Nonlinear Analysis of Phononic Comb Generation in High-Q Quartz Resonators

We report on a nonlinear analysis of high-fidelity, high-Q, phononic frequency combs in AT-cut 100-MHz shear-mode quartz resonators. The comb generation was observed on anharmonic modes above the fundamental mode resonance. These modes exhibited the strongest nonlinearities when driven slightly off resonance at power levels of +11 to +22 dBm. Teeth spacings as large as 250 kHz have been observed, which can allow frequency locking to particular teeth. The combs appear to be generated by a multi-wave mixing process between the drive frequency and nearby resonances. A two-mode nonlinear 1D analytical analysis is presented, which matches several of the comb features using measured quartz input parameters and realistic drive conditions.