Pillar-based phononic crystal structures for high-frequency applications
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The physical mechanisms of phononic bandgap (PnBG) formation in the pillar-based phononic crystals (PnCs) are theoretically studied. The comparison of PnBGs in three different lattice types (i.e., square, triangular, and honeycomb) with different pillar geometries shows that different PnBGs have varying degrees of dependency on the lattice symmetry based on the interplay of the local resonances and the Bragg effect. The details of this interplay are discussed. The significance of locally resonating pillars on PnBGs is discussed and verified by examining the PnBG position and width in perturbed lattices. It is shown that the PnBGs caused by the local resonance of the pillars are more resilient to the lattice perturbations than those caused by Bragg scattering. Furthermore, strong experimental evidence is presented for the existence of a complete phononic bandgap, for Lamb waves, in the high frequency regime (i.e., 800 MHz) for a pillar-based PnC membrane with a triangular lattice of gold pillars on top. The results of experiments are analyzed, and the physics behind the attenuation in different spectral windows is explained methodically by assessing the type of Bloch modes and the in-plane symmetry of the displacement profile. In addition, a theoretical design for a waveguide/resonator device operating at the GHz frequency range based on the pillar-based PnC membranes is presented and experimental evidence is provided for the waveguiding property of the proposed structure. Additionally, several designs for surface acoustic wave (SAW) PnCs and PnC-based waveguides are introduced and theoretically studied. These designs are optimized to provide low radiation loss and high design flexibility in terms of engineering the frequency and the number of guided modes.