Flat lens criterion by small-angle phase

We show that a classical imaging criterion based on angular dependence of small-angle phase can be applied to any system composed of planar, uniform media to determine if it is a flat lens capable of forming a real paraxial image and to estimate the image location. The real paraxial image location obtained by this method shows agreement with past demonstrations of far-field flat-lens imaging and can even predict the location of super-resolved images in the near-field. The generality of this criterion leads to several new predictions: flat lenses for transverse-electric polarization using dielectric layers, a broadband flat lens working across the ultraviolet-visible spectrum, and a flat lens configuration with an image plane located up to several wavelengths from the exit surface. These predictions are supported by full-wave simulations. Our work shows that small-angle phase can be used as a generic metric to categorize and design flat lenses.