Dynamic Analysis and Reservoir Computing Application of a Nonlinear Microring Resonator

A nonlinear microring resonator is governed by a set of coupled differential equations that model the dynamics of the optical field, temperature, and free carrier concentration within the resonator. These equations capture the mechanisms responsible for self-pulsing and memory effects, which are key in neuromorphic applications of microring resonators. One example is their use as nonlinear nodes in reservoir computing (RC). The dynamical state of a microring resonator is influenced by its control parameters: the input optical power and frequency. While previous studies have relied heavily on computationally intensive simulations to determine the resonator's self-pulsing state or identify optimal control parameters for efficient optical computation, we propose a linearization and stability analysis to identify regions in the control parameter space associated with different dynamical behaviors. Using an adiabatic approximation of the cavity field of the mode, we calculated the Jacobian eigenvalues of the linearized system, which serve as reliable indicators of RC performance for specific input characteristics.