Formation, Evolution, and Tuning of Frequency Combs in Microelectromechanical Resonators

This paper presents the formation, evolution, and tuning of frequency combs in a piezoelectric micromechanical resonator, based on nondegenerate parametric pumping. The frequency combs consist of precisely spaced spectral lines located close to the mechanical resonance modes of a drumhead microelectromechanical resonator. We investigate the parameter space of different dynamical regimes, wherein induced signal/idler tones break down into combs, and evolve into triangular-envelope shaped spectrums. Furthermore, we discuss the tuning mechanisms of frequency combs and study the dependency of the center frequency of combs and the frequency spacing between the spectral lines on the pump power and frequency. We demonstrate the evolution of combs in a mechanical system with direct electrical excitation and readout. This paper offers ultra-compact ($30~\mu \text{m}$ in diameter), low-power (-13 dBm of threshold power) and highly tunable integrated frequency comb sources as low-cost alternatives to optomechanical frequency combs.