Effect of Pump Frequency and Power on 1:1 Mechanical Frequency Combs

We report on an experimental and theoretical analysis of the effect on pump frequency and amplitude on the spacing of the generated phononic frequency comb (PFC) in an aluminum scandium nitride $(\text{Al}_{1-\mathrm{x}}\text{Sc}_{\mathrm{x}}\mathrm{N})(\mathrm{x}=0.2)$ drumhead nanomechanical resonator. The spacing increases with the frequency detuning and power with slopes of 1.2595 kHz/kHz and 4.593 kHz/V respectively which can be predicted with the presented theoretical framework. It is shown in the theoretical framework that the change in spacing with frequency detuning includes (1) a linear regime, where the effects of Duffing nonlinearity and pump power are negligible, and (2) a nonlinear regime, where the Duffing nonlinearity and pump power determine the comb spacing. For the first time, a theoretical framework considering the effect of each parameter on the comb spacing is introduced to predict the impact of frequency detuning and pump power on spacing.