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

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