Active Nonlinear Silicon Microring Resonators Tomography: Modeling and Characterization

We investigate voltage- and power-dependent optical nonlinearities and the resulting transmission spectra in active silicon-on-insulator microring resonators. We develop a unified theoretical model based on coupled nonlinear equations for the intracavity optical field, free carriers, and temperature, incorporating Joule heating from photocurrent and defect-induced linear absorption under different bias voltages. We systematically analyze and compare the contributions of Kerr, thermal, and free-carrier effects to nonlinear loss and refractive-index change. Experimentally, we characterize the power- and voltage-dependent changes in extinction ratio and resonance shift in active silicon microresonators with a continuous-wave pump laser. Under reverse bias, the free-carrier lifetime is markedly reduced, and significant additional resonance detuning is also observed, which we attribute to Joule heating. As a key step for theory-measurement comparison, we extract important design parameters (propagation loss and coupling loss) and time constants (thermal relaxation time and free-carrier lifetime) under different reverse-bias voltages. We then incorporate these measured parameters into our theoretical model and compare the simulated and measured power- and voltage-dependent nonlinear response, obtaining good agreement. Our combined theoretical and experimental study provides guidance for the use of active silicon microresonators in nonlinear-optic applications with reduced and controllable carrier lifetime.