Nonlinear resonances and phononic frequency combs in MEMS

Phononic frequency combs are the mechanical analogue of optical frequency combs. These features were experimentally observed for the first time in a piezoelectrically driven micromechanical device1 in ambient conditions, confirming recent theoretical predictions of such phenomena in FPU chains2. The formation of phononic frequency combs is mediated by parametric back-action and nonlinear mixing in a system of coupled nonlinear resonances, and comb-like spectra in the RF can be generated from a single-tone drive signal. The original experimental observations were made in a system comprising two coupled modes, and this has been recently followed by observations of the same phenomena in micromechanical systems comprising three coupled modes3, and in coupled devices where multiple comb regimes can co-exist4, with comb features defined by the system and drive parameters, and initial conditions. Specific characteristics of phononic frequency combs are discussed, including dependencies on drive conditions and modal properties, that define the onset of the comb response and subsequent evolution, including features such as the number and spacing of comb lines. While the engineering of optical frequency combs has significantly impacted the fields of time and frequency metrology, and molecular spectroscopy; phononic frequency combs have the potential to enable other applications such as stable tracking of resonant frequencies in physical sensors without the requirement of a feedback oscillator5, and spread-spectrum information encoding for wireless telecommunications.  The talk will also discuss other observations associated with nonlinear effects in such devices such as intrinsic localized modes, setting the scene for employing such accessible experimental test-beds to probe a variety of nonlinear phenomena not accessible in more conventional mechanical systems. 

References:
1. A. Ganesan, C. Do, and A. A. Seshia, "Phononic Frequency Comb via Intrinsic Three-Wave Mixing," Physical Review Letters, vol. 118, p. 033903, 2017.
2. L. S. Cao, D. X. Qi, R. W. Peng, M. Wang, and P. Schmelcher, "Phononic Frequency Combs through Nonlinear Resonances," Physical Review Letters, vol. 112, p. 075505, 2014.
3. A. Ganesan, C. Do, and A. A. Seshia, "Phononic frequency comb via three-mode parametric resonance," Applied Physics Letters, 2018, in press.
4. A. Ganesan, C. Do, and A. A. Seshia, “Excitation of coupled phononic frequency combs via two-mode parametric three-wave mixing,” Physical Review B, 2018, in press. 
5. A. Ganesan, and A. A. Seshia, “Tracking the resonant frequency of a micromechanical resonator using phononic frequency combs,” arXiv preprint arXiv:1710.07058, 2017.