Giant energy exchange rate in mode-coupled resonators enables supercontinuum mechanical frequency combs

Mechanical frequency combs (MFCs), built upon wave mixing in mode-coupled micromechanical resonators, are often limited by their narrow and sparse spectra due to small energy exchange rates. However, the ability to model and enhance the energy exchange rate remains insufficiently explored. Here, we systematically propose coupling enhancement schemes for different architectures, and present a coupling-enhancement anchor design to achieve the giant energy exchange rate between the coupled modes of our device, enabling the broadening of comb spacing to overlap harmonic clusters of MFCs, leading to the generation of supercontinuum frequency combs. A theoretical model describing the physical relationship between the energy exchange rate and resonator parameters is developed, which is validated by the consistent correlation between the energy exchange rate and the induced mode amplitude under varying driving frequencies. Our finding builds a design-oriented approach to raise the energy exchange rate in mode-coupled resonators and to construct decade-wide dense spectral range of MFCs, paving the way for their potential applications in precision timekeeping and signal processing.