Phase singularities are loci of darkness surrounded by monochromatic light in
a scalar field, with applications in optical trapping, super-resolution
imaging, and structured light-matter interactions. Although 1D singular
structures, such as optical vortices, are the most common due to their robust
topological properties, uncommon 0D (point) and 2D (sheet) singular structures
can be generated by wavefront-shaping devices such as metasurfaces. Here, using
the design flexibility of metasurfaces, we deterministically position ten
identical point singularities in a cylindrically symmetric field generated by a
single illumination source. The phasefront is inverse-designed using phase
gradient maximization with an automatically-differentiable propagator. This
process produces tight longitudinal intensity confinement. The singularity
array is experimentally realized with a 1 mm diameter TiO2 metasurface. One
possible application is blue-detuned neutral atom trap arrays, for which this
light field would enforce 3D confinement and a potential depth around 0.22 mK
per watt of incident trapping laser power. Metasurface-enabled point
singularity engineering may significantly simplify and miniaturize the optical
architecture required to produce super-resolution microscopes and dark traps