Design principle: a broadband achromatic metalens

We propose a design principle for broadband achromatic metalenses built from a single, simple meta-atom geometry in a dispersive material. The optical path length (OPL) of a meta-atom, rather than its phase, is used as the design criterion: a wavelength-independent OPL is equivalent to a constant group delay with vanishing group-delay dispersion, and it reduces the dispersion-engineering problem to a single scalar figure of merit, the OPL difference (ΔOPL) across the operating band, which can be evaluated directly from a phase library. Among circular and square rods, fishnets, and circular and square holes in a 600 nm thick GaN layer on sapphire, square air holes minimize (ΔOPL) over 450-700 nm. The aperture of the metalens is limited so that the required phase does not exceed 2π at the longest wavelength, which removes phase wrapping. Metalenses with target focal lengths of 5, 7, and 10 µm and numerical apertures of 0.39-0.54 focus within 2.3% of the targets, suppress the chromatic focal shift of a conventional diffractive lens (f∝1/λ) by 80%-84%, produce focal spots within 1.12-1.20 times the diffraction limit, and reach absolute focusing efficiencies of 0.46-0.68 within the Airy disk. The design is robust against random critical-dimension variations and sidewall angles up to 6°. The principle can be applied to other transparent dispersive materials and spectral ranges.