Collective Resonances of a Chain of Coupled Phononic Microresonators

Abstract

We study experimentally a chain of defect resonators in a phononic crystal slab and observe its collective resonances at ultrasonic frequencies of a few megahertz. A phononic crystal of cross holes is fabricated in a thin fused-silica plate by femtosecond-laser writing followed by $\mathrm{KOH}$ etching. A chain of 17 coupled resonators is defined with no definite spatial periodicity but similar coupling strength between nearest-neighbor resonators. The full phononic band gap ensures that only evanescent waves in the crystal can tunnel between adjacent resonators in the plane. The resulting evanescent-coupling strength decreases exponentially with distance. Collective resonances are excited by a frequency-driven piezoelectric vibrator attached at one end of the chain and imaged along the chain with a laser Doppler vibrometer. A discrete spectrum of resonances is observed and explained by a model representing the chain as a phononic polymer. The theoretical analysis is supported by finite-element simulations that agree well with experimental results. Chains of evanescently coupled microresonators forming phononic polymers could find applications in ultrasonic sensing, for implementation in topological phononics, and for the design of optomechanical resonator chains.