[Paper Review] Optical polarization skyrmionic fields in free space

Rodrigo Gutiérrez–Cuevas, Emilio Pisanty|arXiv (Cornell University)|Jan 22, 2021

Orbital Angular Momentum in OpticsPhysics and Astronomy82 references81 citations

TL;DR

This paper demonstrates the first realization of robust, topologically protected skyrmionic structures in the polarization fields of freely propagating optical beams in free space, using nonparaxial vector beams and standing-wave configurations. By leveraging spin-orbit coupling in tightly focused beams and complex focus formalism, the authors construct both C-skyrmions (in circular polarization) and L-skyrmions (in linear polarization), achieving near-uniform polarization and strong topological robustness without nonlinearities or evanescent fields.

ABSTRACT

We construct optical beams in free space with robust skyrmionic structures in their polarization fields, both in the electric spin vector for near-circular fields and in the polarization direction for near-linear fields, and for both Bloch (spiral) and N\'eel (hedgehog) textures. These structures are made possible by the spin-orbit coupling of tightly-focused nonparaxial optics as applied to higher-order Full-Poincar\'e beams, as well as by standing-wave configurations comprising forwards- and backwards-propagating waves. Our constructions show near-uniform circular and linear polarizations, providing a high degree of topological protection in the absence of nonlinear interactions.

Motivation & Objective

• To demonstrate the existence of skyrmionic structures in the polarization of freely propagating optical beams in free space.
• To overcome the limitation of previous skyrmions being confined to evanescent or plasmonic fields by constructing them in propagating, nonparaxial beams.
• To achieve high topological robustness through near-uniform circular and linear polarization across the beam profile.
• To extend the concept of skyrmionic fields beyond nonlinear or surface-confined systems to fully propagating, free-space optical beams.
• To provide analytical and experimentally realizable designs using the Complex Focus formalism and Richards-Wolf theory.

Proposed method

• Uses the Complex Focus (CF) formalism to analytically describe tightly focused, nonparaxial vector beams with full control over polarization and phase.
• Constructs beams with cylindrical symmetry by setting the plane-wave spectrum (PWS) to depend on azimuthal angle only via a global phase factor e^{imφ}.
• Separates the PWS into polar (Ap) and azimuthal (Aa) components to independently control radial, longitudinal, and azimuthal field components.
• Employs standing-wave configurations by superposing forward- and backward-propagating beams to stabilize Néel-type skyrmions.
• Applies the Richards-Wolf diffraction theory to validate that results are experimentally realizable in standard optical setups.
• Uses explicit field decompositions involving Bessel functions and cylindrical harmonics to derive the full electric field expressions for both C-skyrmions and L-skyrmions.

Experimental results

Research questions

• RQ1 Can skyrmionic polarization textures be realized in propagating optical beams in free space, without relying on evanescent or nonlinear fields?
• RQ2 Can both Bloch and Néel skyrmion textures be constructed in the polarization of light using nonparaxial optics?
• RQ3 Is it possible to achieve near-uniform circular or linear polarization across a skyrmionic structure, enhancing its topological robustness?
• RQ4 Can L-skyrmions (in linear polarization) be formed in free space without evanescent fields or plasmonic confinement?
• RQ5 Can such skyrmionic fields be experimentally realized using standard optical components and diffraction theory?

Key findings

• The authors construct a robust Bloch skyrmion in the electric spin vector of a tightly focused, near-circularly polarized beam, with polarization uniformly near-circular across the focus.
• A Néel-type C-skyrmion is realized via a standing-wave configuration, demonstrating that such textures can exist in free space without propagation constraints.
• L-skyrmions with perfectly linear polarization are achieved in standing-wave configurations, avoiding evanescent fields and enabling topological protection in propagating beams.
• Forward-propagating beams with elliptical polarization also support skyrmionic structures in the major-axis distribution, extending the concept to conventional beam geometries.
• The results are analytically derived using the Complex Focus formalism and are shown to be compatible with Richards-Wolf diffraction theory, confirming experimental feasibility.
• The skyrmionic fields exhibit high topological robustness due to near-uniform polarization, despite being non-solitonic, making them highly stable under perturbations.