High-Order Harmonics Frequency Comb Generation of a Single Driven Nonlinear NEMS Mode

This work reports on the experimental demonstration, along with a comprehensive theoretical framework of generation of multiple frequency combs with locked frequency spacing, centered at harmonics of a mechanical resonance mode. We show that high-order frequency combs can be generated using a single driven nanomechanical resonance mode. The resonator is an Aluminum Scandium Nitride membrane resonator, modelled with a one degree of freedom (1-DoF) mass-spring-damper system. The equation of motion uses quadratic and cubic nonlinearities of the spring constant, and is solved to capture the frequency response up to the 10th-order harmonic, showing generated combs centered at each harmonic. It is shown that all the simulated combs have a fixed spacing of 12 kHz, perfectly matching the measured results. Furthermore, we theoretically show that the spacing and number of the spectral lines (i.e. comb teeth) is adjustable by controlling the quadratic nonlinear terms. Due to shortcomings of the equation of motion in simulating the effects of frequency detuning, Hamiltonian dynamics is used to investigate the effect of frequency detuning on comb generation.