Selective Parametric Amplification of Degenerate Modes in Electrostatically Transduced Coupled Beam Resonators

TL;DR

This paper demonstrates selective parametric amplification of degenerate modes in coupled beam resonators, revealing phase-dependent nonlinear dynamics and achieving significant gain for potential applications in sensing and phononic control.

Contribution

It introduces a novel method for selective amplification of degenerate modes via parametric excitation through the coupling spring, enabling phase-controlled mode manipulation.

Findings

Achieved ~13 dB parametric gain in the out-phase mode.

Demonstrated phase-dependent modulation of amplification.

Revealed nonlinear and linear responses of different phase modes.

Abstract

Parametric excitation in coupled mechanical systems has enabled advances in sensing, computation, and phonon control. The function of distinct phase modes using parametric driving remains insufficiently explored. Here, we investigate the nonlinear and parametric response of degenerate phase modes in a Double Ended Tuning Fork (DETF) resonator. Our measurements reveal pronounced nonlinearity and parametric amplification in the out-phase mode, attributed to the dominant contribution of the coupling beam, while the in-phase mode remains predominantly linear. Uniquely, we demonstrate parametric excitation through the coupling spring, enabling selective amplification and de-amplification controlled via the relative phase between harmonic and parametric drives. A parametric gain of $\sim$13 dB is achieved in the out-phase mode, with phase-dependent modulation of amplification, indicating its suitability for signal processing, logic operations, and memory elements based on degenerate modes. These results establish a new approach to exploiting mode-specific nonlinear dynamics in coupled resonators for emerging applications in sensing and phononic control.