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

Abstract

When the positions of two generic singularities of equally signed topological index coincide, a higher-order singularity with twice the index is created. In general, singularities tend to repel each other when sharing the same topological index, preventing the creation of such higher-order singularities in 3D generic electromagnetic fields. Here, we demonstrate that in 2D random vector waves higher-order polarization singularities-known as polarization vortices-can occur, and we present their spatial correlation. These polarization vortices arise from the overlap of two points of circular polarization (C points) with the same topological index. We observe that polarization vortices of positive index occur more frequently than their negative counterparts, which results in an index-symmetry breaking unprecedented in singular optics. To corroborate our findings, we analyze the spatial correlation of C points in relation to their line classification and link the symmetry breaking to the allowed dipolar and quadrupolar moments of the field at a polarization vortex.

Effective pair-interaction of phase singularities in random waves

“…The plot shows the average residual R[g (j) ] between measured and expected pair correlation function at every iteration j, for both same-and opposite-sign singularities. tion singularities in 2D random light, where singularities with different topological charge exhibit different spatial correlations [11,12]. All of the specific properties can now be mapped into interaction potentials, possibly offering further insights on the role of singularities in wave fields.…”

“…Instead, the singularities' spatial distribution actually exhibits the hallmarks of a liquid-like system [3]. This behaviour of the phase singularities can be most clearly observed in the pair correlation function [3][4][5][6][7][8][9][10][11][12][13], one of the most used tools to describe the spatial arrangement of discrete systems of any kind [14][15][16]. Additionally, these singularities have a topological charge, also hinting at analogies with interacting particles, with mechanisms like same-charge repulsion [17,18] and topological screening [19][20][21][22].…”

Poynting singularities in the transverse flow-field of random vector waves

“…For this transverse field to be zero, the obvious cases are that either H z = 0, or E x = E y = 0, both of which can occur in a generic TE field [13,26]. Another option occurs when H z (E y , −E x ) becomes completely imaginary, and hence the real part vanishes.…”

“…Note that the magnetic type singularities are also phase singularities of H z . Since the electric types require two field components to be zero, as opposed to only one for the magnetic types, they occur only very rarely (< 1% of all singularities) [26]. Therefore we will not treat them further, although their occurrence is interesting on its own.…”

Observing polarization patterns in the collective motion of nanomechanical arrays

“…Surprisingly, the topological nature of spatially inhomogeneous polarization patterns in wave fields was analyzed much more recently [16,17], opening a novel domain of inquiry that continues to draw fresh attention and enables modern applications, e.g. in nano-optics [18][19][20][21].…”