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

Abstract

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.

Computation of the pressure field generated by surface acoustic waves in microchannels

“…The PML parameters were checked, like in our previous works, [51][52][53][54][55][56][57][58] by comparing the wave fields computed at different sizes of domains 1-5 representing the parts of the actual structure (Fig. 1).…”

“…Note that we have already investigated the SAW scattering in various cases by FEM in combination with PML. [51][52][53][54][55][56][57][58] An analogous method is also used in ref. 59.…”

Existence theory for a system of coupled multi‐term fractional differential equations with integral multi‐strip coupled boundary conditions

“…Here we emphasize that the first integral multi‐strip boundary condition (likewise the second integral multi‐strip condition) states that distribution of x ( s ) on the interval [0,1] equals the multi‐strip contributions for the function y ( s ). The nonlocal strip conditions have interesting applications in heat conduction problems with nonuniform boundary conditions, 42 geophysical flows, 43 and acoustic scattering 44 . In computational fluid dynamics (CFD) studies of blood flow problems, integral boundary conditions provide the means to consider an arbitrary shaped cross‐section of blood vessels 45 and help to regularize ill‐posed parabolic backward problems (bacterial self‐regularization model 46 ) For details and applications in engineering problems, see previous studies 47–49 …”

Surface acoustic wave reflection/transmission at vertical borders of piezoelectric substrates

“…These amplitudes are calculated, like in our earlier papers [28][29][30][31][32][33], with the help of the spacial Fourier transform by extracting the harmonic k x ¼ Àk I of the displacement u SC;z ðr; tÞ at z ¼ 0 and the harmonic k z ¼ Àk T of the displacement u SC;x ðr; tÞ at x ¼ 0, respectively. The reflection and the transmission coefficients are defined as the ratio of the normal component of the mechanical displacement of the corresponding wave to the normal component of the mechanical displacement of the incident SAW.…”