A.N. Darinskii

Surface acoustic wave scattering from steps, grooves, and strips on piezoelectric substrates

The paper studies, by the finite element method, the reflection of surface acoustic waves from single obstacles of regular shapes on the surface of piezoelectric materials. The so-called perfectly matched layer is used to truncate the computational domain. The following types of imperfections are considered: single steps, grooves, and projections, as well as metallic strips overlaying the substrate or inset into it. The absolute values and the phases of the reflection coefficients are computed for YZ and 128°YX LiNbO3 substrates as functions of the height-to-wavelength and the width-to-wavelength ratios. In addition, the reflectivity of gratings comprising a finite number of grooves or electrodes is computed and compared with the analytic estimations based on the coupling-of-modes theory.

Rayleigh wave reflection from single surface imperfections on isotropic substrates

The specific features of the Rayleigh wave reflection from single surface imperfections of an isotropic substrate are studied by the finite element method. Six types of the imperfections are considered, namely, upstep and downstep, projection and groove, and strip of foreign material coating the substrate and buried into it. The dependence is found and analyzed of the absolute value and the phase of the reflection coefficients on the geometrical parameters of defects and the angle of incidence. Numerical results are compared to analytical predictions based on a development of the reflection coefficient in powers of the defect height to wavelength ratio h/λ and limited to the first-order term. In particular, this comparison reveals that in some cases approximate expressions are able to provide a good precision. At the same time situations are met when the linear approximation fails to describe the behavior of the reflection coefficient even at fairly small h/λ.

Usage of symmetry in the simulation of interdigital transducers

This paper discusses the application of the finite element method to the simulation of surface acoustic wave generation on piezoelectric substrates and the possibility of reducing the number of computations by taking into account the symmetry of the problem. It is shown that the computations can be performed in only one half of the structure provided that the substrate assumes particular orientations. The class of allowed orientations encompasses the majority of crystal cuts used in practice. A test computation of the electric admittance agrees well with experimental results. The perfectly matched layer method is implemented to truncate the computational domain.

Rayleigh wave scattering from a vertical edge of isotropic substrates.

The paper numerically studies the harmonic Rayleigh wave scattering at the 90-degree corner of isotropic substrate. The finite element method is used. The main attention is paid to two cases. The first one is the apex of the substrate corner is rounded off. The second one consists in that a layer of foreign material is deposited on the face which scatters the Rayleigh wave. The dependence of the reflection and the transmission coefficients on the Poisson ratio, the angle of incidence, the fillet radius, and the layer thickness are obtained. It is found that if the Rayleigh wave is incident perpendicularly to the substrate border, then the fillet of small radius as compared to the wavelength increases the reflection coefficient and decreases the transmission coefficient by factors 1.3-1.8. At normal incidence, the Poisson ratio does not change qualitatively the dependence of the reflection and transmission coefficients on the fillet radius. But the Poisson ratio can substantially affect the angle dependence of these coefficients if the wave is incident obliquely on the corner rounded off. It is also found out that a layer can modify the conditions of scattering such that the incident wave is totally reflected without transmission and conversion into bulk waves in a wide interval of angle of incidence, although, in principle, the bulk wave generation is allowed within a part of this angle interval.

Mutual conversion of bulk and surface acoustic waves in gratings of finite length on half-infinite substrates. I. FE analysis of surface wave generation

The paper studies numerically the bulk acoustic wave generation by the surface acoustic wave propagating across a grating created on the surface of an elastically anisotropic half-infinite substrate. The computations are fully based on the finite element method. Applying the discrete Fourier transformation to the displacement field found inside the substrate and using an orthogonality relation valid for plane modes we determine separately the spatial spectrum of the quasi longitudinal and the quasi transverse bulk waves, that is, the dependence of the amplitudes of these waves on the tangential component of the wave vector. The dependence is investigated of the central spectral peak height and shape on the frequency of the incident surface wave as well as on the thickness, the width, and the number of strips forming the grating. In particular, it is found that under certain conditions the central peak can be approximated fairly precisely by the central peak of a sinc-function describing the spectrum of the bounded acoustic beam of rectangular shape and of width equal to the length of the grating.

Anisotropy effects in the reflection of surface acoustic waves from obstacles

The paper studies the difference between the reflection coefficients of a surface acoustic wave incident on a groove or strip along the inverse directions. This difference occurs because of the crystallographic anisotropy of the substrate and/or the asymmetry of the shape of the obstacle. The numerical computations are carried out by the finite element method. A perfectly matched layer is implemented to truncate the computational domain. Some general properties of the transmission and reflection coefficients of surface acoustic waves are also discussed.

Electromagnetic Surface Wave Attenuation Caused by Acoustic Wave Radiation

Abstract In theoretically studying electromagnetic surface wave propagation in crystals possessing piezoelectric properties, we found that, if the frequency is smaller than typical phonon frequencies (not exceeding 1012–1013 Hz), then electric fields are able to generate elastic vibrations because of the piezoelectric effect. In this case, an electromagnetic surface wave is coupled with bulk acoustic modes propagating from the interface to the interior of the structure. As a result, the surface wave attenuates because of the radiation of acoustic waves. The attenuation factor is proportional to the parameter τ2 va/vel, where τ is the electromechanical coupling coefficient, and va and vel are typical speeds of acoustic and electromagnetic waves in the crystal, respectively.

Enhanced sensing of molecular optical activity with plasmonic nanohole arrays

Prospects of using metal-hole arrays for the enhanced optical detection of molecular chirality in nanosized volumes are investigated. Light transmission through the holes filled with an optically active material is modeled, and the activity enhancement by more than an order of magnitude is demonstrated. The spatial resolution of the chirality detection is shown to be of a few tens of nanometers. From comparing the effect in arrays of cylindrical holes and holes of complex chiral shape, it is concluded that the detection sensitivity is determined by the plasmonic near-field enhancement. The intrinsic chirality of the arrays due to their shape appears to be less important.

Acoustic waves in the vicinity of the normal to the surface of piezoelectric crystals

The acoustic wave propagation in the vicinity of the normal to the plane surface confining a piezoelectric crystal of arbitrary symmetry is theoretically studied. An octet formalism arid a perturbation theory have been put forward to describe the wave fields in the region of concern. The developed mathematical approach has been applied to several problems. Specifically, the derivation of the transfer matrix for the normal direction to the surface has been discussed. Furthermore, we have discussed how to estimate the electric potential induced outside the piezoelectric material by a normally incident wave. In addition, an analytical expression has been derived for the numerical factor in the function describing the asymptotic behavior of quasielectrostatic Greens function for half-infinite piezoelectric substrates at small values of the wave vector

Finite element analysis of the Rayleigh wave scattering in isotropic bi-material wedge structures.

The numerical study is performed of the harmonic Rayleigh wave scattering in a composite structure constructed from two elastically isotropic 90°-wedges. These wedges are in contact along one pair of their faces. It is assumed that either the perfectly sliding contact or the perfectly rigid one is realized. The other pair of faces forms a plane border between the resulting bi-material wedge and the exterior half-infinite space occupied by vacuum. The finite element method is used. The perfectly matched layer spatially confines the computational domain. The dependences of the reflection and transmission coefficients of the Rayleigh wave on the angle of incidence, the Poisson ratio and the type of contact are obtained and analyzed for different combinations of materials. The behavior of the coefficient of the Rayleigh wave conversion into the interfacial wave which may exist on the internal boundary of the structure is also investigated. A number of relations between the coefficients of conversion are derived from symmetry considerations for structures with sliding contact and composed of identical isotropic materials.