Spatial Bunching of Same-Index Polarization Singularities in Two-Dimensional Random Vector Waves

Topological singularities are ubiquitous in many areas of physics. Polarization singularities are locations at which an aspect of the polarization ellipse of light becomes undetermined or degenerate. At C points, the orientation of the ellipse becomes degenerate and light’s electric field vector describes a perfect circle in time. In 2D slices of 3D random fields, the distribution in space of the C points is reminiscent of that of interacting particles. With near-field experiments, we show that when light becomes truly 2D, this has severe consequences for the distribution of C points in space. The most notable change is that the probability of finding two C points with the same topological index at a vanishing distance is enhanced in a 2D field. This case is an unusual finding for any system that exhibits topological singularities, as same-index repulsion is typically observed. All of our experimental findings are supported with theory, and excellent agreement is found between theory and experiment.