Singularity engineering: sculpting the dark

Optical singularities are dark regions of a light field that exhibit rich and nonintuitive behaviors such as local wavenumbers that far exceed the light field wavenumber. For example, helical beams have a one dimensional singularity along the axis of the optical vortex where the phase is undetermined. We demonstrate that both phase and polarization singularities can be engineered and that in addition to the common one-dimensional string-like topologies, we can produce a broader family of 0D (point) and 2D (sheet) singularities. As a potential application, we design an array of point singularities to serve as identical blue-detuned cold atom traps with three-dimensional confinement. Singularity engineering imbues microscale wavefront engineering tools with the ability to produce exotic forms of light deterministically and on-demand and has wide applicability to other wave-like systems in physics.