Uncoupled photonic band gaps

We theoretically investigated the symmetry properties of the modes in two-dimensional square lattice photonic crystals in order to study phenomena that would enable new frontiers in the applications of photonic crystals. Using group theory, symmetry analysis of the photonic crystals bands has been done. Particular attention was given to the search for the uncoupled B modes that cannot be excited by the external plane wave because they are symmetry forbidden. The existence of the uncoupled modes enabled to define new physics phenomena: uncoupled photonic band gaps. For the frequency ranges inside the uncoupled photonic band gaps, zero transmission is obtained. Therefore, there are two different types of photonic gaps in the photonic crystals: photonic band gaps and uncoupled photonic band gaps. The appearance of uncoupled photonic band gaps in photonic crystals could at least improve the application of the existing photonic materials and structures or even enable the usage of new ones for devices like waveguides, filters, and lasers.     

Analysis of the effect of blocking mass at corner interface of two plates at arbitrary angles on transmission of plane bending waves

Vibration energy transmission at corner interface of two infinite plates rigidly jointed at arbitrary angles was studied by wave approach so as to investigate the effect of blocking mass used for reducing plane bending wave transmission.Two local coordinate sys- tems were introduced and six new non-dimensional coefficients implying corresponding ratio governing characteristic impedances of plates or blocking mass were introduced to simplify for- mulations of transmission and reflection coefficients.Five samples were tested in experiment. Discussions were carried out based on the comparison between prediction and experiment in terms of insertion loss.It is concluded that blocking mass at corner interface acts like a"low- pass filter",effective for vibration attenuation above certain frequency.The value of TL and IL in"attenuation band"depends mainly on mass per unit length and band width of"attenuation band"on mass moment of inertia per unit length of the blocking mass.     

一维光子晶体光学特性的复平面波展开法研究

应用复平面波展开法对一维光子晶体的光子带隙, 透射特性进行了分析. 通过对色散关系和透射系数的数值计算发现一维光子晶体周期结构个数以及折射率分布对光学晶体透射系数以及光子带隙的影响. 对于含有整数个周期结构的光子晶体有共振点出现在光子帯隙外的频率范围内, 共振点的个数比周期结构个数少1. 带隙倾斜斜率等于折射率的比值. 折射率比值越大, 带隙的范围越大.     

Dependence of second harmonic generation efficiency on the density of the optical mode

The results of numerical simulations of second harmonic generation in photonic band gap structures with GaAs/AlAs and SiO₂/GaAs quarter-wave layers under the action of a femtosecond pulse pump are presented. The transmission and reflection coefficients and the density of the optical modes for these photonic band gaps were calculated.     

The band gaps of Lamb waves in a ribbed plate: A semi-analytical calculation approach

In this paper a semi-analytical method is proposed to investigate the transmission band gaps of Lamb waves through repetitive structures in a waveguide. For a unit cell the scattering matrix is obtained by the Lamb mode matching technique at each artificially sliced interface and then substituted into the Bloch theorem to solve the eigenproblem incurred by cell repetition. The method is implemented on a ribbed plate. The band gaps in the dispersion curves are confirmed by the dips of Lamb wave transmission coefficients, and attributed to the coupled vibrations of Lamb modes in different sliced sections of the unit cell.     

Acoustic characteristics of circular bends in pipes

The acoustic properties of circular bends in pipework systems are investigated by calculation of the mode shapes and propagation constants of the acoustic modes of the bend, the torus modes, and by evaluation of the transmission and reflection coefficients at a bend in an otherwise infinite straight pipe. The coefficients for the first three cylinder and torus modes are plotted against frequency for the case of a plane wave incident upon a 90° bend. The pipe walls are assumed to be rigid.     

Design guidelines of 1-3 piezoelectric composites dedicated to ultrasound imaging transducers, based on frequency band-gap considerations

Periodic piezoelectric composites are widely used for imaging applications such as biomedical imaging or nondestructive evaluation. In this paper such structures are considered as phononic crystals, and their properties are investigated with respect to periodicity. This approach is based on the investigation of band gaps, that strongly depend on the properties of the considered composites (geometry, size, nature of materials). It is motivated by the fact that band gaps in principle allow one to excite the thickness mode without exciting other parasitic propagating waves. The used plane-wave-expansion method has already been applied to periodic piezoelectric composites, but, in contrast to previous approaches, not only waves propagating in the symmetry plane of the composite are considered, but also waves propagating with a nonzero angle of incidence with this plane. The method is applied to a representative 1-3 connectivity piezocomposite in order to demonstrate its potentialities for design purposes. The evolution of band gaps is explored with respect to the wave vector component parallel to piezoelectric transducer-rod axis. All bulk waves that contribute to the setting up of plate modes in the vicinity of the thickness mode are found and identified.     

Band structures of Fibonacci phononic quasicrystals

The paper studies the band structures of a two-component Fibonacci phononic quasicrystal which is considered as a phononic crystal disordered in a special way. Oblique propagation in an arbitrary direction of the in-plane elastic waves with coupling of longitudinal and transverse modes is considered. The transfer matrix method is used and the well-defined localization factors which are used to study the ordered and disordered phononic crystals are introduced to describe the band gaps of the phononic quasicrystals. The transmission coefficients are also calculated and the results show the same behaviours as the localization factor does. The results show the merits of using the localization factors. The band gaps of the phononic quasicrystal and crystals with translational and/or mirror symmetries are presented and compared to the perfect phononic crystals. More band structures are exhibited when symmetries are introduced to the phononic quasicrystals.     

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.     

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.     

One-dimensional photonic crystals with a planar oriented nematic layer: Temperature and angular dependence of the spectra of defect modes

Transmission spectra of a one-dimensional photonic crystal (PC) formed by two multilayer dielectric mirrors and a planar oriented layer of 5CB nematic liquid crystal (LC) that is sandwiched between these mirrors and serves as a structure defect are investigated experimentally. Specific features of the behavior of the spectrum of defect modes as a function of the angle of incidence of light on the crystal are studied for two polarizations: parallel and perpendicular to the director of the LC; the director either lies in the plane of incidence or is perpendicular to it. It is shown that, for the configurations considered, the maxima of the defect modes shift toward the short-wavelength region as the tilt angle of incidence radiation increases; this tendency is more manifest for the parallel-polarized component, when the director lies in the plane of incidence. In the latter case, the width of the photonic band gap (PBG) appreciably decreases. The temperature dependence of the polarization components of the transmission spectra of a PC is investigated in the case of normal incidence of light. The spectral shift of defect modes due to the variation of the refractive index of the LC at the nematic-isotropic liquid phase transition point is measured. It is shown that, in real PCs, the amplitude of defect modes decreases when approaching the center of the band gap, as well as when the number of layers in the dielectric mirrors increases. Theoretical transmission spectra of the PCs calculated by the method of recurrence relations with regard to the decay of defect modes are in good agreement with experimental data.     

Band gap behaviours of periodic magnetoelectroelastic composite structures with Kagome lattices

In this paper, the elastic wave propagation in periodic cylinder magnetoelectroelastic composite structures is studied using the plane wave expansion method. The band structure characteristics of magnetoelectroelastic rods embedded in polymer matrix and the reverse case are investigated taking the electric, magnetic and mechanical coupling effects into account. The generalised eigenvalue equation is derived to analyse the in-plane and out-of-plane modes, respectively. The numerical calculations for both the cases with Kagome lattices are performed. The relation between the gap widths and filling fractions are discussed in detail. The effects of the magnetoelectricity on the band structures and widths of band gaps are analysed. The band gap characteristics are illustrated further and the results will be helpful to design such kind of composite structures.     

Band structures of phononic-crystal plates in the form of a sandwich-layered structure

This study investigates the propagation of Lamb waves in phononic-crystal plates in the form of a sandwich-layered structure. The composite plates are composed of periodic layers bilaterally deposited on both sides of the homogeneous core layer. Using the analyses of the band structures and the transmission spectra, it is revealed that the core layer may induce significant modulations to the lower-order Lamb modes. The modulations are ascribed to the reshaped particle displacement fields of the eigenmodes. Prominently, the core layer made of soft material (rubber) combines the identical eigenmodes of the periodic layers into a pair of asymmetric and symmetric modes in which case the periodic layers vibrate independently. However, the core layer made of hard material (tungsten) or medium hardness material (silicon) couples the periodic layers tightly, in which case the composites vibrate as a whole. In addition, it is found that the phononic band gaps are very sensitive to the thickness of the core layer; this could be indispensable to practical applications such as bandgap tuning.     

Band structure of superconducting photonic crystals

The band structure of a two-dimensional superconducting photonic crystal is investigated. This crystal is considered a periodic system of nonoverlapping cylinders that have a circular cross section and are infinite in length. The results are obtained using the method of plane wave expansion of eigenfunctions. The photonic band structure is analyzed for two temperatures, namely, in the vicinity of the superconducting transition point and far from it. The two-dimensional superconducting photonic crystal is found to have complete and incomplete band gaps at low temperatures. As the temperature increases, these band gaps shift toward the short-wavelength range.     

Optical properties of multilayered Period-Doubling and Rudin-Shapiro porous silicon dielectric heterostructures

To investigate the optical properties in quasi-regular porous-silicon-based dielectric Period-Doubling and Rudin-Shapiro multilayer systems, we study here the reflection of light from these structures. The Period-Doubling and Rudin-Shapiro structures are fabricated in such a way that the optical thickness of each layer is one quarter of 600 and 640 nm respectively. We find that porous silicon Period-Doubling dielectric multilayers could demonstrate the optical properties similar to the classical periodic Febry–Perot interference filters with one or multiple resonant peaks, but with an advantage of having total optical thickness much lesser than the periodic structures. Additionally, light propagation in porous silicon Rudin-Shapiro structures is investigated for the first time, both theoretically and experimentally. The reflectance spectra of the structures exhibit photonic band gaps centered at predetermined wavelengths. In both cases, numerical simulation of light transmission is performed using transfer matrix method.     

Multiband polaritonic filter made of piezoelectric superlattices

The polaritonic band structures and transmission spectra of piezoelectric-modulated superlattices are investigated for a variety of supercell configurations. In the absence of a defect layer a polaritonic-like band gap exists and relative band gap can reach as large as 19% for superlattices made of LiNbO₃. In the presence of a defect layer, the positions and number of defect modes can be controlled directly by the number of domains in a supercell, the widths of defect modes are determined by layer thickness difference between defect domain and the periodic domain. Such uniformly distributed in-gap modes make them ideal candidates for the potential multiband filters.     

二维八重准晶有机光子晶体平板的光学传播特性

采用时域有限差分法研究了二维八重准晶有机光子晶体的光传输特性,重点分析了光束在聚苯乙烯空气柱平板结构和聚苯乙烯介质柱结构中的透射特性与光局域特性。研究结果表明,即使在低折射率对比度的情况下,两种完整八重准晶平板结构中均出现了可见光波段的光子带隙和本征模,且光子带隙中心位置随着平板厚度的增大而红移。当在两种准晶结构中引入缺陷微腔时,带隙内的缺陷模产生位置和波长红移特性随着微腔结构的变化规律明显不同,这种差异性是由两种物理机制(即光子晶体缺陷能级变化与微腔所支持的驻波条件)共同作用的结果。这一研究结果将为实验制备有机准晶发光器件提供一定的理论基础。     

局域共振复合单元声子晶体结构的低频带隙特性研究

本文提出了一种新型局域共振复合单元声子晶体结构, 并结合有限元方法对结构的带隙机理及低频共振带隙特性进行了分析和研究. 共振带隙产生的频率位置由所对应的局域共振模态的固有频率决定, 并且带隙宽度与局域共振模态的品质因子及其与基体之间的耦合作用强度有关. 采用局域共振复合单元结构可以实现声子晶体的多重共振, 在低频范围能打开多条共振带隙, 但受到共振单元排列方式的的影响. 由于纵向和横向局域共振模态的简并, 复合单元结构能在200 Hz以下的低频范围打开超过60%宽度的共振带隙, 最低带隙频率低至18 Hz. 这为声子晶体结构获得低频、超低频带隙提供了一种有效的方法. 关键词： 局域共振 低频带隙 复合单元 声子晶体     

SH wave propagation in magnetic–electric periodically layered plates

In this paper, dispersive behavior and band structure of SH waves in magnetic–electric (ME) periodically layered plate are investigated by the transfer matrix method. Two kinds of unit cell form, one is piezoelectric (PE)/piezomagnetic (PM)/PE, and the other is PM/PE/PM, are considered in detailed. A peculiar case of the generalized single-celled plate is first presented and then the multi-celled periodical layered plates for discussion on the propagation behaviors and the band characteristics of SH waves, respectively. The effects on dispersive curves of four kinds of ME boundary conditions at the free surface of plates are discussed. Numerical examples for phase velocities or frequencies all show that the zero-order mode is non-dispersive both for single-celled and multi-celled periodically layered plates. The high modes of dispersive curves tend to the shear wave velocity of the slower sub-layer as frequencies increase both for these two structures. The frequency pass-band and frequency band gaps appear in multi-layered ME periodically layered plates. Electrical and magnetic boundary conditions, respectively, determine the dispersive curves for SH waves in the PE/PM/PE and PM/PE/PM periodically layered plates.     

Modal decomposition method for modeling the interaction of Lamb waves with cracks

The interaction of the low-order antisymmetric (a0) and symmetric (s0) Lamb waves with vertical cracks in aluminum plates is studied. Two types of slots are considered: (a) internal crack symmetrical with respect to the middle plane of the plate and (b) opening crack. The modal decomposition method is used to predict the reflection and transmission coefficients and also the through-thickness displacement fields on both sides of slots of various heights. The model assumes strip plates and cracks, thus considering two-dimensional plane strain conditions. However, mode conversion (a0 into s0 and vice versa) that occurs for single opening cracks is considered. The energy balance is always calculated from the reflection and transmission coefficients, in order to check the validity of the results. These coefficients together with the through-thickness displacement fields are also compared to those predicted using a finite element code widely used in the past for modeling Lamb mode diffraction problems. Experiments are also made for measuring the reflection and transmission coefficients for incident a0 or s0 lamb modes on opening cracks, and compared to the numerical predictions.