Parametric oscillation, frequency mixing and injection locking of strongly coupled nanomechanical resonator modes

TL;DR

This paper investigates the locking phenomena, frequency mixing, and parametric oscillation in strongly coupled nanomechanical resonator modes, demonstrating frequency tuning, injection locking, and four-wave-mixing effects in silicon nitride resonators.

Contribution

It introduces controlled parametric drive and dielectric tuning to observe nonlinear effects like injection locking and four-wave-mixing in coupled nanomechanical modes.

Findings

Observation of parametric oscillation and frequency mixing.

Demonstration of injection locking phenomena.

Identification of satellite resonances due to four-wave-mixing.

Abstract

We study locking phenomena of two strongly coupled, high-quality factor nanomechanical resonator modes subject to a common parametric drive at a single drive frequency. By controlled dielectric gradient forces we tune the resonance frequencies of the flexural in-plane and out-of-plane oscillation of the high stress silicon nitride string through their mutual avoided crossing. For the case of the strong common parametric drive signal-idler generation via parametric oscillation is observed, analogously to the framework of nonlinear optical effects in an optical parametric oscillator. Frequency tuning of the signal and idler resonances is demonstrated. When the resonance frequencies of signal and idler get closer to each other, partial injection locking, injection pulling and complete injection locking to half of the drive frequency occurs depending on the pump strength. Furthermore, satellite resonances, symmetrically off-set from signal and idler by their beat-note, are observed which can be attributed to degenerate four-wave-mixing in the highly nonlinear mechanical oscillations.