Resonantly enhanced polariton wave mixing and Floquet parametric instability

Recent experiments by Cartella et al. [1] demonstrated terahertz optical amplification in SiC insulator following a strong mid-IR pump that resonantly excited the SiC stretching mode. Motivated by these experiments we study the problem of light reflection from a slab of insulating material with a strongly excited polariton mode. We introduce a new theoretical approach for analyzing this system using the Floquet formalism, in which polariton oscillations provide periodic time modulation. We present an analytic solution of the Fresnel light reflection problem. We demonstrate discontinuous dependence of the reflection coefficient on the incoming photon frequency, which we attribute to the existence of unstable polariton modes. We interpret these instabilities as resonantly enhanced polariton parametric wave mixing. Our results provide a simple physical interpretation of light amplification observed in recent experiments by Cartella et. al. [1]. Moreover, we argue that Floquet parametric instability could already be present in these experiments. Our approach utilizing the Floquet formalism is applicable to a broad class of systems.
[1] A. Cartella et. al, PNAS 115, 12148 (2018),