Optimizing achromaticity in metalenses, and development of a layered thin-film metalens

Abstract

Metalenses are ultrathin optical devices designed to replicate behavior of conventional refractive lenses, or lens arrays, utilizing nanoscale resonant structures to redirect incident light. These are often comprised of discrete meta-atoms such as nanoscale dielectric pillars. Achromatic focusing - associated with traditional multi-element refractive counterparts - is frequently attempted with single-layer metalens designs, which has proven difficult to achieve with bounded refractive indices and total lens thickness. A recent study (F.Presutti and F.Monticone, 2020) formalized this, applying optical delay-line limitations to metalenses, resulting in a generalized trade-off in achromaticity for focusing systems. In this work, we (1) theoretically explore achromaticity in metalens design, and (2) propose a thin-film multilayer design as an alternative to the discrete meta-atom approach for large numerical aperture (NA) achromatic metalenses. It is shown that wavefront modulation can also be achieved with spectrally-varying transmission magnitudes, rather than purely matching a phase profile. In fact, even with a bounded refractive index, perfect achromatic operation over a given spectral range can be offset by imperfect operation elsewhere, resulting in a NA limited by the smallest general spectral feature controlled. These considerations lead to a generalized phase-matching optimization routine, and a thin-film metalens is simulated, utilizing layered TiO2/MgF2 with total thicknesses under 1 {\mu}m (20 layers), focusing across 6 simultaneous wavelengths (350-740 nm, {\Delta}{\lambda}~65 nm). A significant proportion (>40% spectral average) of the reflected light is focused for moderate NA (~0.35). With the maturity of the optical coating industry, the conformal thin-film approach reduces manufacturing complexity from its discrete nanoscale meta-atom equivalents.