Achromatic diffractive lens limits

Over the recent years, there have been many reports of achromatic metalenses and diffractive lenses. However, very few (if any) practical applications of such achromatic flat lenses have been demonstrated, which raises questions about the potential of these lenses to provide solutions for real world cases which involve broadband illumination. A recent paper placed limits on the performance of achromatic metalenses. However, is this limit also valid for a diffractive lens? Not necessarily so. In this paper we derive the limits on the performance of achromatic diffractive lenses. In particular, we show that achromatic diffractive lenses can cover a wide spectral range, limited only by loss of efficiency caused by manufacturing limitations related to feature depth and size. On the other hand, we show that achromatic diffractive lenses can provide near diffraction limited performance only at very low Fresnel numbers, i.e. they cannot provide large focusing power and broadband response simultaneously. We then go on to compare the limits of achromatic metalenses and diffractive lenses, in attempt to understand the potential of different types of flat lenses. Our findings may set the ground for better evaluation of flat lens performance, understanding of their capabilities and limitations, and for exploring novel design concepts and applications.