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.