Inverse-designed gyrotropic scatterers for non-reciprocal analog computing.

While conventional von Neumann based machines are increasingly challenged by modern day requirements, electromagnetic analog computing devices promise to provide a platform that is highly parallel, efficient and fast. Along this paradigm, it has been shown that arrays of subwavelength electromagnetic scatterers can be used as solvers of partial differential equations. Inverse design offers a powerful tool to synthesize such analog computing machines, utilizing engineered non-local responses to produce the solution of a desired mathematical operation encoded in the scattered fields. So far, this approach has been largely restricted to linear, reciprocal scatterers, limiting its generality and applicability. Here we demonstrate how arrays of gyrotropic scatterers can be used to solve a more general class of differential equations. Through inverse design, with a combination of evolutionary and gradient based algorithms, the position of the scatterers is optimized to achieve the desired kernel response. Introducing gyrotropic media, we also demonstrate improved accuracy by >2 orders of magnitude compared to similarly sized reciprocal systems designed with the same method.