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 χ2 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 nonreciprocal transmission would be achieved by breaking the antiPT 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.