Massively parallel and programmable photonic differential equation solver

Calculus equations are fundamental mathematical tools, whose numerical solution is crucial. Existing solvers with optical analog computing struggle to simultaneously integrate programmability and parallel processing, thus constraining computational speed and density. Herein, we propose a reconfigurable all-optical platform capable of solving variable-coefficient first-order ordinary differential equations in parallel. We utilize the electrically tunable liquid crystals (LCs) as computing kernels to address these equations. The solver's applicability to canonical scientific problems, such as heat conduction and resistor-capacitor circuit dynamics, is further showcased with simultaneous solving of 158 equations with only one single forward propagation of light. Experimental results confirm the efficacy of the platform in solving equations in an ultra-fast, reconfigurable, broadband, and parallel manner.