Absolute band gaps and waveguiding in free standing and supported phononic crystal slabs

Using the finite element method (FEM), we investigate the existence of absolute band gaps and localized modes associated with a guide in thin films of phononic crystals. Two different structures based on two-dimensional (2D) phononic crystals are considered, namely a free standing plate and a plate deposited on a silicon substrate. The 2D phononic crystal is constituted by a square array of cylindrical holes drilled in an active piezoelectric PZT5A matrix. We demonstrate the existence of absolute band gap in the band structure of the phononic crystal plate and, then, the possibility of guided modes inside a linear defect created by removing one row of air holes. In the case of the supported plate, we show the existence of an absolute forbidden band in the plate modes when the thickness of the substrate significantly exceeds the plate thickness.     

Quality enhancement and insertion loss reduction of a rectangular resonator by employing an ultra-wide band gap diamond phononic crystal

We report on an ‘in plane mode’ band gaps investigation of a novel diamond CRS (circle-rectangle-square) shaped holey phononic crystals in the desired operating frequency ranges. An ultra-wide band gap for diamond in the ‘in plane mode’ is observed. We also investigate an ultra-wide acoustic band gap for a finite one-dimensional (1D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’, and an ultra-wide acoustic band gap of a finite two-dimensional (2D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’ based on the FEA (Finite Element Analysis) method. We analyze that the transmission response of diamond in the length extension and width extension manner is more reasonable. Ultra-wide peak attenuations in the transmission spectra of a CRS shaped diamond phononic crystal successfully reveal the complete band gaps. The wide band gap of a CRS shaped diamond phononic crystal and the wide peak attenuation strongly agree in the same frequency region. It is analyzed that when a CRS-diamond phononic crystal is employed for MEMS resonators with different tether widths the quality Q of the resonators improved, and the energy losses decrease with extremely low insertion loss. In addition, it is observed that the vibrational displacement of a resonator is reduced by employing a diamond phononic crystal.     

Transmission mode of one-dimensional phononic crystal based on coupling of total evanescent waves

In order to obtain the transmission properties of one-dimensional phononic crystal under total evanescent waves, we design structure model. Basing on the basic acoustic wave equations and boundary condition as well as the Bloch theory, we study the band structure of one-dimensional phononic crystal. We summarize the properties of the mode based on the coupling of total evanescent waves and explain its physical mechanism. There are three transmission modes in phononic crystal. Based on the coupling of total evanescent waves, the number of perfect transmission peaks is just equal to the number of structure period, and the thickness of period can be much less than the wave length.     

Angle-resolved transmission measurements through anisotropic two-dimensional plasmonic crystals

We report on high-accuracy angle-resolved optical transmission measurements through anisotropic 2D plasmonic crystals made of gold films with large-area rectangular arrays of nanoscale square holes, deposited on GaAs substrates. The measurements reveal the dispersion relations of air-gold and gold-GaAs surface plasmon polaritons. The crystal anisotropy induces a separation between plasmonic modes propagating in different directions. Their symmetry and dispersion properties are discussed.     

Effective velocity of 2D phononic crystals with rectangular lattice

The effective velocity of elastic waves for two-dimensional (2D) phononic crystals with rectangular lattice in the long-wavelength limit is studied by numerical simulations. It is demonstrated that, for all three propagating modes, not only the modes polarized in-plane (L wave and SV wave), but also the mode polarized out-plane (SH wave), the effective velocities are distinctly anisotropic and the slowness curves exhibit twofold symmetry. The anisotropy increases as the filling fraction increases or as the width to length ratio of the lattice decreases, and high anisotropy can be obtained in phononic crystals with large contrast between material parameters, which is much higher in rectangular lattice than in square lattice with the same material parameters. Owing to these dependences, the effective velocity can be controlled in engineering.     

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.     

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     

二维正方晶格多点缺陷声子晶体实验研究

基于超声浸水透射技术, 实验研究了有限尺寸二维正方晶格钢/水声子晶体多点缺陷模态性质. 利用COMSOL Multiphysics软件建立该声子晶体有限元计算方法, 求解了9×9超胞多点缺陷声子晶体能带结构, 把缺陷局域模态频率与数值仿真和实验结果进行对比, 结果表明: 实验数据和理论值能够很好符合. 进一步分析发现, 点缺陷数量影响声波局域效应、本征模态和传播特性, 为设计有限尺寸声波器件提供理论依据. 关键词： 声子晶体 多点缺陷 实验研究 有限元     

有效抑制光子晶体加载矩形谐振腔中模式竞争的方法

研究了光子晶体加载矩形谐振腔,针对传统光子晶体加载无法完全抑制模式竞争的问题,提出了特性阻抗和介质加载方法进行改进,完全实现了谐振腔的高次模式的单模工作,为抑制高次模式工作的谐振腔中模式竞争的问题提供了一种新方法.在此基础之上,采用解析方法以及高频仿真软件HFSS,设计了一个采用TM₅₃₀高次模式工作的传统光子晶体加载的谐振腔,进一步采用了该新方法对其进行改进,并深入分析了采用这种方法抑制模式竞争的物理原因.计算结果表明,新方法能有效抑制模式竞争,实现谐振腔的高次工作模式的单模工作. 关键词： 光子晶体 谐振腔 模式竞争 特性阻抗     

Optomechanical dynamics in detuned whispering-gallery modes cavity

The dynamics of a microresonator in detuned whispering-gallery modes (WGM) cavity opto-mechanical system are investigated by the quantum Langevin equation. A WGM cavity coupling to two parallel waveguides is devised to study the transmission and reflection of this system. In single mode WGM cavity, without optomechanical coupling, both the transmission and reflection of the cavity present a Lorentzian dip and peak. When the coupling between the cavity mode and mechanical mode is considered, the transmission and reflection of the optomechanical cavity show “W” and “M” shape mode splitting. Moreover, under the action of a controlling and a probe laser, the output field at the probe frequency presents electromagnetically induced transparency (EIT)-like spectrum in the system. We give the physical origin of EIT-like and the pump-probe response for the WGM shares all the features of the Λ system in atoms. Further, due to backscattering, the two traveling waves in WGM are coupled with a rate γ. The transmission and reflection of the optomechanical cavity display three modes splitting in the spectra with optomechanical coupling between the two cavity modes and the mechanical mode.     

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d₁, diameters of outer core holes d₂ and hole to hole pitch Λ on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.     

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.     

声波在一维声子晶体中共振隧穿的研究

通过从实验和理论方面对声波在一维声子晶体单晶体和被小的共振腔分开的双晶体中传播时发生的隧穿和共振隧穿现象的研究，观察到了声子晶体单晶体在带隙频率范围内发生的隧穿现象，而对于双晶体样品，在带隙频率范围内出现了很强的共振透射峰.共振发生时，实验测得的群时间很大，但是没有共振时，群速度却很快. 关键词： 声波 声子晶体 隧穿 共振     

基于局域共振单元实现声子晶体低频多通道滤波

从理论上提出一种由局域共振单元组成的声子晶体低频多通道滤波模型.在二维三组元局域共振声子晶体中引入不同填充率的共振单元构成波导结构,通过有限元法计算出其能带结构、透射曲线和透射场图.结果显示:这种设计能够在低频带隙范围内不同填充率散射体的共振频率附近产生新的分立模,且这些分立模能够使相应的声波在声子晶体中沿波导方向传播;这些分立模只与相应的共振单元相关,抗干扰能力强.所得结果为低频多通道滤波器的设计提供了一种新的理论依据.     

Band Gap and Waveguide States in Two-Dimensional Disorder Phononic Crystals

The influences of the configurational disorders on phononic band gaps and on waveguide modes are investigated for the two-dimensional phononic crystals consisting of water cylinders periodically arrayed in mercury. Two types of configurational disorders, relevant to the cylinder position and cylinder size respectively, are taken into account. It is found that the phononic band gap and the guide band are sensitive to the disorders, and generally become narrower with the increasing disorders. It is also found that the waveguide side walls without disorder can significantly prevent the guide modes in the waveguide from influence by the disorders in the crystals to a large amount.     

Si-based two-dimensional photonic crystals coupled to one-dimensional Bragg mirrors

Planar two-dimensional photonic crystals can be combined with a one-dimensional Bragg mirror to control the quality factor and out-of-plane coupling of optical Bloch modes. We have investigated the optical properties of such structures fabricated on silicon. The photonic crystals are fabricated in the upper Si layer deposited on top of quarter-wave thick SiO₂-polycrystalline Si layers. The optical properties are probed by the room-temperature photoluminescence of Ge/Si self-assembled islands as an internal source. We show that an enhancement of the quality factor can be obtained by controlling the thickness of the silicon upper layer in which the two-dimensional photonic crystal is etched and by controlling the air filling factor of the photonic crystal. Quality factors of 2200 around 1100 nm are obtained by this method for defect-free photonic crystals with a square lattice pattern. The experimental results are supported by three-dimensional finite-difference time-domain (FDTD) calculations of the radiated modes for the investigated structures.     

弹性波通过一维复合材料系统的透射性质

提出了不同结构的一维弹性波复合材料系统模型,包括一维周期结构声子晶体、标准Fibonacci准周期结构声子晶体、广义Fibonacci准周期结构声子晶体以及完全无序结构的复合材料系统. 采用模式匹配理论法,数值计算了弹性波通过一维复合材料系统的透射系数. 计算结果表明,利用特殊的准周期结构声子晶体可获得比周期结构声子晶体更宽的带隙范围,准周期结构排列的复合材料系统相当于在周期结构中引入了缺陷体一样,带隙内出现了丰富的局域模式. 对弹性波/声波在复合材料系统中局域态性质的研究有助于弹性波/声波滤波器、导波器 关键词： 弹性波复合材料 局域化     

偶极子位置及偏振对激发光子晶体H1微腔的影响

光子晶体微腔和量子点的集成是实现量子信息处理非常具有潜力的平台之一,利用微腔和量子点的耦合可以制备纠缠光子对,实现对量子态的操控.因为光子晶体微腔具有品质因子高、模场体积小等优点,可以极大地增强光与物质之间的相互作用,从而易于实现量子态在不同物理体系之间的转换.通过单量子点和光子晶体H1微腔的耦合可以产生纠缠光子对,因为H1微腔具有简并的、模式偏振正交的基态模式.通常微腔模式的激发随着量子点在微腔中的位置变化而改变,本文用时域有限差分方法研究了偶极子光源的位置及偏振对激发光子晶体H1微腔模式的影响.结果表明:通过改变偶极子光源位置可以选择性地激发H1微腔简并模式中的一个;具有某一偏振的偶极子光源只能激发相应偏振的微腔模式;模式激发强度的大小也是由偶极子光源在微腔中的位置决定的.鉴于目前量子点在微腔中的位置尚不能精确控制,所以微腔模式受激发光源位置的影响的研究具有重要意义.     

Localized photonic modes in photonic crystal heterostructures

In this work, interface modes of two-dimensional photonic crystal heterostructures have been investigated by usage of the supercell method. The photonic crystal heterostructure is made of two photonic crystals with square symmetry in which one of them is composed of circular dielectric rods in air background and the other one is constructed by drilled square holes in dielectric. It is shown that using of a proper supercell plays an important role in obtaining the correct interface modes. We have also showed that the guided interface modes and single mode which is different from those reported in some published works are nearly dispersionless.     

由光子晶体局域模对称关系分析其简并性

使用平面波展开法计算了二维正方格子介质柱光子晶体在改变中央介质柱半径的情况下谐振腔的模式，根据所计算的局域模式场分布的对称关系，研究了二维光子晶体谐振腔模式的简并性.结果表明：具有C4v对称群光子晶体谐振腔，存在着二重简并偶极模和二重简并六极模，同时也存在非简并单极模和四极模，二重简并模的90°旋转态与其形成简并对.模式的简并与非简并可以直观地通过考察模式场分布的对称关系而得到.