Cavity-mode calculation of L3 photonic crystal slab using the effective index perturbation method

This paper mainly describes that the effective index perturbation (EIP) technique in combination with two-dimensional (2D)/three-dimensional (3D) PWE methods predicts resonant mode frequencies and mode patterns for the L3 photonic crystal slab cavity, which substantially reduces the computation time and computer memory without losing accuracy. The simulation results show that when the perturbed effective index by matching dielectric band edge is used, the fundamental resonant mode has small calculation frequency error; however, when the effective index obtained by the standard effective index method (EIM) is used, it is appropriate for predicting higher-order resonant modes, and the micro-photoluminescence experiments verify the predictions of the theoretical model. In addition, mode profiles of the L3 cavity with both the displacement of the end-holes and the base cavity structure can also be accurately predicted.     

Electromagnetic response of a compound plasmonic–dielectric system with coupled-grating-induced transparency

We propose a compound plasmonic–dielectric system consisting of one-dimension metallic gratings made of core–shell membranes and a Si grating waveguide with periodic grooves on one side, to investigate the coupled-grating-induced transparency (CGIT) effect. Both elements of the system can support certain resonant modes respectively, which have almost identical resonant frequencies but highly different quality factors, which are demonstrated by a theory model and the coupled mode theory. The electromagnetic response of the compound plasmonic–dielectric system induces coupling between these two types of gratings resonators and causes a transparency phenomenon due to the destructive interference of the resonant modes. The results show that the CGIT effect is associated with remarkable improvement of the group index corresponding to high transmission efficiency.     

Theoretical analysis of whispering-gallery mode ring dielectric resonator

A new type of whispering-gallery mode ring dielectric resonators are first proposed. Theoretical analysis and a method for determination of the resonant frequencies is presented by the mode matching method. The numerical results show good agreement with theoretical analysis.     

Free vibration characteristics of double-walled carbon nanotubes embedded in an elastic medium

In this Letter, a theoretical analysis of the resonant vibration of double-walled carbon nanotubes (DWCNTs) and the DWCNTs embedded in an elastic medium is presented based on Euler-Bernoulli beam model and Winkler spring model. The vibration modes of DWCNTs are quite different from those of single-walled carbon nanotubes (SWCNTs). The resonant vibrations of DWCNTs are found to have in-phase and anti-phase modes, in which the deflections of the inner and outer nanotubes occur in the same and opposite directions, respectively. For the vibration of DWCNTs with the same harmonic numbers, the resonant frequencies of anti-phase mode are larger than the ones of in-phase mode. Moreover, influence of the surrounding medium on the resonant vibrations is investigated using the Winkler spring model. The results show that surrounding medium makes a strong impact on the vibration frequencies of in-phase mode, but little on those of anti-phase mode.     

Influence of the dielectric background on the quality factors of metallo-dielectric photonic crystals

The effect of varying the dielectric background on the quality factor of two-dimensional metallo-dielectric photonic crystals is theoretically studied. The studied metallo-dielectric photonic crystal consists of a square lattice of circular metallic rods embedded into a dielectric background with a defect rod on the center that creates resonant modes within the photonic band gap. The metal is modeled with the Drude dispersion relation. A combination of the finite-difference time-domain method together with a frequency filtering technique is used to estimate accurately the resonant frequencies and their quality factors. The results show that the quality factors increase with increasing background dielectric constant. If a dielectric background material such as Silicon is used instead of air, an enhancement in the quality factor of up to eight times can be achieved, depending on the resonant mode. We also show that, depending on the modes, there exists an optimal size for the defect rod that gives the maximum quality factor.     

Normal modes and quality factors of shielded composite dielectric spherical resonators

Electromagnetic field analysis of shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials has been made. Characteristic equations for the TE_nmℓ and TM_nmℓ modes have been derived. From these characteristic equations, the resonant frequencies and quality factors have been calculated using numerical method. Computations of the resonant frequencies and quality factors have been made for resonators with parameters suitable for the optical and microware regions. In this paper we have presented the analysis and the results obtained from the numerical computations for shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials. Starting from the Maxwell’s equations for such a resonators have been derived and resonant frequencies and quality factor’s have been calculated for the TE_nmℓ and TM_nmℓ modes using numerical method.     

一种计算和分析二维光子晶体缺陷模式的方法

通过改进时域有限差分(FDTD)法,计算和分析了二维光子晶体的缺陷模式。运用一维时域有限差分算法和线性插值法在总场散射场(TF-SF)连接边界引入入射平面波,采用完全匹配层(PML)技术对外行波进行了有效吸收。计算和分析结果表明,在光子晶体非对称方向入射的平面波能激发所有的缺陷模式,选取合适的探测点位置收集电场值,经快速傅里叶变换(FFT)能得到所有的共振峰值。另外,采用该方法研究了二维正方介质柱光子晶体缺陷模的共振频率与缺陷介质柱半径和介电常量之间的关系。结果表明通过改变缺陷的半径和介电常量大小可以在光子晶体禁带中一定的范围内调节缺陷模式的共振频率大小。     

Optical properties and photonic bands of GaAs photonic crystal waveguides with tilted square lattice

Reflectance measurements at variable angle of incidence are performed on GaAs photonic crystal waveguides with unconventional square lattices. The technique yields the dispersion of photonic bands for the investigated lattices, as first shown by Astratov et al. [Phys. Rev. B 60, R16225 (1999)]. A sample with a square lattice of air rings and small air fraction yields narrow resonant structures and a dispersion of photonic modes close to that of free photons. Another sample with a square lattice of dielectric squares and large air fraction leads to broader structures and to a dispersion of photonic modes which differs strongly for the two polarizations of light: this sample has a pseudo-gap around 1 micron wavelength. The experimental results are in good agreement with theoretical calculations of the reflectance and of the photonic mode dispersion in the photonic crystal slabs. Received 16 January 2002     

All-optical switch based on photonic crystal microcavity with multi-resonant modes

We present a design of all-optical switches based on one-dimensional photonic crystals (1D PhC) doped with nonlinear optical materials. The 1D PhC switch structure is composed of a PhC cavity sandwiched by two accessional PhC microcavities. The center PhC cavity has two resonant frequencies with nearly the same quality factors (Q), while the accessional PhC cavities have the same resonant frequency, which is equal to one of the resonant frequencies of the center cavity. The two accessional PhC cavities cause reduction of Q value in this resonant frequency and result in different Q values of two modes. We realize all-optical switch effect by selecting pump light wavelength at the low Q mode and probe light wavelength at the other mode. The theoretical simulations by using the finite difference time domain method show that the pump light intensity required to realize optical switch effect in the designed switch is 50 times smaller than that in one-dimensional photonic crystals cavity with only one resonant mode.     

Experimental and numerical investigations of resonant vibration characteristics for piezoceramic plates.

Electronic speckle pattern interferometry (ESPI) is a full field, non-contact technique for measuring the surface displacement of a structure subjected to static loading or, especially, to dynamic vibration. In this article we employ an optical system called the amplitude-fluctuation ESPI with out-of-plane and in-plane measurements to investigate the vibration characteristics of piezoceramic plates. Two different configurations of piezoceramic plates, namely the rectangular and the circular plates, are discussed in detail. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes is demonstrated. The resonant frequencies of the piezoceramic plates are also measured by the conventional impedance analysis. From experimental results, we find that the out-of-plane vibration modes (type A) with lower resonant frequencies cannot be measured by the impedance analysis and only the in-plane vibration modes (type B) will be shown. However, both the out-of-plane (bending) and in-plane (extensional) vibration modes of piezoceramic plates are obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. It is shown that the numerical calculations and the experimental results agree fairly well for both the resonant frequencies and the mode shapes.     

Comparative modal analysis of NRD parallelepiped dielectric resonators

The resonance modes of dielectric resonators having parallelepiped shape are extensively investigated in this work referring to the nonradiative dielectric (NRD) topology. Different numerical techniques, both rigorous and approximated (boundary elements, point matching, finite elements, transmission line approaches), are proposed and implemented to compute the relevant resonance spectrum as a function of the involved geometric and electromagnetic parameters. The theoretical results are discussed and compared also in connection with experimental investigations, carried out on suitable prototypes of NRD components. Qualitative and quantitative information is thus achieved to characterize with accuracy and efficiency the basic parameters (resonant frequencies, field configurations, etc.) involved in filter design and in other applications at microwaves and millimeter waves.     

Iteration methods and algorithms for dielectric-resonator integral equations of the field

Quasi-eigenmodes of open cylindrical and rectangular dielectric resonators (DRs) are determined by the method of iterative solution of the volume integral and integro-differential equations with corresponding functionals. New forms of equations and iteration algorithms for the nonlinear input of the desired complex parameter are proposed. Frequencies and Q-factors of the H_01δ and H₀₁₁ modes of a cylindrical DR and the H mode of a rectangular DR for the uniform and nonuniform cases are obtained numerically. The influence of a thin semiconductor layer located at the ends of the DR and irradiated by high-power laser pulses on the frequencies and Q-factors of the DR modes is examined. It is shown that an up to ten or more percent tuning of resonant frequencies can be reached by transformation of a low conducting state to a high conducting state.     

Resonant frequencies and quality factors in lossy NRD cylindrical resonators

In this paper the fundamental effects of losses on resonant parameters (frequencies and quality factors) are analyzed for circular-cylindrical dielectric resonators inserted between metal plates, in the configuration also called NRD (Non-Radiative Dielectric).Power dissipations are considered both in the dielectric and in the conductors. Complex resonant frequencies and closed-form expressions for the relevant quality factors are derived rigorously for arbitrary resonant modes, even without circular symmetry. Numerical results are presented and discussed, making also use of experimental data obtained by means of a suitable NRD set-up.The present analysis accurately provides the basic information for a more realistic design of up-to-date millimeter-wave frequency-selective devices in NRD circuitry.     

Operating modes of relativistic rising-sun and A6 magnetrons

The operating characteristics of a relativistic 16-vane rising-sun magnetron were investigated with particular emphasis on determining the operating regimes of different modes. The magnetron performance was studied as a function of voltage, magnetic field, cathode geometry, axial boundary conditions, and output coupling. Operation was observed in the 3π/8 mode at 3.3 GHz, in the π/2 or 3π/8 mode at 3.5 GHz, and in the π or 7π/8 mode at 4.6 GHz. A maximum power of 80 MW was emitted in the 3π/8 mode with an efficiency of 4.5%. Typical pulse lengths were 40-50 ns. Cold tests were performed to measure the resonant frequencies and azimuthal electric fields in the interaction space which agreed within 1-4% of theoretical calculations. The operating modes were inferred from close agreement between hot-test frequencies and cold-test results and because high-power RF emission occurred at, or just above, the Buneman-Hartree threshold calculated for these modes. The characteristics of a six-vane A6-magnetron operating in the π and 2π modes were also studied. A unique transmitting-receiving system, which was used as a microwave diagnostic, is described     

On internal mode resonance in a nonlinearly vibrating volumetrically charged dielectric drop

In the approximation quadratic in the amplitude of an arbitrary initial deformation of an equilibrium spherical uniformly (volumetrically) charged drop of a dielectric liquid, an analytical expression for the drop surface generatrix as a function of time is derived in the case when the drop shape executes axisymmetric vibrations. A condition that must be imposed on mode frequencies in order for resonant interaction between modes to take place in the quadratic approximation is found. It is shown that many resonances, rather than one known previously, are realized when the self-charge is insufficient (subcritical) for drop surface instability against self-charge to arise. Nonlinear two-and three-mode resonant interactions are studied.     

Coaxial Waveguide Slot Bridge Cell for Liquid Substances Study

The experimental method suggested suppose the studying of energy characteristics of slot bridge (SB) cells in the multi mode operating regime based on the preliminary numerical investigation of scattering resonant characteristics of SB (solution of boundary value problem and investigation of eigen frequencies and relevant field modes). The configuration of experimental model of SB cell is computed accordingly to required frequency band and preliminary information about dielectric parameters of materials chosen for tests. Ethanol scattering characteristics of SB cell are computed by software, developed on the base of rigorous solution of the boundary value problem, providing numerical data with any required accuracy.     

Second- and third-harmonic generations for a nondilute suspension of coated particles with radial dielectric anisotropy

We derive expressions for the effective nonlinear susceptibility tensors for both the second harmonic generation (SHG) and induced third harmonic generation (THG) of nonlinear composite materials, in which nondilute coated particles with radial dielectric anisotropy are randomly embedded in the linear host. Two types of coated particles are considered. The first is that the core possesses a second order nonlinear susceptibility and the shell is linear and radially anisotropic, while the second is that the core is linear with radial anisotropy and the shell has a second order nonlinear susceptibility. We observe greatly enhanced SHG and THG susceptibilities at several surface plasmon resonant frequencies. For the second model, due to the coating material being metallic, there exists two fundamental resonant frequencies ω_c1 and ω_c2, whose difference ω_c2-ω_c1 is strongly dependent on the interfacial parameter and the radial dielectric anisotropy. Furthermore, in both systems, the adjustment of the dielectric anisotropy results in larger enhancement of both SHG and induced THG susceptibilities at surface plasmon resonant frequencies than the corresponding isotropic systems. Therefore, both the core-shell structure and the dielectric anisotropy play important roles in determining the nonlinear enhancement and the surface resonant frequencies.     

EXPERIMENTAL MEASUREMENTS BY AN OPTICAL METHOD OF RESONANT FREQUENCES AND MODE SHAPES FOR SQUARE PLATES WITH ROUNDED CORNERS AND CHAMFERS

Most of the work done on vibration of plates published in the literature includes analytical and numerical studies with few experimental results available. In this paper, an optical system called the amplitude-fluctuation electronic speckle pattern interferometry for the out-of-plane displacement measurement is employed to investigate the vibration behavior of plates with rounded corners and with chamfers. The boundary conditions are traction free along the circumference of the plate. Based on the fact that clear fringe patterns will appear only at resonant frequencies, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present method. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Good agreements are obtained for both results. It is interesting to note that the mode number sequences for some resonant modes are changed. The transition of mode shapes from the square plate to the circular plate is also discussed.     

Resonant Mandelstam-Brillouin light scattering and Raman scattering in semiconductors with intermediate exciton states belonging to discrete exciton bands and the continuous spectrum

The results of a theoretical and experimental investigation of resonant Mandelstam-Brillouin light scattering by thermal acoustic phonons with k=0 near the direct absorption edge (in the case of ZnSe crystals) are analyzed. The appearance of a new type of resonant increase in the intensity of Raman scattering by optical phonons with k≠0, which corresponds to resonance with the scattered light in the output channel, near the indirect absorption edge (in the case of semi-insulating GaP:N crystals) is also reported. The resonant gain reaches ∼4×10³ at frequencies corresponding to overtone scattering assisted by LO(X) and LO(L) phonons. Exciton states belonging to both discrete exciton bands and to the continuous spectrum are considered as the intermediate states involved in the scattering processes in calculations of the resonant scattering tensors. In addition, all the intraband transitions, as well as the interband transitions between the conduction band, the valence bands, and the spin-orbit split-off band are taken into account, and good agreement with the experimental results is obtained. Fiz. Tverd. Tela (St. Petersburg) 40, 938–940 (May 1998)     

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.