title: Dielectric metasurfaces solve differential and integro-differential equations.
abstract: Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering optical waves both spatially and spectrally. However, inherent ohmic losses concomitant with low coupling efficiencies pose fundamental impediments over their practical applications. Not only can all-dielectric metasurfaces tackle such substantial drawbacks, but also their CMOS-compatible configurations support both Mie resonances that are invariant to the incident angle. Here, we report on a transmittive metasurface comprising arrayed silicon nanodisks embedded in a homogeneous dielectric medium to manipulate phase and amplitude of incident light locally and almost independently. By taking advantage of the interplay between the electric/magnetic resonances and employing general concepts of spatial Fourier transformation, a highly efficient metadevice is proposed to perform mathematical operations including solution of ordinary differential and integro-differential equations with constant coefficients. Our findings further substantiate dielectric metasurfaces as promising candidates for miniaturized, two-dimensional, and planar optical analog computing systems that are much thinner than their conventional lens-based counterparts.
authors.forename: Sajjad
authors.initials: S
authors.lastname: Abdollahramezani
authors.forename: Ata
authors.initials: A
authors.lastname: Chizari
authors.forename: Ali Eshaghian
authors.initials: AE
authors.lastname: Dorche
authors.forename: Mohammad Vahid
authors.initials: MV
authors.lastname: Jamali
authors.forename: Jawad A
authors.initials: JA
authors.lastname: Salehi