  Diffraction gratings disperse light in a rainbow of colors with the opposite
order than refractive prisms, a phenomenon known as negative dispersion. While
refractive dispersion can be controlled via material refractive index,
diffractive dispersion is fundamentally an interference effect dictated by
geometry. Here we show that this fundamental property can be altered using
dielectric metasurfaces, and we experimentally demonstrate diffractive gratings
and focusing mirrors with positive, zero, and hyper negative dispersion. These
optical elements are implemented using a reflective metasurface composed of
dielectric nano-posts that provide simultaneous control over phase and its
wavelength derivative. In addition, as a first practical application, we
demonstrate a focusing mirror that exhibits a five fold reduction in chromatic
dispersion, and thus an almost three times increase in operation bandwidth
compared to a regular diffractive element. This concept challenges the
generally accepted dispersive properties of diffractive optical devices and
extends their applications and functionalities.
