Metasurfaces enable the shaping of wavefronts in arbitrary ways, by dispersion engineering of the meta-atoms. Here I will review my group research on singularity engineering, including arrays of equally spaced 0D singularities, 2D singular sheets of arbitrary shapes and topoiogically protected singularities in the 4D space encompassing real space and wavelength. In the latter when a perturbation is added to the metasurface the singularity in the focal spot is preserved but shifts in wavelength, signaling topological protection.
Phase singularities are loci of darkness surrounded by light in a scalar field. We engineer an array of closely-spaced identical point singularities structured along the optic axis. The array is experimentally realized with a TiO2 metasurface under 760 nm narrowband illumination. We study possible application in blue-detuned neutral atom trap arrays, for which this field would enforce 3D confinement and a potential depth around 0.22 mK per watt of trapping power. The field is tolerant to around 10 nm changes in wavelength with a 0.11 degree angular bandwidth. Metasurface-enabled point singularity engineering may simplify and miniaturize the architecture required for super-resolution microscopes and dark traps.
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