  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.
