Generic photonic integrated linear operator processor

Photonic integration platforms have been explored extensively for optical computing with the aim of breaking the speed and power efficiency limitations of traditional digital electronic computers. Current technologies typically focus on implementing a single computation iteration optically while leaving the intermediate processing in the electronic domain, which are still limited by the electronic bottlenecks. Few explorations have been made of all-optical recursive architectures for computations on integrated photonic platforms. Here we propose a generic photonic integrated linear operator processor based on an all-optical recursive system that supports linear operations ranging from matrix computations to solving equations. We demonstrate the first all-optical on-chip matrix inversion system and use this to solve integral and differential equations. The absence of electronic processing during multiple iterations indicates the potential for an orders-of-magnitudes speed enhancement of this all-optical computing approach compared to electronic computers. We realize matrix inversions, Fredholm integral equations of the second kind, 2^{nd} order ordinary differential equations, and Poisson equations using the generic photonic integrated linear operator processor.