Metasurface Empowered Fourier Optics Beyond Paraxial Regime.

Fourier optics, the principle of using Fourier Transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and has been widely applied to optical information processing, imaging, holography etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e. the paraxial approximation, which put a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Here, we experimentally demonstrate a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array, which is capable of performing Fourier transform for a large incident angle range and a broad operating bandwidth. Thus our device significantly expands the operational Fourier space, benefitting from the large numerical aperture (NA), and negligible angular dispersion at large incident angles. Our Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size.