Tackling the focal shift effect for metalenses

We present a theoretical analysis aimed at comprehending and mitigating the focal shift phenomenon in planar dielectric metalenses. To conduct this analysis, we introduce metalens designs consisting of silicon and germanium nanoblocks on a calcium fluoride substrate, operating in the mid-IR frequency range. The lensing performance of these metalenses is investigated using the finite-difference time-domain method, and they operate at wavelengths of 3 and 4 µm with a polarization conversion efficiency close to unity. Our findings indicate a strong correlation between the focal shift phenomena on dielectric metalenses and the numerical aperture (NA), revealing that increasing the Fresnel number is not always an effective approach to minimizing the focal shift. In contrast to previous studies, we define a critical NA, independent of the lens size, where the focal shift reaches a minimum, resulting in a symmetric focal intensity distribution and ultimately yielding a better-performing metalens. We demonstrate that for NAs greater than the determined critical value, a positive focal shift is observed on planar metalenses, diverging from the conventional negative shift predicted by existing models. Additionally, we show that by selecting a metalens within a specific NA range and with smaller diameters, high focusing efficiencies can be achieved. The focusing efficiency of the studied metalenses is measured as high as 70%, marking one of the best values reported for the IR range to date. These results serve as a guide for improving the agreement between experimental and designed metalens features, enhancing their practical applications.