Bandwidth bounds for wide-field-of-view dispersion-engineered achromatic metalenses

Optical systems with wide field-of-views (FOV) are crucial for many applications such as high performance imaging, optical projection, augmented/virtual reality, and miniaturized medical imaging tools. Typically, aberration-free imaging with a wide FOV is achieved by stacking multiple refractive lenses (as in a "fisheye" lens), adding to the size and weight of the optical system. Single metalenses designed to have a wide FOV have the potential to replace these bulky imaging systems and, moreover, they may be dispersion engineered for spectrally broadband operation. In this paper, we derive a fundamental bound on the spectral bandwidth of dispersion-engineered wide-FOV achromatic metalenses. We show that for metalenses with a relatively large numerical aperture (NA), there is a tradeoff between the maximum achievable bandwidth and the FOV; interestingly, however, the bandwidth reduction saturates beyond a certain FOV that depends on the NA of the metalens. These findings may provide important information and insights for the design of future wide-FOV achromatic flat lenses.