A general flat lens criterion

We introduce a general criterion to predict conditions under which a flat planar medium is capable of imaging a point source. Such a planar medium, known as a flat lens, is attractive due to its potential for imaging over unbounded aperture dimensions. The criterion first assumes a point source on one side of the medium and then evaluates the position of the image based on the phase of the paraxial plane waves exiting the medium. The benefit of this criterion is that it makes no a priori assumption of the medium composition and is thus highly general. We apply this criterion to study a recent class of flat-lens structures made of nano-layers of metal and dielectric. The criterion is validated by comparison against past results. We use the criterion to design new flat lenses, such as a lens for transverse-electric polarization and a broad-band flat lens operating over the UV-visible spectral range.