Fundamental limits and design principles of doublet metalenses

Metalenses are nanostructured surfaces with great potential for delivering miniaturized and integrated optical systems. A key property of metalenses is that, by using a double layer configuration, or doublet, they can achieve both diffraction-limited resolution and wide field-of-view imaging. The physical operation and limitations of such doublet systems, however, are still not fully understood, and designs are still based on numerical optimization of the phase profiles. Here, we show the fundamental limits of doublet systems and provide a universal design strategy without any need to resort to numerical optimization. We find an analytical relationship between the focal length and the spacer thickness; we identify the physical principles underlying the limitations on performance and obtain a universal dependence of the field of view as a function of resolution (numerical aperture). Our results will allow researchers to appreciate the regimes of resolution and field of view that are accessible for specific applications, to identify the conditions for optimum performance (such as required spacer thickness), and to conveniently design doublets without needing to resort to numerical optimizations.