  Metasurfaces have the potential to miniaturize and improve the performance of
any optical element, with applications spanning telecommunications, computing
and wearable optics. However, the ability to retain functionality over a
continuous, broad range of wavelengths is essential for their widespread
adoption. So far, efforts to achieve this have been limited to either a
reflection configuration or operation at wavelengths other than the visible.
Here, we show that by judicious choice of nanostructures, one can independently
control both the phase and group delay, leading to broadband transmissive
achromatic metalenses and metalenses with tunable dispersion across the visible
spectrum. We demonstrate diffraction-limited broadband focusing and achromatic
imaging using metalenses across wavelengths from 470 nm to 670 nm, with focal
length change of a few percent across this 200 nm bandwidth. This approach
requires only a single layer metasurface whose thickness is on the wavelength
scale, and does not involve spatial multiplexing or cascading.
