Abstract
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 charge at a vanishing distance is enhanced in a 2D field. This is an unusual finding for any system which exhibits topological singularities as same-charge repulsion is typically observed. All our experimental findings are supported with theory and excellent agreement is found between theory and experiment.
Highlights
Light-based technology has transformed today’s society and will continue to do so, with applications that range from energy harvesting to telecommunications and quantum informatics [1,2,3]
We investigated the spatial correlation of C points in 2D random light
We demonstrated that confining the optical field to propagate in two dimensions induces severe changes in the spatial distribution of its C points
Summary
Light-based technology has transformed today’s society and will continue to do so, with applications that range from energy harvesting to telecommunications and quantum informatics [1,2,3]. The question arises as to how limiting the propagation of light to a truly 2D situation, e.g., by confining it on a flat optical chip, would be to the spatial distribution of its polarization singularities. In such a case, transverse propagation would set a one-to-one relation between the wave propagation direction and the direction of the electric field. We demonstrate that confining light propagation in two dimensions leads to a large increase in the probability of finding, at close proximity, C points with the same topological charge, i.e., their index This is an exotic behavior for topological singularities, which usually exhibit same-charge repulsion. We relate our experimental findings to light’s handedness and excellently describe them with a new theoretical model developed for the two-dimensional case
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