Analysis of SAW propagation in gratings on ZnO/diamond substrates

The space harmonic method is used to analyze surface acoustic wave (SAW) propagation under an infinite periodic metal grating on ZnO/diamond composite layered substrates. Dispersion properties for shorted and open gratings are derived as a function of the thickness of the grating electrodes. From these dispersion relations, the coupling of modes (COM) parameters are derived. Energy profiles inside ZnO/diamond show that the energies contained in each of the ZnO and diamond layers are of the same order when the thickness of the ZnO layer is P/pi (P = grating period) and that the energy is contained within two wavelengths below the ZnO/diamond interface.     

Focusing-grating-coupler arrays for uniform and efficient signal distribution in a backboard optical interconnect

Several one-dimensional arrays of focusing grating couplers are designed for uniform distribution of incident optical powers to several processing boards in a backboard interconnection scheme. As main design parameters, both the length and the duty cycle of each focusing grating coupler are determined on the bases of ray-optic propagation-mode analysis in a slab waveguide and of rigorous coupled-wave diffraction analysis for out-coupled radiation modes. The backboard interconnection scheme incorporating the one-dimensional focusing-grating-coupler arrays, when used to distribute a guided optical power of TE(0) mode to several converging waves radiated only toward a glass substrate, displayed a power uniformity of 5% and a total coupling efficiency of 99.1%, which can be highly acceptable in practical use.     

Fiber mode coupling in transmissive and reflective tilted fiber gratings

Whereas core-mode reflection and core-mode-to-radiation-mode coupling in tilted fiber Bragg gratings is well understood, as is coupling between a core mode and higher-order core and cladding modes in untilted gratings, here we analyze in detail the coupling among core modes and cladding modes in reflective and transmissive tilted fiber gratings. We show that strong coupling between an LP(01) core mode and the exact (1m) cladding modes occurs in a transmissive tilted grating for nearly any tilt angle except angles close to 90 degrees , whereas the LP(01)-to-(lm) cladding mode coupling (l not equal 1) is appreciable only for tilt angles just below 90 degrees (~88 degrees ). In a reflective grating, strong coupling between the LP(01) core mode and the exact (1m) cladding modes occurs only for angles less than ~5 degrees , whereas coupling to (1m) cladding modes for m > 1 occurs only for angles greater than ~5 degrees . Coupling among bound core modes exhibits a similar behavior, except that in general the coupling is stronger. Experimentally we show coupling to both higher-order bound core modes and cladding modes in a transmissive tilted grating at visible and near-infrared wavelengths.     

A P-matrix-based model for the analysis of SAW transversely coupled resonator filters, including guided modes and a continuum of radiated waves

When designing transversely coupled resonator filters, unexpected spurii are often observed on the high-frequency side of the transfer function. These spurii cannot be described using only the classical waveguide model. Discrete transverse modes inside the grating can be identified if one assumes that the modes have exponential decay outside the grating; however, a continuum of solutions exist in the case of propagating waves outside the grating. A large part of the source excitation may be coupled to these radiated waves. To include this phenomena in the model, a decomposition on the above mentioned continuum was performed. We describe our P-matrix-based model for transversely coupled structures. This model takes into account all guided modes and the continuum. It allows the use of an arbitrary number of acoustical layers and electrical ports. A comparison of the measured and simulated frequency responses is presented for different filters and different metallization thickness showing an excellent agreement.     

Polarization-independent wideband mixed metal dielectric reflective gratings

A polarization-independent wideband mixed metal dielectric grating with high efficiency of the -1st order is analyzed and designed in Littrow mounting. The mixed metal dielectric grating consists of a rectangular-groove transmission dielectric grating on the top layer and a highly reflective mirror composed of a connecting layer and a metal film. Simplified modal analysis is carried out, and it shows that when the phase difference accumulated by the two propagating modes is odd multiples of π/2, the diffraction efficiency of the -1st order will be high. Selecting grating depth and duty cycle for satisfying the phase difference condition for both TE (electric field parallel to grooves) and TM (magnetic field parallel to grooves) polarizations, a polarization-independent high-efficiency grating can be designed. Using rigorous coupled-wave analysis and a simulated annealing algorithm, geometric parameters of the reflective grating are exactly obtained. The optimized grating for operation around a wavelength of 800 nm exhibits diffraction efficiencies higher than 90% for both TE and TM polarizations over a 120 nm wavelength bandwidth. The simplified modal analysis can be applied in other types of reflective gratings if the top layer is a dielectric transmission grating.     

Photothermal effects in fiber Bragg gratings

Writing a fiber Bragg grating in optical fiber generates an intrinsic broadband absorption term that can result in photothermal heating during subsequent use with fiber core guided light. This, in turn, can cause a significant shift of a grating resonance via the thermo-optic coefficient, even at low in-fiber light powers. The magnitude of the absorption term and its dependence on the grating strength are detailed. We further show how the degree of heating can be influenced by the particular environment in which the grating is placed and that, while the shift can be quite deleterious for some applications, its effect can be mitigated. A simple conductive model is developed.     

Extremely asymmetrical scattering of optical waves in nonuniform periodic Bragg arrays

The extremely asymmetrical scattering (EAS) of bulk and guided electromagnetic waves in nonuniform periodic Bragg arrays with steplike variations of the grating amplitude is analyzed theoretically by means of a recently developed approach based on allowance for the diffractional divergence of the scattered wave. Arrays of finite and infinite widths are investigated. It is shown that, for thin nonuniform arrays, EAS has the same pattern as for uniform arrays with mean grating amplitude. On the contrary, for wide nonuniform arrays, the scattered wave amplitudes are well determined by local values of the grating amplitude. In this case, the energy of the scattered wave is shown to concentrate mainly in regions with smaller grating amplitude. The sensitivity of EAS to small imperfections of periodic arrays is investigated theoretically. The physical explanation of the observed effects is based on the diffractional divergence of the scattered wave.     

Effects of symmetrical and asymmetrical bumps on plasmonic behavior in a metallic grating

The influence was investigated of symmetrical and asymmetrical bumps on plasmonic behavior in a metallic grating. Compared with the resonant peaks of a smooth-slit grating, the peaks of odd (even) modes exhibit a blue-shift (red-shift) and the transmission properties are tunable by the size of bumps when the bumps are laid symmetrically. However, the peaks of all modes only exhibit a red-shift when the grating is engraved with a bump and a cut in the same slit (namely bend slit), and the bend slit can achieve the properties of a straight slit. Additionally, it is found that the dips in transmission spectrum can be adjusted by altering the size of the bumps if the bumps are set asymmetrically. Fabry–Pérot-like resonance, field interference and phase resonance mechanisms have been suggested for the physical origins of these observations.     

Statistical Methods (7th ed.)

In this article we propose to use different single-index models for observations in different regions of the sample space. This approach inherits the estimation efficiency of the single-index model in each region, and at the same time allows the global model to have multidimensionality in the sense of conventional dimension reduction. On the other hand, the model can be seen as an extension of CART and a piecewise linear model proposed. Modeling procedures, including identifying the region for every single-index model and estimation of the single-index models, are developed. Simulation studies and real data analysis are employed to demonstrate the usefulness of the approach. Computer code and technical details of the method are provided as supplementary material online.     

Broadening the angular tolerance in two-dimensional grating resonance structures at oblique incidence

Broadening of the angular response of two-dimensional (2D) guided mode resonant spectral filters at oblique incidence is investigated. Coupling into multiple fundamental guided resonant modes having the same propagation constant but propagating in different planes (inherent multiple-plane diffraction by 2D gratings) is shown to significantly broaden the angular tolerance while maintaining narrow linewidth. Resonances have symmetric and broad angular responses when the incident wave is coupled to four resonant modes in a structure with a hexagonal grating pattern. Further broadening is implemented by enhancing the second Bragg diffraction of the 2D grating structure. Resonance with a narrow spectral linewidth (Dlambda(FWHM) approximately 1.6 x 10(-4)lambda(0)) and angularly tolerant to an ~6 mum beam diameter is obtained. A second approach utilizing a dual 2D grating configuration with a second grating on the substrate side is shown to increase the lateral confinement, causing the merging of two successive resonant bands. This results in further improvement of the angular/spectral linewidth ratio by ~80%.     

A network model for arbitrarily oriented IDT structures

A network model approach for analyzing arbitrarily oriented short-circuited SAW grating structures is extended to include interdigital transducers (IDTs) that are also arbitrarily oriented. The IDT structure is divided into cells, each modelled by a sequence of mismatched transmission lines consisting of a metallized and unmetallized region. The model includes: the impedance difference between metallized and free regions, the reflection coefficient at the metallization upstep, the reflection coefficient at the downstep for a counterpropagating wave, all deduced from the Datta-Hunsinger perturbation formula; the velocity difference between the free and metallized regions obtained using SAW propagation calculation software for arbitrarily oriented multilayers; and the energy storage susceptance at each finger discontinuity. Since only ordinary network elements are combined in accordance with the IDT geometry, this model permits good physical insight into the structure's characteristics and allows simple procedures for finding high directivity orientations.     

Improved reflectivity and velocity model for aluminum gratings on YZ LiNbO3

Lithium niobate has recently been used for SAW tags and temperature sensors because of its high coupling coefficient and high reflectivity. To increase the device operating frequency for a given electrode line resolution, harmonic operation of the reflector is a very attractive option. When used in conjunction with harmonically operated transducers, the device operating frequency can be increased for a given photolithographic line width resolution. To design and accurately predict the behavior of these devices, it is necessary to model the electrode reflectivity and velocity for both fundamental and second-harmonic operation. The coupling of modes (COM) model has been used to model these devices, however the COM model uses empirically determined coefficients to model reflectivity. In this paper, the reflectivity and velocity of aluminum electrodes is extracted experimentally for fundamental and second-harmonic operation versus metalization ratios ranging from 0.2 to 0.9 and versus normalized metal thickness ranging from 0.4% to 4%. A least-squares fit is then performed on the data using physical terms in the transmission line model to yield equations that can be used in the COM model to predict device behavior over varying metallization ratios and normalized metal thicknesses. Orthogonal frequency-coded (OFC) SAW tags were designed and fabricated and experimentally obtained data are compared with the COM modeled responses for the tags at fundamental and second-harmonic operation to verify the predictions.     

列车车轮振动模态声辐射效率研究

根据列车车轮的几何对称性,用有限元法建立车轮的轴对称模型和90°扇区模型,计算不同节径数下的振动模态。在模态分析的基础上,应用边界元法计算了50—6000Hz频率范围内车轮振动模态的声辐射效率。结果显示,在低频段车轮振动模态声辐射效率较低,在高频段的辐射效率趋向于1。两种模型的计算结果一致,与理论相符。     

Role of photonic bandgaps in polarization-independent grating waveguide structures

Polarization independence in a one-dimensional resonant grating waveguide structure involves the simultaneous excitation of two guided modes propagating in different directions. Possible simultaneous excitations occur when the two excited guided modes have either the same polarization, i.e., TE-TE (transverse electric) or TM-TM (transverse magnetic), or different polarizations, i.e., TE-TM. Simultaneous excitations may result in bandgaps and singularities. We confirm and show that in order to achieve polarization independence, it is necessary to find the conditions that minimize the effects of such bandgaps and singularities and experimentally demonstrate tunable polarization independence for simultaneously excited TE-TM-guided modes.     

取样光纤布拉格光栅特性的研究

用传输矩阵法从理论上计算了取样光纤布拉格光栅的反射谱特性。这种方法将光栅视为多层均匀薄膜的叠加,利用每一层的传输矩阵相乘获得了光栅的反射谱特性。研究表明,随着光栅长度的增加和采样率、折射率调制深度的减少,反射峰的均匀性得到了改善,旁瓣的反射率变小,带宽明显变窄,而反射峰间隔保持不变。反射峰的间隔由光栅周期决定,与采样率无关,而某些文献则要求采样率小于10%。这与频谱分析所得结论相吻合。     

声表面波滤波器的离散Green函数分析法

日本学者Hashimoto提出栅格有效介电常数和离散Green函数,并结合有限元方法分析了短路金属栅阵中声表面波的传输特性。由此开发了相应的Fortran应用程序。国际上许多从事声表面波器件的研发公司都使用该程序设计他们的产品。以Rayleigh波在128°YX-LiNbO3基片、铝金属栅中传播为例,给出根据Hashimoto程序运算的结果,读取禁带下边缘和禁带上边缘所对应的相对频率的数值,代入COM理论色散关系的数学表达式中,该表达式的图形就是由COM理论色散关系而确定的波数色散曲线,以提取耦合模参数。     

Development of a generalized model for analyzing phase characteristics of SAW devices under mass and fluid loading

vA generalized model that integrates the Navier-Stokes equation and coupling-of-modes (COM) model for biosensing SAW devices is developed in this paper. The SAW device is separated into three regions: interdigital transducer (IDT), substrate (delay line), and sensing regions. To evaluate the effects of metal thickness, mass loading caused by bioreaction, and different viscous fluid loading, the sensing region is further divided into three layers: piezoelectric substrate, metal layer, and fluid layer. In contrast to the conventional study, which is focused on the change of phase velocity, this model can evaluate the insertion loss and phase shifts under different sensing conditions. It can be shown that the integration of the COM model can provide guidelines for designing the bio-sensing device such as choosing the proper number of IDT, the width of the overlap, and the thickness of the metal layer. Furthermore, the generalized model can be utilized to evaluate the optimal thickness of the metal layer to achieve the maximum sensitivity.     

Ultrasensitive guided-mode resonance biosensors superimposed with vertical-sidewall roughness

In this paper, we present our investigations of the effects of vertical-sidewall roughness (VSR) on guided-mode resonance (GMR) filters made of subwavelength grating for applications to ultrasensitive biosensors operated under IR illumination. We designed the spectral FWHM of the grating filter to be as narrow as possible in order to emphasize the sensitivity and VSR effects. Three types of VSR morphologies on the grating-in terms of the correlation length ξ and the rms of the maximum roughness deviation σ-were considered and evaluated. Rigorous coupled-wave analysis was then implemented to quantify the shifts in the reflective resonance peak wavelength value (PWV) of the grating filter. Our simulations show that for specific ξ values, the PWVs remain constant even if σ becomes as large as 10?nm; this indicates dramatic bandgaplike stripes, which are similar to the bandgaps observed in the band diagrams of photonic crystals in the ξ-σ diagram that we have proposed in this study. In other words, the effects of VSR on the GMR biosensor performance are insignificant when ξ is located at certain bands; therefore, this type of roughness is highly tolerable even if the linewidth of the filter is decreased to only a few tens of nanometers.     

Reflective grating interferometer in a noncollimated configuration

A third-order aberration analysis for a reflective grating interferometer (RGI) is developed for a noncollimated configuration. In such a configuration the RGI is still a folded and reversing interferometer that is sensitive only to coma aberration, as it is in the collimated configuration. However, for an unaberrated input beam converging on a plane grating, the reflective grating of the interferometer introduces self-aberrations. Consequently, a nonnull fringe pattern is obtained. Nevertheless, a RGI in the noncollimated configuration has the potential to be applied for isolating and measuring coma, and a possible configuration for this application is proposed. As an example of the application, the coma of a large mirror could be isolated and measured by use of a converged configuration to avoid the main limitation in using the RGI in a configuration with a nearly collimated beam.     

Combined FEM and Green's function analysis of periodic SAW structure, application to the calculation of reflection and scattering parameters

Because of more and more stringent requirements on SAW filter performances, it is important to compute, with very good accuracy, the SAW propagation characteristics, which include the calculation of reflection and scattering parameters. For that reason, the analysis of periodic structures on a semi-infinite piezoelectric substrate is one of the most important problems being investigated by SAW researchers. For infinite periodic grating modeling, we developed numerical mixed FEM/BEM (finite element method-boundary element method) models using an efficient interpolation basis function that takes into account the singularity at both edges of each electrode. In this paper, a review of the numerical program that has been developed during the past few years will be presented. For an infinite periodic grating, it is convenient to solve the propagation problem in the Fourier domain (wave number space and harmonic excitation), and important efforts have been spent to properly integrate the so-called periodic harmonic Green function. Using this numerical model together with the general P-matrix formalism, it is possible to compute all of the basic parameters with a very good accuracy. These consist of the single strip reflectivity, acoustic wave-phase velocity, and position offset between reflection and transduction centers. Simulations and comparisons with experiments are shown for each model