Computational inverse design for ultra-compact single-piece metalenses free of chromatic and angular aberration

We present full-Maxwell topology-optimization design of a single-piece multlayer metalens, about 10 wavelengths~$\lambda$ in thickness, that simultaneously focuses over a $60^\circ$ angular range and a 23\% spectral bandwidth without suffering chromatic or angular aberration, a "plan-achromat." At all angles and frequencies it achieves diffraction-limited focusing (Strehl ratio $> 0.8$) and absolute focusing efficiency $> 50$\%. Both 2D and 3D axi-symmetric designs are presented, optimized over $\sim 10^5$ degrees of freedom. We also demonstrate shortening the lens-to-sensor distance while producing the same image as for a longer "virtual" focal length and maintaining plan-achromaticity. These proof-of-concept designs demonstrate the ultra-compact multi-functionality that can be achieved by exploiting the full wave physics of subwavelength designs, and motivate future work on design and fabrication of multi-layer meta-optics.