Phononic Frequency Combs in Stand-Alone Piezoelectric Resonators

Abstract

This work reports on the generation and frequency tuning mechanisms of resonant-based phononic frequency combs. The reported mechanical frequency combs are realized in an integrated standalone piezoelectric platform and are excited via non-degenerate parametric pumping. Two flexural resonance modes of a thin Aluminum Nitride (AlN)-on-silicon circular membrane are targeted due to their low onset of nonlinearity and excited simultaneously. When the resonator is pumped with a single tone at a frequency close to the sum of the two mechanical modes, phononic frequency combs are generated close to each mechanical mode, under certain and repeatable pump frequency and power conditions. The phononic combs consist of a set of equally-distanced phase-coherent spectral lines; we demonstrate such combs centered around 6 MHz, with a tunable spacing of around 55 kHz, corresponding to the $u_{11}$ resonance mode of the circular membrane. The center frequency and frequency spacing of the comb can be tuned by tuning the pump frequency and amplitude. We take advantage of the mode coupling between two high- $Q$ resonance modes in the same acoustic cavity, and demonstrate the smallest piezoelectric frequency comb, with a 30 $\mu \mathrm{m}$ diameter circular footprint, which requires a very low threshold power of only −4 dBm to excite a fine-tooth comb.