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 MHz. A phononic crystal of cross-holes is fabricated in a thin fused silica plate by femtosecond laser writing followed by 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 there are only evanescent waves in the crystal which 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 micro-resonators forming phononic polymers could find applications for ultrasonic sensing, for implementation in topological phononics, and for the design of optomechanical resonator chains.

Phononic Coupled-Resonator Waveguide Micro-Cavities

“…Displacements larger than 0.3 pm can be recorded with this setting. The measurements reveal a sequence of very sharp resonance peaks, in agreement with previous results on a sample with a single chain of seventeen coupled resonators [15]. Compared with that sample, however, the resonance peaks are distributed over a larger span of frequencies, especially in the range from 2.1 to 2.3 MHz.…”

“…The resonant states are collective vibrations of the chain, as we have shown recently in the case of a chain of seventeen resonators implemented in a two-dimensional fused silica phononic crystal slab, and are rather independent of the path followed over the surface of the slab [15].…”

“…Experimental details regarding sample preparation and characterization are identical with Ref. [15] and are not repeated here.…”

“…In Ref. [15], we introduced a dynamical matrix model to predict the resonant frequencies of a phononic polymer, or a generalized chain of coupled resonators that is not necessarily organized along the principal axes of the supporting phononic crystal. Here we extend the model to the more general case of unequal coupling coefficients.…”

“…In this paper, we experimentally explore how a set of a few phononic coupled-resonator waveguide cavities, coupled weakly through evanescent elastic waves, can form collective vibrations where the resonance modes of the individual phononic cavities are essentially preserved but can be excited at once. Experimentally, we rely on the phononic crystal slab technology developed for our previous work based on femtosecond laser writing followed by KOH etching of a fused silica plate [15], but extend our considerations to the set of three short phononic cavities shown in Figure 1. In the following, we first present the experimental results and the numerical simulations that sustain them, before discussing the observed collective vibrations in the light of a dynamical matrix model with one degree of freedom per defect and the nearest-neighbor approximation.…”