Multiobjective optimization of achromatic metalenses
Modeling of multiwavelength metasurfaces relies on adjusting the phase of individual nanoresonators at several wavelengths. The traditional procedure neglects the near-field coupling between the nanoresonators, which dramatically reduces the overall diffraction efficiency, bandwidth, numerical aperture, and device diameter. Another alternative design strategy is to combine a numerical optimization technique with fullwave simulations to mitigate this problem and optimize the entire metasurface at once. In this work, we develop a global multiobjective optimization technique that utilizes a statistical learning method to optimize RGB spherical metalenses at visible wavelengths. The optimization procedure, coupled to a high-order fullwave solver, accounts for the near-field coupling between the resonators. High-numerical-aperture RGB lenses (NA = 0.47 and 0.56) of 8 and 10 μm diameters are optimized with numerical average focusing efficiencies of 55% and 45%, respectively, with an average focusing error of less than 6% for the RGB colors. The fabricated and experimentally characterized devices present 44.16% and 31.5% respective efficiencies. The reported performances represent the highest focusing efficiencies for high NA > 0.5 RGB metalenses obtained so far. The integration of multiwavelength metasurfaces in portable and wearable electronic devices requires high performances to offer a variety of applications ranging from classical imaging to virtual and augmented reality.
Results for one of the best design along the Pareto front, where three objectives are maximized simultaneously for a lens with diameter 10.22 μm. (a): focusing efficiency calculated as the ratio of the power at the focal plane to the the power passing through an aperture of diameter 10.22 μm. (b): cut along z at the center of the lens for the RGB colors. The vertical line refers to the target focusing position along z = 7.5 μm. The fabricated lens is depicted in (c), besides, the corresponding intensity profiles at the x − z plane are given in (g-i), where the intensity is measured at λ = 490 nm, 550 nm and 660 nm for B, G and R colors, respectively. The numerical focusing intensity for each color is drawn in (d-f).
M.M.R. Elsawy, A. Gourdin, M. Binois, R. Duvigneau, D. Felbacq, S. Khadir, P. Genevet and S. Lanteri
Multiobjective statistical learning optimization of RGB metalens