We consider a high-Q microresonator with ${\chi }^{\left(2\right)}$ nonlinearity under conditions when the coupling rate between the sidebands around the pump and its second harmonic exceeds the damping rates, implying the strong coupling regime (SC). Using the dressed-resonator approach we demonstrate that this regime leads to the dominance of the Hermitian part of the operator, driving the sideband dynamics over its non-Hermitian part responsible for the parametric gain. This has allowed us to introduce and apply the cross-area concept of the polariton quasiparticles and their effective masses in the context of ${\chi }^{\left(2\right)}$ ring microresonators. We further use polaritons to predict the modified spectral response of the resonator to the weak probe field, and to reveal the splitting of the bare-resonator resonances, avoided crossings, and Rabi dynamics. Polariton basis also allows the deriving of a discrete sequence of the parametric thresholds for generation of sidebands of different orders.

中文翻译：

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χ（2）微谐振器中的光子-光子极化子

我们认为高Q微谐振器具有 ${\chi }^{（2）}$当泵周围的边带与其二次谐波之间的耦合率超过阻尼率时，则表明存在强非线性，这表明存在强耦合机制（SC）。使用穿戴式谐振器方法，我们证明了这种机制导致了操作员的埃尔米特部分的主导地位，使边带动力学超过了负责参数增益的非埃尔米特部分。这使我们能够在以下情况下引入和应用极化子准粒子及其有效质量的跨区域概念。${\chi }^{（2）}$环形微谐振器。我们进一步使用极化子来预测谐振器对弱探针场的修改后的频谱响应，并揭示裸谐振器谐振的分裂，避免的交叉和拉比动力学。极化子基础还允许推导参数阈值的离散序列，以生成不同阶次的边带。