies from a broad band input signal.The presented simulation data is validated through comparison with the published research,and can be extended in the development of resonators and MEMS verification.     

k=0处的类狄拉克锥

狄拉克锥在电子和经典波体系中分别被发现, 由于其线性能带关系, 伴随着很多独特的现象. 除了一般存在于布里渊区边界处的狄拉克锥, k=0处也存在包含线性能带关系的类狄拉克锥. 这个类狄拉克锥可以由单极子和偶极子的偶然简并而形成. k=0处的类狄拉克锥可以通过两维电介质光子晶体来实现, 利用等效媒质理论, 此时的光子晶体在类狄拉克点频率可以等效为介电常数和磁导率都为零的材料. 电介质双零折射率材料既可以避免阻抗的不匹配, 也可以避免体系推广到高频所引起的强烈损耗. 此外, k=0处的类狄拉克锥与双零折射率的概念可以从两维体系拓展到三维体系, 而且还可以从电磁波体系推广到声波和弹性波体系. 利用具有类狄拉克点的两维光子晶体, 在材料参数都偏离类狄拉克点条件的两个半无限大光子晶体所构成的界面中, 一定存在界面态. 这些界面态的存在可以通过层状多重散射理论得到的表面阻抗以及体能带的几何相位来彻底解释.     

高质量三维胶体光子晶体中慢光速与超光速的实验研究

利用飞秒脉冲自相关技术研究了高质量三维胶体光子晶体中的慢光速和超光速效应.实验中使用的胶体光子晶体是采用压力控制的绝热沉积技术（PCIHVD）制备的、由聚苯乙烯小球组成的人工蛋白石结构.由于其中的缺陷和位错密度很低,它们具有很高的通带透过率和陡峭的能带边缘.测量了从通带到带边直至带隙中央群速度的变化,在只有20层左右小球的样品中观察到低至0.43c的慢光速以及高至1.34c的超光速现象.此外,利用时域有限差分（FDTD）方法对短脉冲在三维光子晶体中的群速度进行了数值模拟,并且和 关键词： 三维胶体光子晶体 慢光速 超光速 脉冲自相关     

Elastic band structures of two-dimensional solid phononic crystal with negative Poisson's ratios

In this paper, the elastic band structures of two-dimensional solid phononic crystals (PCs) with both negative and positive Poisson's ratios are investigated based on the finite difference domain method. Systems with different combinations of mass density ratio and shear modulus ratio, filling fractions and lattices are considered. The numerical results show that for the PCs with both large mass density ratio and shear modulus ratio, the first bandgap becomes narrower with its upper edge becoming lower as Poisson's ratio of the scatterers decreases from −0.1 to −0.9. Generally, introducing the material with a negative Poisson's ratio for scatterers will make this bandgap lower and narrower. For the PCs with large mass density ratio and small shear modulus ratio, the first bandgap becomes wider with Poisson's ratio of the scatterers decreasing and that of the host increasing. It is easy to obtain a wide low-frequency bandgap by embedding scatterers with a negative Poisson's ratio into the host with a positive Poisson's ratio. The PCs with large filling fractions are more sensitive to the variations of Poisson's ratios. Use of negative Poisson's ratio provides us a way of tuning bandgaps.     

Quasidislocation stoneley wave and Eshelby dislocation Scholte wave

A quasidislocation (a dislocationlike entity described here for the first time) moves at the speed of a Stoneley surface wave that travels at the interface between two different elastic solids. An Eshelby glide edge dislocation moves at the speed of a Scholte surface wave that travels at the interface between a solid and an ideal liquid. The quasidislocation and the glide edge dislocation (that moves at the Eshelby velocity) are the Green's functions of their waves. Scholte waves are planar distributions of transonic moving glide edge dislocations. They are not Stoneley waves, although often called by that name, because Stoneley waves are planar distributions of subsonic moving quasidislocations.     

High-frequency susceptibility of a superlattice with 2D inhomogeneities

We investigate the high-frequency susceptibility (Green function) of an initially sinusoidal 1D superlattice with 2D phase inhomogeneities that model the deformations of the interfaces between the superlattice layers. For waves propagating along the superlattice axis (the geometry of a photon or magnon crystal), we have found a peculiar behavior of the imaginary part of the Green function that consists in a significant difference between the peaks corresponding to the edges of the band gap in the wave spectrum. The peak corresponding to the lower-frequency band edge remains essentially unchanged as the root-mean-square fluctuation of the 2D inhomogeneities γ₂ increases, while the peak corresponding to the higher-frequency band edge broaden and decreases sharply in height until its complete disappearance with increasing γ₂. This behavior of the peaks corresponds to a band gap closure mechanism that differs from the traditional one characteristic of 1D and 3D inhomogeneities. These effects can be explained by a peculiarity of the energy conservation laws for the incident and scattered waves for 2D inhomogeneities in a 1D superlattice.     

Elastic waves in carbon 2D supracrystals

The elastic moduli and propagation velocities of elastic waves in 2D supracrystalline nanoallotropes of carbon have been calculated. It has been shown that these velocities in sp ² nanoallotropes are close to those in graphene and exceed the propagation velocities of elastic waves in single-crystal diamond by a factor of 2. The propagation velocities of both longitudinal and transverse elastic waves in carbon 2D supracrystalline sp ³ nanoallotropes are several times lower than those in sp ² nanoallotropes.     

基于集中质量法的一维声子晶体弹性波带隙计算

通过将一维声子晶体中的原胞简化为有限多个自由度的弹簧振子结构，引入了一种基于集中 质量法的一维声子晶体弹性波带隙计算方法.与传统平面波展开法相比，该方法的计算结果 与之相符合，而且在收敛性方面较之有很大改善.通过使用集中质量法，可在得到同样计算 精度的条件下，显著降低计算量，提高计算速度. 关键词： 声子晶体 弹性波带隙 集中质量法 平面波展开法     

Negative refraction imaging of solid acoustic waves by two-dimensional three-component phononic crystal

By using of the multiple scattering methods, we study the negative refraction imaging effect of solid acoustic waves by two-dimensional three-component phononic crystals composed of coated solid inclusions placed in solid matrix. We show that localized resonance mechanism brings on a group of flat single-mode bands in low-frequency region, which provides two equivalent frequency surfaces (EFS) close to circular. The two constant frequency surfaces correspond to two Bloch modes, a right-handed and a left-handed, whose leading mode are respectively transverse (T) and longitudinal (L) modes. The negative refraction behaviors of the two kinds of modes have been demonstrated by simulation of a Gaussian beam through a finite system. High-quality far-field imaging by a planar lens for transverse or longitudinal waves has been realized separately. This three-component phononic crystal may thus serve as a mode selector in negative refraction imaging of solid acoustic waves.     

Transition radiation of seismic waves at the atmosphere-earth interface

The method of contour integration is used for solving the problem of transition radiation of elastic waves by a mass source, which travels uniformly in a gas normal to the interface between homogeneous gaseous and elastic halfspaces and disappears at the time it touches the solid surface. We have obtained asymptotic formulas for the field of transition radiation, which hold true near the fronts of longitudinal and transverse spherical waves and a conical wave. An exact analytical expression for the field of transition radiation has been obtained for the observation points located on the source trajectory extension in a solid. The influence of interaction between longitudinal and transverse waves, which occurs on the surface of elastic medium, on the space distribution of the field of transition radiation is analyzed. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1210–1223, October, 1997.