Substrate aberration and correction for meta-lens imaging: an analytical approach.

Meta-lenses based on flat optics enabled a fundamental shift in lens production-providing an easier manufacturing process with an increase in lens profile precision and a reduction in size and weight. Here we present an analytical approach to correct spherical aberrations caused by light propagation through the substrate by adding a substrate-corrected phase profile, which differs from the original hyperbolic one. A meta-lens encoding the new phase profile would yield diffraction-limited focusing and an increase of up to 0.3 of its numerical aperture without changing the radius or focal length. In tightly focused laser spot applications such as direct laser lithography and laser printing, a substrate-corrected meta-lens can reduce the spatial footprint of the meta-lens.