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