Singular knot bundle in light

As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal polarization effects become non-negligible and the electric and magnetic fields differ, leading to intertwined knotted nodal structures in the transverse and longitudinal polarization components which we call a knot bundle of polarization singularities. We analyze their structure using polynomial beam approximations, and numerical diffraction theory. The analysis reveals features of spin-orbit effects and polarization topology in tightly-focused geometry, and we propose an experiment to measure this phenomenon.Comment: Main Article 12 pages, 6 figures; Supplementary Material (Appendix) 3 pages, 1 figur

Knotted Polarizations and Spin in 3D Polychromatic Waves

We consider complex 3D polarizations in the interference of several vector wave fields with different commensurable frequencies and polarizations. We show that the resulting polarizations can form knots, and interfering three waves is sufficient to generate a variety of Lissajous, torus, and other knot types. We describe the spin angular momentum, generalized Stokes parameters and degree of polarization for such knotted polarizations, which can be regarded as partially-polarized. Our results are generic for any vector wave fields, including, e.g., optical and acoustic waves. As a directly-observable example, we consider knotted trajectories of water particles in the interference of surface water (gravity) waves with three different frequencies.Comment: 6 pages, 2 figures, to appear in Phys. Rev. Research (Rapid Communication

Il gruppo delle rotazioni in fisica quantistica.

Lo scopo del presente lavoro è quello di analizzare il ben noto concetto di rotazione attraverso un formalismo matematico. Nella prima parte dell'elaborato si è fatto uso di alcune nozioni di teoria dei gruppi nella quale si definisce il gruppo ortogonale speciale in n dimensioni. Vengono studiati nel dettaglio i casi di rotazione in 2 e 3 dimensioni introducendo le parametrizzazioni più utilizzate. Nella seconda parte si introduce l'operatore di rotazione, il quale può essere applicato ad un sistema fisico di tipo quantistico. Vengono infine studiate le proprietà di simmetria di rotazione, definendone le caratteristiche e analizzando il caso particolare del potenziale centrale

Transverse shifts and time delays of spatiotemporal vortex pulses reflected and refracted at a planar interface

International audienceTransverse (Hall-effect) and Goos-Hänchen shifts of light beams reflected/refracted at planar interfaces are important wave phenomena, which can be significantly modified and enhanced by the presence of intrinsic orbital angular momentum (OAM) in the beam. Recently, optical spatiotemporal vortex pulses (STVPs) carrying a purely transverse intrinsic OAM were predicted theoretically and generated experimentally. Here we consider the reflection and refraction of such pulses at a planar isotropic interface. We find theoretically and confirm numerically novel types of OAM-dependent transverse and longitudinal pulse shifts. Remarkably, the longitudinal shifts can be regarded as time delays, which appear, in contrast to the well-known Wigner time delay, without temporal dispersion of the reflection/refraction coefficients. Such time delays allow one to realize OAM-controlled slow (subluminal) and fast (superluminal) pulse propagation without medium dispersion. These results can have important implications in various problems involving scattering of localized vortex states carrying transverse OAM

Polarization singularities and Möbius strips in sound and water-surface waves

International audienceWe show that polarization singularities, generic for any complex vector field but so far mostly studied for electromagnetic fields, appear naturally in inhomogeneous yet monochromatic sound and water-surface (e.g., gravity or capillary) wave fields in fluids or gases. The vector properties of these waves are described by the velocity or displacement fields characterizing the local oscillatory motion of the medium particles. We consider a number of examples revealing C-points of purely circular polarization and polarization M€ obius strips (formed by major axes of polarization ellipses) around the C-points in sound and gravity wave fields. Our results (i) offer a new readily accessible platform for studies of polarization singularities and topological features of complex vector wave fields and (ii) can play an important role in characterizing vector (e.g., dipole) wave-matter interactions in acoustics and fluid mechanics

Particle-like topologies in light

Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions, that realise integer topological numbers in their configuration via homotopic mappings from real space to the hypersphere (sphere in 4D space) or the 2D sphere. They have received tremendous attention as exotic textures in particle physics, cosmology, superfluids, and many other systems. Here we experimentally create and measure a topological 3D skyrmionic hopfion in fully structured light. By simultaneously tailoring the polarisation and phase profile, our beam establishes the skyrmionic mapping by realising every possible optical state in the propagation volume. The resulting light field’s Stokes parameters and phase are synthesised into a Hopf fibration texture. We perform volumetric full-field reconstruction of the Π3 mapping, measuring a quantised topological charge, or Skyrme number, of 0.945. Such topological state control opens avenues for 3D optical data encoding and metrology. The Hopf characterisation of the optical hypersphere endows a fresh perspective to topological optics, offering experimentally-accessible photonic analogues to the gamut of particle-like 3D topological textures, from condensed matter to high-energy physics