On-chip all-optical second-order ordinary differential equation solver based on a single microdisk resonator

This paper proposes an all-optical second-order ordinary differential equation (SODE) solver based on a single microdisk resonator. We validate the feasibility of our structure for constant and complex coefficient SODE solutions for Gaussian and super-Gaussian pulses. The results demonstrate a good agreement between the solutions obtained with the designed structure and those obtained through mathematical calculations for both constant and complex coefficient SODEs. We also discuss the influence of input optical signal pulse width on solution result deviations. Furthermore, we validate the capability of the designed structure to achieve tunable solutions for complex-coefficient SODEs with a tuning power of less than 10 mW. The device footprint is approximately 20×30 μm2, and it is 3-4 times smaller than the current smallest solving unit. The maximum Q-factor reaches 9.8×104. The proposed device avoids the traditional approach of cascading two resonators for SODE solving. Moreover, achieving mode alignment within the same resonator reduces the process challenges associated with aligning multiple devices in a cascade. Furthermore, it offers wider applicability for solving SODEs, namely, the ability to solve both constant and complex coefficient SODEs with complete derivative terms.