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.

• Received 20 July 2020
• Accepted 1 February 2021
• Corrected 8 April 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.L012017

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Published by the American Physical Society