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.

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Vortices, phase singularities, and topological defects of any kind often reflect information that is crucial for understanding physical systems in which such entities arise. With near-field experiments supported by numerical calculations, we determine the fluctuations of the topological charge for phase singularities in isotropic random waves as a function of the size 푅 of the observation window. We demonstrate that for two-dimensional fields such fluctuations increase with a superlinear scaling law, consistent with a 푅 log 푅 behavior. Additionally, we show that such scaling remains valid in the presence of anisotropy.@en

In this thesis, we explore the physics of optical singularities. We investigate them in light waves propagating randomly in a planar nanophotonic chip. With a custom-built nearfield microscope, we map the electromagnetic field resulting from the interference of these light waves. Our technique gives access to the full vectorial and complex nature of such an electromagnetic field, with subwavelength resolution. The resulting information allows us to precisely pinpoint and characterize the multitude of singularities that arise in the random light field. We detect phase singularities in the Cartesian components of light’s vector field, i.e., points where the phase of the field components is undetermined and it circulates in a vortical flow around them (Part II).Moreover, we identify polarization singularities, e.g., C points: locations where the vector of light’s electric field describes a perfect circle in time (Part III)... @en

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.@en

Solid-state nanopores are single-molecule sensors that hold great potential for rapid protein and nucleic-acid analysis. Despite their many opportunities, the conventional ionic current detection scheme that is at the heart of the sensor suffers inherent limitations. This scheme intrinsically couples signal strength to the driving voltage, requires the use of high-concentration electrolytes, suffers from capacitive noise, and impairs high-density sensor integration. Here, we propose a fundamentally different detection scheme based on the enhanced light transmission through a plasmonic nanopore. We demonstrate that translocations of single DNA molecules can be optically detected, without the need of any labeling, in the transmitted light intensity through an inverted-bowtie plasmonic nanopore. Characterization and the cross-correlation of the optical signals with their electrical counterparts verify the plasmonic basis of the optical signal. We demonstrate DNA translocation event detection in a regime of driving voltages and buffer conditions where traditional ionic current sensing fails. This label-free optical detection scheme offers opportunities to probe native DNA-protein interactions at physiological conditions.

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Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be found at the same location, but only when they exhibit opposite topological charge, which results in their mutual annihilation. New pairs can be created as well. With near-field experiments supported by theory and numerical simulations, we study the persistence and pairing statistics of phase singularities in random optical fields as a function of the excitation wavelength. We demonstrate how such entities can encrypt fundamental properties of the random fields in which they arise.@en

Phase singularities can be created and annihilated, but always in pairs. With optical near-field measurements, we track singularities in random waves as a function of wavelength, and discover correlations between creation and annihilation events.@en

Phase singularities arise in scalar random waves, with spatial distribution reminiscent of particles in liquids. Supporting near-field experiment with analytical theory we show how such spatial distribution changes when considering vector waves.@en