Optomechanically tuned Fano resonance and slow light in a quadratically coupled optomechanical system with membranes

Realizing and controlling a Fano resonance is of fundamental significance in physics and may find applications in optical switching and sensitivity-enhanced biochemical sensing. Here we present a practicable scheme to realize Fano resonance and slow light in a quadratically coupled optomechanical system with membranes. It is shown that Fano resonance generation is precisely controlled by changing the frequency detuning between the cavity field and the control field in the quadratically coupled optomechanical system, while additional membrane inside the system can considerably establish a tunable switch between a single Fano resonance and double Fano resonances. In particular, the asymmetric line shape and the number of Fano resonance can be well tuned by the reflectivity of the membranes, the wavelength of the control field and the environment temperature. Furthermore, it is also shown that the slow light effects of the transmitted probe field can be obtained under two-phonon resonance condition and the group delay of the transmitted probe field can be adjusted by the frequency and power of the control field. Our scheme may help to achieve the practical application of Fano resonances relevant to the nonlinear optics.