Optomechanically induced Faraday and splitting effects in a double-cavity optomechanical system

We demonstrate the optomechanically induced Faraday and splitting effects caused by optical mode conversion in a double-cavity optomechanical system. In the scheme, the polarization states of propagating light fields can be arbitrarily tailored to achieve optical Faraday rotation successfully via optomechanical interaction. Meanwhile, the energy-level splitting of the degenerate optical modes leads to the separation of two orthogonal polarization optical modes and the manipulation of spin angular momentum of photons. Moreover, the polarized output component orthogonal to the control field can be manipulated by properly choosing the tunneling interaction between two optical cavities, which enables the complete polarization control of the probe field. Using the polarized control field and optical gain in the auxiliary cavity, we can effectively improve the efficiency of optical Faraday rotation. Finally, we study how to achieve different optical control for different polarization states, which provides an effective method for the implementation of optical isolators in cavity optomechanical systems. Our scheme may benefit future realization of flexible controllability for the vector properties and spin angular momentum of photons, and can promote potential applications in optical nonreciprocal transport, routers, isolators, and circulators.