Inverse-designed metastructures that solve equations.

Metastructures hold the potential to bring a new twist to the field of spatial-domain optical analog computing: migrating from free-space and bulky systems into conceptually wavelength-sized elements. We introduce a metamaterial platform capable of solving integral equations using monochromatic electromagnetic fields. For an arbitrary wave as the input function to an equation associated with a prescribed integral operator, the solution of such an equation is generated as a complex-valued output electromagnetic field. Our approach is experimentally demonstrated at microwave frequencies through solving a generic integral equation and using a set of waveguides as the input and output to the designed metastructures. By exploiting subwavelength-scale light-matter interactions in a metamaterial platform, our wave-based, material-based analog computer may provide a route to achieve chip-scale, fast, and integrable computing elements.