Focusing on Bandwidth: Achromatic Metalens Limits

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.