  Metalenses have shown great promise in their ability to function as
ultracompact optical systems for focusing and imaging. Remarkably, several
designs have been recently demonstrated that operate over a large range of
frequencies with minimized chromatic aberrations, potentially paving the way
for ultrathin achromatic optics. Here, we derive fundamental bandwidth limits
that apply to broadband optical metalenses, regardless of their implementation.
Specifically, we discuss how the product between achievable time delay and
bandwidth is limited in any time-invariant system, and we apply
well-established bounds on this product to a general focusing system. We then
show that all metalenses designed thus far obey the appropriate bandwidth
limit. The derived physical bounds provide a useful metric to compare and
assess the performance of different devices, and offer fundamental insight into
how to design better broadband metalenses.
