On-Chip Tunable Second-Order Differential-Equation Solver Based on a Silicon Photonic Mode-Split Microresonator

We propose and experimentally demonstrate an onchip all-optical differential-equation solver capable of solving second-order ordinary differential equations (ODEs) characterizing continuous-time linear time-invariant systems. The photonic device is implemented by a self-coupled microresonator on a silicon-on-insulator platform with mutual coupling between the cavity modes. Owing to the mutual mode coupling within the same resonant cavity, the resonance wavelengths induced by different cavity modes are self-aligned, thus avoiding precise wavelength alignment and unequal thermal wavelength drifts as in the case of cascaded resonators. By changing the mutual mode coupling strength, the proposed device can be used to solve second-order ODEs with tunable coefficients. System demonstration using the fabricated device is carried out for 10-Gb/s optical Gaussian and super-Gaussian input pulses. The experimental results are in good agreement with theoretical predictions of the solutions, which verify the feasibility of the fabricated device as a tunable second-order photonic ODE solver.