Van der Pol–Duffing oscillator and its application to gain-driven light-matter interaction

We report the observation of frequency nonlinearity within a gain-embedded resonator. A coupling model, integrating the van der Pol--Duffing oscillator, is theoretically proposed. The proposed model is substantiated through experimental verification in coupled LRC circuits, demonstrating bistable behavior. Furthermore, by application of the van der Pol--Duffing oscillator to a gain-embedded microwave cavity, our model is demonstrated as an alternative theoretical perspective for understanding the gain-driven polariton.