Anti-Parity-Time Symmetry and Non-Reciprocal Transmission in Photonic Dimer

In this work, the optical properties and dynamical behaviors of the optical parametric oscillation under the anti Parity-Time (anti-PT) symmetry are studied. The non-Hermitian optical system is composed of two whispering-gallery mode micorcavities with one cavity supports the
$\chi _{2}$
nonliearity. Compared with the previous non-Hermitian system that relies on optical gain and loss, the proposed system could achieve the ultra-fast control of anti-PT symmetry by adjusting the parameter gain and coupling strength. Moreover, by focusing on the anti-PT symmetrical system and asymmetrical gain under linear pumping conditions, we find that the system provides the asymmetric transmission under the anti-PT symmetry, meanwhile the non-reciprocal transmission would be achieved by breaking the anti-PT symmetry. We believe these results may be further applied to optical diodes, optical switches and other optical devices which may pave the way of nanophotonics and quantum information science.