Fig. 2. A nonlocal metamaterial spaceplate.

a A multilayer stack consisting of alternating layers of silicon and silica of various thicknesses is engineered to reproduce the Fourier transfer function H for propagation through vacuum for incident angles smaller than θ = 15° at an optical wavelength of λ = 1550 nm. Plotted is the calculated transmission phase φ_SP of the metamaterial spaceplate (black circles) and a fitted vacuum transfer function phase φ_BG (blue curve). Here, we have subtracted a global phase of φ_G = −0.05 rad. The fitted compression factor is R = 4.9. The inset shows the transmission amplitude |H|. c–e Full-wave simulations of the square of the magnitude of the electric field, |E|², of a focusing Gaussian beam (waist of 3λ, divergence of 6^◦) propagating in c, vacuum (gray), d after propagating an s-polarized beam through the metamaterial (red, to scale), and e after propagating a p-polarized beam through the metamaterial (blue, to scale). b, f The physical layouts of the simulations, to scale. i.e., b is vacuum and f is the spaceplate structure surrounded by vacuum. g A cross section of |E|² along the beam axis. Transmission through the spaceplate advances the focus position along z by Δ = −43.2 µm for both p-polarized (dashed blue) and s-polarized (solid red) light.