Optical multistability and Fano line-shape control via mode coupling in whispering-gallery-mode microresonator optomechanics

We study a three-mode (i.e., a clockwise mode, a counterclockwise mode, and a mechanical mode) coherent coupling regime of the optical whispering-gallery-mode (WGM) microresonator optomechanical system by considering a pair of counterpropagating modes in a general case. The WGM microresonator is coherently driven by a strong control laser field and a relatively weak probe laser field via a tapered fiber. The system parameters utilized to explore this process correspond to experimentally demonstrated values in the WGM microresonator optomechanical systems. By properly adjusting the coupling rate of these two counterpropagating modes in the WGM microresonator, the steady-state displacement behaviors of the mechanical oscillation and the normalized power transmission and reflection spectra of the output fields are analyzed in detail. It is found that the mode coupling plays a crucial role in rich line-shape structures. Some interesting phenomena of the system, including optical multistability and sharp asymmetric Fano-shape optomechanically induced transparency (OMIT), can be generated with a large degree of control and tunability. Our obtained results in this study can be used for designing efficient all-optical switching and high-sensitivity sensor.