Tunable high-order sideband generation in a coupled double-cavity optomechanical system

Tunable high-order sideband generation has important applications in the realization of the optical frequency comb with a varying spectral region (corresponding to the sideband range) and frequency resolution (corresponding to the sideband interval). In this paper, we propose a theoretical scheme to tune both the range and the interval of the high-order sidebands in a coupled double-cavity optomechanical system, which consists of an optomechanical cavity and an auxiliary cavity. Our proposal can be realized by driving the optomechanical cavity with a control field and a probe field simultaneously, driving the auxiliary cavity with a pump field. Furthermore, we assume that the frequency detuning between the control field and the probe field (the pump field) equals ω b /n (ω b /m), where ω b is the mechanical frequency, m and n are integers. When n = m = 1, we find that the sideband range can be effectively enlarged by increasing the pump amplitude or the photon-hopping coupling rate, or by decreasing the auxiliary cavity damping rate. When n = 1 and m > 1, the output spectrum consists of a series of integer-order sidebands, fraction-order sidebands, and the sum and difference sidebands, and the sideband interval becomes ω b /m and can be diminished by simultaneously increasing m and the pump amplitude.