Fig. 6: Inversely designed optical metasurfaces with the adjoint method.

a Freeform shape of the meta-atom under periodic condition for a high-performance waveguide41. b Inverse design–based, an achromatic metalens with extremely high numerical aperture (0.99)35. b.i Schematic of the metalens. b.ii Performance of the metalens in the simulation. b.iii Shape of the metalens, consisting of a non-fabricable two dimensional structure. b.iv Point spread function of the metalens. c Schematic of cylindrical symmetric metalens117. d Design process of the metasurface with the meta-atom consisting of a specific subspace structure118. e Optimization schematic of a large-area metasurface9. e.i Forward simulator based on Chebyshev interpolation to conduct fast forward simulation. e.ii Backward simulation for calculating the gradients of the entire meta-atoms simultaneously with the adjoint method.