  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.
