Nonlocal Scatterer for Compact Wave-Based Analog Computing.

Analog computing based on wave interactions with metamaterials has been raising significant interest as a low-energy, ultrafast platform to process large amounts of data. Engineered materials can be tailored to impart mathematical operations of choice on the spatial distribution of the impinging signals, but they also require extended footprints and precise large-area fabrication, which may hinder their practical applicability. Here we show that the nonlocal response of a compact scatterer can be engineered to impart operations of choice on arbitrary impinging waves, and even to solve integro-differential equations, whose solution is observed in the scattered fields. The lack of strongly resonant phenomena makes the response robust, and the compact nature opens to scalability and cascading of these processes, paving the way to efficient, compact analog computers based on engineered microstructures.