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

Abstract: 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.