Fig. 3: Optimization results for single layer metagrating designs.

We maximize the reflectivity (a) of a TiO₂ cylindrical nanopost (a inset) by optimizing the diameter, inducing a blueshift of the resonance (b), where the black dashed and blue solid curves are the initial and optimized designs, respectively, and the red dotted line denotes the design wavelength of 632 nm. In (a), d, t, and p denote the diameter, thickness, and pitch of the grating as shown. In (c), we maximize the transverse electric (TE) reflectivity r_TE while maximizing the transverse magnetic (TM) transmission t_TM of a TiO₂ rectangular line-based unit cell (c inset) at a design wavelength of 632 nm. In (d), the results of this optimization are shown where the red dotted line denotes the design wavelength, the black thin (thick) dashed line represents the initial TE (TM) reflectivity, while the blue thin (thick) solid line stands for the optimized TE (TM) reflectivity. The optimized design achieved an extinction ratio of transmitted TE to TM light of 22 dB. In (a), w, t, and p denote the width, thickness, and pitch of the grating as shown. We also topology optimize (e) a single-layer silicon grating at 1550 nm (e inset shows the permittivity profile, with silicon in white and SiO₂ in black), achieving an absolute efficiency of 77% of light directed into the first diffraction order (75° deflection) and a relative efficiency of 95% (f).