Dispersion relation of surface plasmons near photonic band gaps: Influence of the interaction with light

Abstract

We present an experimental and theoretical study of the photonic band gap in the propagation of surface plasmons (SPs) on periodically corrugated surfaces. Our main purpose is to investigate the case where the band gap width is larger than the energy distance between the SP dispersion curve for a flat surface and the light line. We introduce a physical model of the interaction of light waves with SPs and derive an analytical expression for the SP wave vector near band gaps based on the coupled-mode approach involving three interacting modes (two of them are SP modes and one is a light mode). By using the interferometric measurement we have studied, for the first time, the SP propagation parameters in the vicinity of the photonic band gap (10 μm wavelength region). The predictions of our theory are in good agreement with the experimental data.     

Localized Modes in Metamaterial-Dielectric Photonic Crystals with a Dielectric-Superconductor Pair Defect

Transmission coefficient and dispersion relation are calculated for a one-dimensional photonic crystal of alternating dielectric-metamaterial slabs with a dielectric-superconductor pair defect. The presence of the superconductor slab in the pair defect layer leads to a strong depletion of the TM transmission coefficient in a frequency range close to the edges of the non-Bragg gap and around the characteristic resonance frequency of the superconductor and introduces TM electromagnetic modes inside such gap. The features of the arising modes depend on the relation between the thicknesses of the layers involved in the defect and a low-frequency mode can arise from the low-frequency continuum of the bulk metamaterial modes at a non-zero in-plane wave vector.     

Damage assessment in layered composites using spectral analysis and Lamb wave

Piezo-ceramic transducers of the surface mounted type are commonly used for structural health monitoring (SHM) techniques. But, there is a disadvantage to use piezo-ceramic transducers of the surface mounted type in Lamb wave application. Due to the symmetric and antisymmetric Lamb wave modes generated by the surface mounted piezo-ceramic transducers simultaneously, the received signals are very complex and it is difficult to extract damage information from the signals.

In this paper, the practical method for SHM was proposed using piezo-ceramic transducers of the surface mounted type and Lamb wave. In order to overcome the difficulties in the signal processing of the simultaneous modes, the symmetric and antisymmetric modes were separated by using the two sensors bonded on the opposite surfaces at the same point. Also, spectral analyses of the separated symmetric and antisymmetric Lamb waves showed that each mode propagated with different frequency characteristics in the exciting frequency range.

By making use of these findings, the changes of power spectrum density in characteristic frequency band of symmetric and antisymmetric modes are proportional to the delamination size in quasi-isotropic Gr/Ep laminates. Therefore, this paper presents the damage assessment technique to extract damage information from the complicated PZT signals that could not be interpreted in time domain.     

Ultrasonic wave characteristics of a monolayer graphene on silicon substrate

The present work deals with an ultrasonic type of wave propagation characteristics of monolayer graphene on silicon (Si) substrate. An atomistic model of a hybrid lattice involving a hexagonal lattice of graphene and surface atoms of diamond lattice of Si is developed to identify the carbon-silicon bond stiffness. Properties of this hybrid lattice model is then mapped into a nonlocal continuum framework. Equivalent force constant due to Si substrate is obtained by minimizing the total potential energy of the system. For this equilibrium configuration, the nonlocal governing equations are derived to analyze the ultrasonic wave dispersion based on spectral analysis. From the present analysis we show that the silicon substrate affects only the flexural wave mode. The frequency band gap of flexural mode is also significantly affected by this substrate. The results also show that, the silicon substrate adds cushioning effect to the graphene and it makes the graphene more stable. The analysis also show that the frequency bang gap relations of in-plane (longitudinal and lateral) and out-of-plane (flexural) wave modes depends not only on the y-direction wavenumber but also on nonlocal scaling parameter. In the nonlocal analysis, at higher values of the y-directional wavenumber, a decrease in the frequency band gap is observed for all the three fundamental wave modes in the graphene–silicon system. The atoms movement in the graphene due to the wave propagation are also captured for all the tree fundamental wave modes. The results presented in this work are qualitatively different from those obtained based on the local analysis and thus, are important for the development of graphene based nanodevices such as strain sensor, mass and pressure sensors, atomic dust detectors and enhancer of surface image resolution that make use of the ultrasonic wave dispersion properties of graphene.     

Long-range surface modes of metal-clad four-layer waveguides

The surface modes of metal-clad four-layer waveguides were theoretically analyzed. We showed that the long-range surface modes can be excited in such waveguides. The long-range surface modes were experimentally studied with the angle scanning attenuated-total-reflection method; the dependence of wave vector and loss of these modes on the waveguide parameters were measured. Experimental results were in good agreement with theoretical calculations.     

Shear wave passage through a vacuum gap between piezoelectric crystals with relative longitudinal displacement

The influence of relative longitudinal displacements of two piezoelectric crystals separated by a vacuum gap on the reflection and transmission of shear waves through the gap between these crystals is considered. We predict the possibility of enhancing the reflected wave under conditions of wave front reversal for the wave transmitted through the gap.     

Measurement of Strains in Turbine Blades Vibrating at Resonance Using Electro-optic Holography

Abstract

Phase-stepped stroboscopic electro-optic holography is employed for the measurement of strains on the surface of a turbine blade vibrating at resonance. The three components of the displacement vector are separated by recording interferograms using four independent illumination beams. The phase-stepping technique supplemented by the Fourier transform method is applied for the extraction of phase changes due to vibration. In-plane strains in a region of interest on the blade surface are calculated for one of the natural modes of vibration.     

Novel techniques of laser acceleration: from structures to plasmas

Compact accelerators of the future will require enormous accelerating gradients that can only be generated using high power laser beams. Two novel techniques of laser particle acceleration are discussed. The first scheme is based on a solid-state accelerating structure powered by a short pulse CO(2) laser. The planar structure consists of two SiC films, separated by a vacuum gap, grown on Si wafers. Particle acceleration takes place inside the gap by a surface electromagnetic wave excited at the vacuum/SiC interface. Laser coupling is accomplished through the properly designed Si grating. This structure can be inexpensively manufactured using standard microfabrication techniques and can support accelerating fields well in excess of 1 GeV m(-1) without breakdown. The second scheme utilizes a laser beatwave to excite a high-amplitude plasma wave, which accelerates relativistic particles. The novel aspect of this technique is that it takes advantage of the nonlinear bi-stability of the relativistic plasma wave to drive it close to the wavebreaking.     

Propagation of transverse bulk and surface acoustic waves in LiNbO (3) variable time-delay devices

Experimental measurements are reported on voltage-controlled acoustic time-delay lines operating at 1 GHz in the nearly pure shear-horizontal (S-H) mode in 38 degrees rotated Y-cut LiNbO(3). The high-acoustic velocity (4800 m/s) in conjunction with the large electroacoustic effect exhibited by this orientation allows high-frequency operation and optimum time-delay tuning sensitivity with a planar, single surface, device geometry. The authors demonstrate fractional time delay of 0.3x10(-6) V(-1 ) for surface electrodes that produce an in-plane E-field. However, the simultaneous excitation and propagation of both a leaky surface-acoustic wave (LSAW) and surface skimming bulk wave (SSBW), both as (nearly pure) S-H waves in these devices, seriously restricts the extent to which it is possible to maximize the time delay modulation sensitivity by reducing electrode gap spacing as done in similar SAW devices. The LSAW and surface-skimming body wave (SSBW) propagate at nearly the same velocity on a free surface, and perturbation of their velocity and relative attenuation rates by surface electrodes causes pronounced interference effects between the two modes for some device geometries.     

Bleustein-Gulyaev-Shimizu surface acoustic waves in two-dimensional piezoelectric phononic crystals

In this paper, we present a study on the existence of Bleustein-Gulyaev-Shimizu piezoelectric surface acoustic waves in a two-dimensional piezoelectric phononic crystal (zinc oxide, ZnO, and cadmium-sulfide, CdS) using the plane wave expansion method. In the configuration of ZnO (100)/CdS(100) phononic crystal, the calculated results show that this type of surface waves has higher acoustic wave velocities, high electromechanical coupling coefficients, and larger band gap width than those of the Rayleigh surface waves and pseudosurface waves. In addition, we find that the folded modes of the Bleustein-Gulyaev-Shimizu surface waves have higher coupling coefficients.     

Guided modes in a uniaxial multilayer

An algorithm is presented for simulation of guided modes in a multilayer uniaxial structure with each layer characterized by its own ellipsoid of refractive indices and direction of optical axis. The proposed approach is based on presenting an electromagnetic field in each layer as a linear combination of ordinary and extraordinary waves coupled through the boundary conditions. The problem is reduced to two dimensions by considering the waves with a given projection of the wave vector on the plane of the waveguide. No a priori assumption about the guided-mode polarization is required in this method. Hybrid polarized modes appear naturally as solutions of a system of linear equations with respect to the amplitudes of the ordinary and extraordinary waves. The proposed approach covers a wide variety of important practical cases including isotropic waveguides, surface waves at the boundary between positive uniaxial crystal and isotropic medium, surface plasmons at metallic interfaces, uniaxial multilayers in a very general form, and leaky modes in such structures.     

Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses

We simulate and calculate numerically the electromagnetic field and energy flux around a surface crack of an Nd-doped phosphate laser glass by using the finite-difference time-domain method. Because of a strong interference between the incident wave and the total internal reflections from the crack and the glass surface, the electric field is redistributed and enhanced. The results show that the electric-field distribution and corresponding energy flux component depend sensitively on the light polarization and crack geometry, such as orientation and depth. The polarization of the incident laser beam relative to the crack surfaces will determine the profile of the electric field around the crack. Under TE wave incidence, the energy flux peak is always inside the glass. But under TM wave incidence, the energy flux peak will be located inside the glass or inside the air gap. For both incident modes, the light intensification factor increases with the crack depth, especially for energy flux along the surface. Because cracks on the polished surfaces are the same as the roots extending down, the probability for much larger intensification occurring is high. The results suggest that the surface laser-damage threshold of Nd-doped phosphate may decrease dramatically with subsurface damage.     

Thermal control of a dual mode parametric sapphire transducer

We propose a method to control the thermal stability of a sapphire dielectric transducer made with 2 dielectric disks separated by a thin gap and resonating in the whispering gallery (WG) modes of the electromagnetic field. The simultaneous measurement of the frequencies of both a WGH mode and a WGE mode allows one to discriminate the frequency shifts due to gap variations from those due to temperature instability. A simple model, valid in quasi-equilibrium conditions, describes the frequency shift of the 2 modes in terms of 4 tuning parameters. A procedure for their direct measurement is presented.     

Coupled Dielectric Nanoparticles Manipulating Metamaterials Optical Characteristics

In this paper, we investigate the concept and theory of all-dielectric metapatterned structures that manipulate electric and magnetic optical characteristics. A 3-D array of dielectric particles is designed, where the spheres operate in their magnetic modes and their couplings offer electric modes. An analytical solution for the problem of plane wave scattering by 3-D array of dielectric nanospheres is presented. FW multipole expansion method is applied to express the optical fields in terms of the electric and magnetic dipole modes and the higher order moments. By enforcing the boundary conditions at the surface of each sphere, with the use of the translational addition theorem for vector spherical wave functions, required equations to determine the scattering coefficients are obtained. Novel materials features in optics are demonstrated. Electric and magnetic scattering coefficient resonances around the same frequency band are obtained. It is highlighted how a metapatterned structure constructed from dielectric nanosphere unit cells can provide electric and magnetic modes resulting in backward wave phenomenon. A comprehensive circuit model based on the RLC (resistor, inductor, and capacitor) realization is presented to successfully analyze the scattering performance of a dielectric nanosphere. To better understand the physics of an array of spheres, circuit models for the interactions, and couplings between spheres are also accomplished. The engineered dispersion diagram for a 3-D array of identical highly coupled nanospheres is scrutinized, verifying that the high couplings between spheres can offer the backward wave characteristics.     

Experimental study of holographic generation of fractional Bessel beams

We demonstrate the experimental generation of a fractional Bessel beam by holographic means. Such fractional modes of Bessel beams possess an intrinsic opening gap across concentric intensity rings on propagation. We also show that the opening gaps within the fractional modes are diffraction free for a working distance while a fractional helical wave front is maintained.     

Propagation of QSH (quasi shear horizontal) acoustic waves in piezoelectric plates

The characteristics of QSH (quasi shear horizontal) acoustic waves propagating in thin plates of Y-cut, X-propagation lithium niobate are investigated theoretically and experimentally. The fractional velocity change (Deltanu/nu) produced by electrical shorting of the surface is calculated as a function of the normalized plate thickness h/lambda (h=plate thickness, lambda=acoustic wavelength). It was found that values of Deltanu/nu as high as 0.18 could be obtained. Experimental measurements show good agreement with theory. The properties of QSH waves propagating in the presence of a perfectly conducting electrode separated from the piezoelectric plate by a small air gap have been studied theoretically and experimentally. It was found that by varying the height of the gap, the phase shift through a 3.2-MHz QSH wave delay line can be varied by more than 230 degrees . We have also theoretically investigated the influence of a thin layer of arbitrary conductivity on the velocity and attenuation of the QSH wave. Calculations show that the variations in these parameters can be as high as 18% and 5 dB per wavelength for a change in layer surface conductance from 10(-7) to 10(-5) S. Results obtained in this paper confirm the attractive properties of QSH waves for a variety of sensing and signal processing applications.     

Band gaps of elastic waves in 1-D phononic crystal with dipolar gradient elasticity

The dispersive relations of Bloch waves in the periodic laminated structure formed by periodically repeating of two different gradient elastic solids are studied in this paper. First, the various wave modes in the gradient elastic solid, which are different from those in the classical elastic solid, are formulated. Apart from the dispersive P wave and SV wave, there are two evanescent waves, which become the P type and S type surface waves at the interface of two different gradient elastic solids. Next, the continuity conditions of displacement vector, the normal derivative of the displacement vector and the monopolar and dipolar tractions across the interface between two different gradient elastic solids are used to derive the transfer matrix of the state vector in a typical single cell. At last, the Bloch theorem of Bloch waves in the periodical structure is used to give the dispersive equation. The in-plane Bloch waves and the anti-plane Bloch waves are both considered in the present work. The oblique propagation situation and the normal propagation situation are also considered, respectively. The numerical results are obtained by solving the dispersive equation. The influences of two microstructure parameters of the gradient elastic solid and the microstructure parameter ratio of two different gradient elastic solids on the dispersive relation are discussed based on the numerical results.     

Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides

A nanoscale gap between two metal surfaces can confine propagating surface plasmon polaritons (SPPs) to very small dimensions, but this geometry makes it inherently difficult to image SPP propagation at high resolution. We demonstrate the near-field probing of these SPPs, propagating within a 50 nm thick Si 3N 4 waveguide with Ag cladding layers for frequencies ranging from the blue to the near-infrared. Using near-field SPP interferometry, we determine the wave vector, showing that the wavelength is shortened to values as small as 156 nm for a free-space wavelength of 532 nm.     

有限长叉指换能器激发表面波及体波声场的数值模拟

采用数值方法,模拟了有限长叉指换能器(IDT)在半无限大压电晶体中激发的表面波和体波声场在晶体界面上的分布情况。在数值模拟所得结果的基础上,将频率域内的位移分量做傅立叶反变换得到时间域内声波脉冲振幅随时间的分布,并对界面上三个位移分量含有的声波模式进行分析,其中场位移分量1沿波的传播方向,位移分量2为平行于IDT指条方向,位移分量3沿基片表面法线方向。分析结果表明,界面上各位移分量中除Rayleigh波外,还含有不同比例的体波成分。其中,在位移分量1和位移分量3中占主要成分的是准纵波,在位移分量2中占主要成分的是准慢切变波。它们均按照指数方式在表面上进行传播衰减,其中准慢切变波的衰减速度小于准纵波的衰减速度。IDT指条数相对较多时的体波振幅要大于指条数相对较小时的体波振幅,且在距离IDT较近的范围内IDT指条数相对较多时体波衰减更快。     

Excitation of acoustic waves from cylindrical polyvinylidene fluoride (PVDF) film confined in a concentric wall

This paper investigates acoustic wave radiation from cylindrical polyvinylidene fluoride (PVDF) film mounted inside a concentric wall with a small air gap. In such a structure, propagation is allowed only in the gap between the film and the wall surface, and the wave propagates in the axial direction of the cylinder. The radiation impedance of the cylindrical transducer inside the concentric wall has been calculated using a one-dimensional propagation model. After calculating the mechanical impedance of the cylindrical PVDF film, the generated acoustic wave has been calculated as a function of frequency with various air gaps between the PVDF film and the wall. It has been found that the excited acoustic wave becomes stronger for a narrower air gap and shows a maximum at a specific air gap. This phenomenon has been explained as the match between the transducer impedance and the radiation impedance of the air gap. When the gap is too small, the radiation impedance exceeds the transducer's mechanical impedance, the acoustic wave radiation decreases with the decreasing gap, and the resonance frequency increases due to loading by the imaginary part of the excessive radiation impedance. All these theoretical results have been experimentally confirmed.