Optomechanically induced transparency in the mechanical-mode splitting regime

We employ a decoupled Heisenberg-Langevin equation for the observation and physical interpretation of mechanical-mode splitting (MMS) of the movable mirror in a generic optomechanical system. Then we identify some observable and significant features of MMS in a two-mode cavity. That is, the second control field coupled to another optical mode is input to the system to modify the mechanical mode, leading to the suppression of transmission, the appearance of the doublet in the spectrum of the anti-Stokes field, and the emergence of optomechanically induced transparency in corresponding new mechanical modes. Furthermore, we open two transparent windows in virtue of MMS and find the second splitting of the mechanical mode in this two-mode optomechanical system.