Fig. 3: An engineered heart-shaped optical phase-singularity sheet (λ0 = 532 nm).
a Isosurface of low field intensity for the simulated singularity sheet. The phase gradient was maximized in the directions indicated by the arrows on the gray z = 10 mm plane, at the locations of the yellow dots. b Inverse-designed phase profile, located at z = 0 mm, which realizes the heart-shaped optical singularity. c The 1D cut profile of intensity, phase, and phase gradient magnitude |∇⊥ϕ| = [(∂xϕ)2 + (∂yϕ)2]1/2 for the dotted blue line in d, overlaid with the corresponding quantities for a Laguerre–Gaussian vortex beam. d Simulated relative intensity and g phase profile of the singularity sheet, at z = 10 mm. e Relative intensity profile obtained experimentally with a fabricated metasurface and h phase profile (obtained from iterative phase retrieval), at z = 10 mm. As a comparison, the results of Gerchberg–Saxton (GS) iterative optimization to get the same heart pattern on the z = 10 mm plane are plotted in f for the intensity and in i for the phase at the target plane, which demonstrates lower pattern fidelity and contrast as compared to the phase gradient maximization result.
