Imaging properties of large field-of-view quadratic metalenses and their applications to fingerprint detection

Dielectric metasurfaces, extremely thin nanostructured dielectric surfaces, hold promise to replace conventional refractive optics, such as lenses, due to their high performance and compactness. However, designing large field-of-view (FOV) metalenses, which are of particular importance when imaging relatively big objects at short distances, remains one of the most critical challenges. Recently, metalenses implementing a quadratic phase profile have been put forward to solve this problem with a single element, but despite their theoretical ability to provide $180^\circ\,$FOV, imaging over very large FOV has not been demonstrated yet. In this work, we provide an in-depth analysis of the imaging properties of quadratic metalenses and, in particular, show that due to their intrinsic barrel distortion or fish-eye effect, there is a fundamental trade-off between the FOV achievable in a given imaging configuration and the optical resolution of the metalens and/or the detector resolution. To illustrate how to harness the full potential of quadratic metalenses, we apply these considerations to the fingerprint detection problem, and demonstrate experimentally the full imaging of a $5\,$mm fingerprint with features of the order of $100\,\mu$m, with a metalens ten times smaller in size and located at a distance of only $2.5\,$mm away from the object. This constitutes the most compact system reported so far for the fingerprint detection.