Abstract
In this paper, we report a theoretical investigation of surface acoustic waves propagating in one-dimensional phononic crystal. Using finite element method eigenfrequency and frequency response studies, we develop two model geometries suitable to distinguish true and pseudo (or leaky) surface acoustic waves and determine their propagation through finite size phononic crystals, respectively. The novelty of the first model comes from the application of a surface-like criterion and, additionally, functional damping domain. Exemplary calculated band diagrams show sorted branches of true and pseudo surface acoustic waves and their quantified surface confinement. The second model gives a complementary study of transmission, reflection, and surface-to-bulk losses of Rayleigh surface waves in the case of a phononic crystal with a finite number of periods. Here, we demonstrate that a non-zero transmission within non-radiative band gaps can be carried via leaky modes originating from the coupling of local resonances with propagating waves in the substrate. Finally, we show that the transmission, reflection, and surface-to-bulk losses can be effectively optimised by tuning the geometrical properties of a stripe.
Highlights
We comparatively investigate finite phononic crystals (PnCs) for which transmission, reflection, and surface-to-bulk losses are calculated by the frequency response FEM model
Making use of FEM, we studied surface acoustic waves (SAWs) dispersion and propagation through PnCs made of an array of rectangular stripes on the (001) surface of Si
We showed dispersion features such as zone folding, band gaps originating from Bragg reflections and local resonances, the latter splitting Rayleigh surface waves (RSWs) into Rayleigh- and Sezawa-like waves, and the presence of longitudinal leaky surface acoustic waves (LLSAWs)
Summary
Since the first study by John Strutt (3rd Lord Rayleigh) in 1885, Rayleigh surface waves (RSWs), the simplest of surface acoustic waves (SAWs), have become the subject of a large number of papers, monographs, applications, and patents. The experimental and theoretical studies of the propagation of SAWs in periodically corrugated surfaces of the 1970s and 1980s initiated informally the field of phononic crystals (PnCs). The artificial second-order periodicity, introduced by an array of grooves or metallic stripes, was shown to result in the appearance of surface Brillouin zones, zone folding, pseudo-SAWs, and in particular cases frequency band gaps. The research from the last twenty years has pointed out numerous attractive properties of PnCs over wide length and frequency scales, which can be applied to, e.g., seismic waves filters, coherent phonon sources, tunable acoustic filters, waveguides, and thermal management.. The experimental and theoretical studies of the propagation of SAWs in periodically corrugated surfaces of the 1970s and 1980s initiated informally the field of phononic crystals (PnCs).. Contrary to the previous reports, we show a way to sort surface-like solutions and distinguish true- and pseudo-SAWs within a framework of the FEM eigenfrequency analysis. With this background, we comparatively investigate finite PnCs for which transmission, reflection, and surface-to-bulk losses are calculated by the frequency response FEM model. Besides the novelty of the provided models, which can be extended to 3D, our findings show the importance of pseudo-SAWs in the design and optimisation of PnCs based high efficiency acoustic filters, reflectors, or waveguides
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