Phase-controlled higher-order exceptional points and nonreciprocal transmission in an optomechanical system

The higher-order exceptional point (EP) and reconfigurable nonreciprocal transmission have been investigated in a four-mode optomechanical system, consisting of two passive cavities and two active mechanical modes. A phase diagram of multiple EPs including higher than third-order EP is divided into different regions with a certain EP pattern, the variation of which with the parameters are demonstrated by analyzing the eigenspectrum of the system. In particular, the emergence, coalescence, and separation of the multiple EPs are strongly dependent on the relative phase between different paths in the cavity optomechanics system. On the other hand, the optical nonreciprocity with a large isolation about 50 dB can be achieved by incorporating mechanical gain. It is shown that the optical nonreciprocity at the relative phase $\ensuremath{\varphi}$ exhibits exchange symmetry with that in the case of the phase $2\ensuremath{\pi}\ensuremath{-}\ensuremath{\varphi}$. Additionally, the system presents a special nonreciprocal spectra at different EPs, which can provide a means to identify the type of multiple EPs. Our scenario shows that the optical nonreciprocity associated with the multiple EPs may provide a useful platform for realizing optical communications and exploring the physics related to the higher-order EPs.