Compact all-optical differential-equation solver based on silicon microring resonator

We propose and numerically demonstrate an ultrafast real-time ordinary differential equation (ODE) computing unit in optical field based on a silicon microring resonator, operating in the critical coupling region as an optical temporal differentiator. As basic building blocks of a signal processing system, a subtractor and a splitter are included in the proposed structure. This scheme is featured with high speed, compact size and integration on a siliconon-insulator (SOI) wafer. The size of this computing unit is only 35 μm 45 μm. In this paper, the performance of the proposed structure is theoretically studied and analyzed by numerical simulations.