Resonant attenuation of surface acoustic waves by a weakly bonded layer

Abstract

We investigate the propagation of surface acoustic waves (SAWs) in a layered half-space system comprising a continuous, sub-wavelength-thick layer weakly adhering to a substrate. Using finite element simulations, we demonstrate that this configuration - without requiring surface structuration - gives rise to frequency ranges bounded in k-space and characterized by strong SAW attenuation, which we term adhesion-induced resonant attenuation zones. We show that these attenuation zones closely mimic the resonant behavior typically observed in locally resonant metamaterials and can be understood through a mass-spring analogy, where the adhesion between the layer and substrate governs the frequency and width of the attenuation zones. As a practical demonstration, we propose a bilayer configuration as a practical route to experimentally realize adhesion-induced resonant attenuation of SAWs, where a soft and thin interfacial film serves as an intermediate adhesive bonding between the layer and substrate, providing a realistic and tunable interfacial stiffness. Our findings offer a simplified route to achieving SAW manipulation through continuous layered media with tunable adhesion, providing a practical alternative to complex structural designs in SAW-based devices across a broad frequency range.

Figures (6)

• Figure 1: Dispersive behavior of a SAW interacting with (a) isolated resonant elements characterized by a resonance frequency $f_r$, and (b) a thin elastic layer weakly adhering to the substrate via an interfacial stiffness $K_n$.
• Figure 2: (a-b) FE configurations used for the eigenfrequency and frequency response studies respectively. Dispersion curves and transmission spectra computed for (c) weak ($5 \times 10^{13}$ N/m$^3$), (d) intermediate ($2 \times 10^{14}$ N/m$^3$) and (e) good adhesion ($10^{16}$ N/m$^3$) of the layer to the substrate. The colorscale in the dispersion curves corresponds to the normalized maximum of the vertical displacement. In geometries (a-b), dimensions are expressed as a function of the SAW wavelength $\lambda$. PBC: Periodic Boundary Conditions, LRBC: Low-Reflecting Boundary Conditions. BAWs: Bulk Acoustic Waves
• Figure 3: Comparison between local resonators and adhesive layer through their (a) dispersion curves and (b) transmission spectra. The frequency scale is normalized by the frequency corresponding to the minimum of the transmission spectrum. The lower and upper boundary of the attenuation zone are represented in (a) by $k_{low}$ and $k_{up}$. (c) Variation of the group velocity of the lower branch as a function of $kh$, showing a minimum at $k_{low}$. (d) Depth profiles of the vertical displacement at $kh$ = 0.17 with $x_2 = 0$ at the substrate's surface, $x_2 > 0$ being in the substrate and $x_2 < 0$ in the layer/resonator. The displacement is normalized by the maximum of the displacement in the depth (located in the layer or in the resonator).
• Figure 4: (a-d) Dispersion curves for different values of $K_n$, normalized by the upper boundary of the attenuation zone, $f_{up}$ and $k_{up}$. The lower branch is plotted only up to $k_{low}$, to highlight the range of validity of the analogy with mass-spring resonators. The green background in (a-c) denotes the presence of an attenuation zone in the dispersion curve. The light red background in (d) indicates the closure of the attenuation zone. (e-f) Variation of $\Delta f$ and $f_{c}$ as a function of the interfacial stiffness, respectively.
• Figure 5: FE frequency-response simulations on bilayer structures using a PMMA layer as an adhesive layer between a gold film and a glass substrate (a) Schematic of the simulated structure. Inset shows an analogous mass-spring resonator structure. Varying the PMMA thickness, $h_p$, which mimics changes in the interfacial stiffness $K_n$, modifies the central frequency and width of the attenuation zone are modified. The gold-layer thickness $h_g$ also influences the central frequency, as predicted in Equation \ref{['eq:eq5']}. (b) Transmission curves (in dB) for three cases, for which the thickness of the gold film and the PMMA layer are equal. In these cases, $h_g = h_p$ = 200nm, 350 nm and 500 nm. (c) Central frequency of the attenuation zone as a function of $h_{p}$ for different values of $h_g$, extracted from the position of the transmission minimum. (d) Width of the attenuation zone as a function of $h_p$, determined from the full width at half minimum. Open circles denote values obtained from the FE simulations, and dashed curves correspond to values given by the analytical expressions \ref{['eq:eq4']} and \ref{['eq:eq5']}.