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

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 lights 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.

Index-symmetry breaking of polarization vortices in 2D random vector waves

“…First, gr clearly tends to zero when r ≈ 0, indicating that polarization vortices are never to be found in close proximity regardless of their mutual sign, unlike C points. Second, the oscillation of this correlation function exhibits a much clearer contrast compared to the one displayed by C points [27] and phase singularities [25]. The first peak reaches values ≥4, more than twice as high as the values observed in the pair correlation function for C points.…”

“…However, a different physics governs the behavior of polarization singularities in 2D random light. In this case, the vicinity of same-index C points is promoted with respect to opposite-index ones [27], suggesting that despite their non-generic nature, polarization vortices might be abundant in these 2D fields.…”

“…We experimentally investigate polarization vortices in a twodimensional random light field with a home-made polarizationand phase-resolving near-field microscope [28]. This allows us to map the in-plane optical field generated by the random interference of TE waves in a chaotic cavity [25,27,29]. The chaotic cavity [ Fig.…”

“…Figure 4(a) presents the pair correlation function of C points for the cases in which both the singularities that constitute the pair have either positive (g A , orange data) or negative (g A , purple data) topological index, and reside in areas of opposite handedness of circular polarization (symbolized by the superscript A). The restriction to anti-handed C points as origin for polarization vortices is here given by the vanishing correlation function g C same r for co-handed C points as r → 0 [27]. At distances r < λ∕5, g is higher than g by about a factor 2.…”

“…We verify this experimental observation by computing the theoretical expectations for the measured pair correlation functions. For the cases of g A and g A the theoretical curves can be computed with the model described in [27] for a 2D TE random field, with the extra care of treating positive and negative topological indices independently. The pair correlation of polarization vortices requires an extension of the model in [27], since in that framework it corresponds to a higher-order correlation function.…”