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.

中文翻译：

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光子二聚体中的反宇称时间对称性和不可逆传输

在这项工作中，研究了反宇称时间（反PT）对称下光学参量振荡的光学性质和动力学行为。非厄米光学系统由两个回音壁模式微腔组成，其中一个腔支持$\chi _{2}$非谎言性。与以往依赖光学增益和损耗的非厄米系统相比，该系统可以通过调整参数增益和耦合强度来实现反PT对称性的超快速控制。此外，通过关注线性泵浦条件下的反PT对称系统和非对称增益，我们发现系统在反PT对称性下提供非对称传输，同时通过打破反PT来实现非互易传输对称。我们相信这些结果可以进一步应用于光学二极管、光开关和其他光学器件，从而为纳米光子学和量子信息科学铺平道路。