Fig. 4: Optimization results for multilayer metagrating designs.

We maximize the reflectivity at an input angle θ of 2.5°, r_2.5°, and the transmissivity at 7.5°, t_7.5°, (a) of a bilayer TiO₂ cylinder (a inset) by simultaneously adjusting the bottom and top layer thicknesses and diameters. In the (a) inset, D₁ (D₂) and t₁ (t₂) denote the top (bottom) cylinder diameter and thickness, respectively, whereas p is the pitch of the grating. In (b), the optimized reflectivity (blue solid line) shows the resulting high reflectivity at an input angle θ of 2.5° (green dotted line), whereas it exhibits a prominent dip at 7.5° (red dot dash line) corresponding to the intended high transmissivity at that angle, whereas the black dashed line (initial design) performs poorly at both angles. In (c), we simultaneously optimize the diffraction of red, green, and blue wavelengths to 60° by maximizing the minimum transmitted diffraction efficiency of the three wavelengths from a multilayer TiO₂ grating (c inset with white as TiO₂ and black as 1.5 index material). To achieve diffraction at the same angle, we fix the pitch at 2.425 μm and optimize the direction of red, green, and blue light into the 3rd, 4th, and 5th diffraction orders, respectively, reaching relative efficiencies exceeding 67%. In (d), the relative efficiencies for red (dots), green (squares), and blue (diamonds) are plotted as a function of diffraction order.