Fig. 3: Comparison of T-matrix method simulations with locally periodic assumption (LPA) simulations.

a Efficiency versus focal length for 25 μm × 25 μm metasurfaces designed from a library of high aspect-ratio scatterers with a large period (silicon cylinders with height 940 nm, radii range of 50–250 nm, lattice period of 1070 nm, and air background; source wavelength of 1550 nm – transmission and phase response shown in Supplementary Fig. 4a, based on scatterer library from Arbabi et al.⁶¹) — efficiencies are computed using the T-matrix approach (blue dots), the commonly-used LPA transmission mask phase sampling approach (black curve), and the LPA field-stitching method (green curve). The metalens efficiency is defined as the ratio of the power within a circle of radius 3 × FWHM in the focal plane to the power incident on the metasurface. The T-matrix and LPA-stitching methods agree fairly well here because the scatterers are high aspect-ratio and the lattice constant is large, hence the interactions between neighboring scatterers is negligible. b Efficiency versus focal length for 15 μm × 15 μm metasurfaces designed from a library of low aspect-ratio scatterers with a small period (silicon cylinders with height 220 nm, radii range of 175–280 nm, lattice period of 666 nm, and background refractive index 1.66; source wavelength of 1340 nm – using scatterer library from Gigli et al.⁶², scatterer transmission and phase response shown in Supplementary Fig. 4b) — efficiencies are computed using the T-matrix approach (blue dots), the commonly-used LPA transmission mask phase sampling approach (black curve), and the LPA field-stitching method (green curve). The metalens efficiency is defined as the ratio of the power within a circle of radius 3 × FWHM in the focal plane to the power incident on the metasurface. The T-matrix and LPA-stitching methods do not agree here because the scatterers are low aspect-ratio and the lattice constant is small, hence the interaction between neighboring scatterers is significant.