Multiple frequency combs via pump modulation in a three-mode optomechanical system

Parametric frequency conversion involving phonons is an intriguing physical issue in cavity optomechanics. Here, this phenomenon is exploited to devise multiple frequency combs in a three-mode optomechanical system assisted by a degenerate parametric amplifier (DPA). In the optomechanical model, the configuration of optical-mechanical-mechanical coupled resonators provides a well-established environment containing photon-phonon and phonon-phonon interactions. When the system satisfies the frequency matching of parametric conversion involving photons, both integral and fractional multiples of phonons, we observe that the two interactions contribute respectively to generating optical frequency combs (OFCs) with a tooth spacing of 1GHz and phonon-based frequency combs (PBFCs) of integer- and fraction-order with a tooth spacing of 80MHz/N_f (N_f is an integer). Since N_f can be adjusted by mechanical pumps operating on the mechanical resonators, the repetition rate of the frequency combs is flexibly modulated, thus enabling the pursuit of an ultra-small tooth spacing. More importantly, we report that by increasing the nonlinear gain coefficient of the DPA, the PBFCs can grow explosively, forming dense plateau regions and summing up to hundreds of comb lines. The proposal may be useful in facilitating dual-comb spectroscopy and achieving the ultrahigh resolution of frequency combs.