Multitwist Möbius Strips and Twisted Ribbons in the Polarization of Paraxial Light Beams

Galvez, Enrique J.; Dutta, Ishir; Beach, Kory; Zeosky, Jon J.; Jones, Joshua; Khajavi, Behzad

doi:10.1038/s41598-017-13199-1

Cited by 50 publications

(43 citation statements)

References 36 publications

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“…The corresponding spatial distribution of the major semiaxis of the polarization ellipse has a discontinuity A → −A highlighted in yellow. This forms the polarization Möbius strip [33][34][35][36][37][38][39]. The transition between the two cases occurs each time that the spatial contour crosses a non-degenerate C-line.…”

Section: B "Poincarana-sphere" Representation and Polarization Möbiumentioning

confidence: 98%

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Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

2019

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Geometric phases are a universal concept that underpins numerous phenomena involving multicomponent wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem.Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincaré sphere and the Majoranasphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization Möbius strips.

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Section: B "Poincarana-sphere" Representation and Polarization Möbiumentioning

confidence: 98%

“…Finally, it follows from Eqs. (4), (37), and (39) that the spin AM density of the cylindrical fields (38) is associated with the geometric-phase increment along the circular contour [45]:…”

Section: Other Propertiesmentioning

confidence: 99%

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

2019

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“…In addition to phase vortices, more OMSs can be obtained by arranging the polarization: the major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three-dimensional optical ellipse fields can be organized into an OMS, as theoretically proposed 98,99 and experimentally observed 49 . Currently, multitwist OMSs can be controlled in both paraxial and nonparaxial vector beams 56,100 . By combining other spatial and optical parameters into OMSs, more complex structures, such as 3D solitons and topological knots, can be proposed for OVs 101 .…”

Section: Properties Of Ovsmentioning

confidence: 99%

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

et al. 2019

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Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin–orbital interactions, Bose–Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

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“…Such polarization singularities organize the topological structure of the ellipse fields in the same way that vortex lines organize the optical phase. When longitudinal polarization is also included, C-lines acquire more complicated three-dimensional properties manifested as optical Möbius bands [18][19][20][21][22] .…”

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confidence: 99%

Reconstructing the topology of optical polarization knots

et al. 2018

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Knots are topological structures describing how a looped thread can be arranged in space. Though most familiar as knotted material filaments, it is also possible to create knots in singular structures within three-dimensional physical fields such as fluid vortices 1 and the nulls of optical fields 2-4. Here we produce, in the transverse polarization profile of optical beams, knotted lines of circular transverse polarization. We generate and observe both simple torus knots and links as well as the topologically more complicated figure-eight knot. The presence of these knotted polarization singularities endows a nontrivial topological structure on the entire three-dimensional propagating wavefield. In particular, the contours of constant polarization azimuth form Seifert surfaces of high genus 5 , which we are able to resolve experimentally in a process we call seifertometry. This analysis reveals a level of topological complexity, present in all experimentally generated polarization fields, that goes beyond the conventional reconstruction of polarization singularity lines.

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Multitwist Möbius Strips and Twisted Ribbons in the Polarization of Paraxial Light Beams

Cited by 50 publications

References 36 publications

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Reconstructing the topology of optical polarization knots

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