3D Zeros in Electromagnetic Fields

Abstract

We present a study of 3D electromagnetic field zeros, uncovering their remarkable characteristic features and propose a classifying framework. These are a special case of general dark spots in optical fields, which sculpt light's spatial structure into matter-moving, information-rich vortices, escape the diffraction limit for single-molecule imaging, and can trap particles for nanoscale manipulation. Conventional dark spots are two-dimensional in two aspects: localised in a plane and having a non-zero out-ofplane field component. We focus on non-paraxial fields, where three-dimensional dark spots can exist non-stably at fully localised points, making distinct imprints in the flux of energy and momentum, and in the light's polarisation texture. With this work, we hope to enhance current dark spot applications, or inspire new ones impossible with lower-dimensional zeros.

Polarization singularities: Topological and dynamical aspects

“…Specific features of the PSs make them valuable instruments of optical metrology [123][124][125]. Like the familiar scalar singularities (e.g., optical vortices), the PSs create conditions for specific energy flow distributions favorable for the particles' trapping, guiding and manipulation in nanoengineering techniques [13,106,126,127].…”

Optical momentum distributions in monochromatic, isotropic random vector fields

“…Further investigations of the isotropic EM case could characterize the generic singularities of the optical currents (isolated points in 3D space) and the statistical geometry of the flows around them, something that has so far only been explored for non-generic zeros of the full complex electric field [31]. More advanced correlation functions (involving more than two positions, evaluated near extrema, etc…) could reveal finer features of the optical currents as well; random fields generally offer endless possibilities of statistical investigation [21].…”

“…An interesting extension of this investigation could be to explore whether or not this relates to some difference in the density of singularities in the orbital and spin flows [11]. The geometry of these singularities, in the special case where all components of the complex electric field vanish, was recently studied in [31], where it was found that the orbital momentum always arranges in elongated 'pseudo vortex lines' in the vicinity of such zeros. Visual exploration of the random fields (not shown) indicates that such a coiling structure seems to occur frequently near generic zeros of both the orbital and spin momenta.…”