Rayleigh Wave Propagation and Bandgap Behavior in Metamaterial-Covered Piezoelectric Substrates

Piezoelectric surface acoustic wave (SAW) devices are extensively applied in communications, sensing, and related fields; however, their performance is often constrained by parasitic mode interference. The bandgap (BG) characteristics of metamaterials provide a promising approach to controlling elastic wave propagation. In this study, we derived the dispersion relation for Rayleigh wave propagation in metamaterial-covered piezoelectric substrates through theoretical analysis and verified the model using finite element simulations. Results show that both the material properties (elastic modulus and density) and structural parameters (rod height, rod radius, and height gradient) of the metamaterial significantly influence the BG behavior of Rayleigh waves. Specifically, the BG frequency increases with elastic modulus but decreases with density; increasing rod height introduces additional BGs; the BG widths expand as the rod radius increases; and when propagating toward decreasing rod height, Rayleigh waves efficiently convert into bulk waves, whereas propagation toward increasing rod height leads to velocity attenuation and wave trapping.