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Resonant metasurfaces are of paramount importance in addressing the growingdemand for reduced thickness and complexity, while ensuring high opticalefficiency. This becomes particularly crucial in overcoming fabricationchallenges associated with high aspect ratio structures, thereby enablingseamless integration of metasurfaces with electronic components at an advancedlevel. However, traditional design approaches relying on lookup tables andlocal field approximations often fail to achieve optimal performance,especially for nonlocal resonant metasurfaces. In this study, we investigatethe use of statistical learning optimization techniques for nonlocal resonantmetasurfaces, with a specific emphasis on the role of near-field coupling inwavefront shaping beyond single unit cell simulations. Our study achievessignificant advancements in the design of resonant metasurfaces. Fortransmission-based metasurfaces, a beam steering design outperforms theclassical design by achieving an impressive efficiency of 80\% compared to theprevious 23%. Additionally, our optimized extended depth-of-focus (EDOF)metalens yields a remarkable five-fold increase in focal depth, a four-foldenhancement in focusing power compared to conventional designs and an opticalresolution superior to 600 cycle/mm across the focus region. Moreover, ourstudy demonstrates remarkable performance with a wavelength-selected beamsteering metagrating in reflection, achieving exceptional efficiency surpassing85\%. This far outperforms classical gradient phase distribution approaches,emphasizing the immense potential for groundbreaking applications in the fieldof resonant metasurfaces.

Advancing Wavefront Shaping with Resonant Nonlocal Metasurfaces: Beyond the Limitations of Lookup Tables