Photon-photon polaritons in chi-2 microresonators

Abstract

We consider a high-Q microresonator with chi-2 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 methodology, which is similar to the well-known theory of the two-levels atoms dressed by the optical fields, we demonstrate that this regime leads to the dominance of the reversible energy transfer between the sidebands over the non-reversible sideband growth due to parametric gain. This observation has allowed us to introduce and apply the cross-area concept of the polariton quasi-particles in the context of chi-2 ring-microresonators, and to use it to predict the modified spectral response of the resonator to the weak probe field. This response reveals the splitting of the bare-resonator resonances, avoided crossings, and Rabi dynamics. Using polaritons as the basis has also allowed us to derive a discrete sequence of the parametric thresholds for generation of sidebands of different orders. These thresholds form spectacular patterns in the parameter space defined by the detunings of the fundamental and 2 nd harmonic fields, Figs (a) and (b).