Paraxial skyrmionic beams

The construction of optical skyrmionic beams was achieved as a superposition of a vortex eigenmode and a non-vortex eigenmode with orthogonal polarizations.

“The construction of optical skyrmionic beams was achieved as a superposition of a vortex eigenmode and a non-vortex eigenmode with orthogonal polarizations 41,43 .”

When 2D optical skyrmionic beams propagate in free space, the topological structure of the vector field can evolve from a Bloch type to a Néel type while the topological number remains unchanged.

“When 2D optical skyrmionic beams propagate in free space, they possess a specific type of topological stability, during which the topological structure of the vector field can evolve from a Bloch type to a Néel type while maintaining an unchanged topological number 41,42 .”

QST determines the quantum-mechanical state of a system by measuring various non-commuting observables on an ensemble of identically-prepared system copies, enabling extraction of the density matrix in a predetermined fashion.

“QST determines the quantummechanical state of a system by measuring various non-commuting observables on an ensemble of identically-prepared system copies, enabling the extraction of the density matrix in a predetermined fashion.”

After substitution of the appropriate Laguerre-Gaussian functions, the Skyrme number simplifies to N = ∆l (1/(1+|g(0)|^2) - 1/(1+|g(∞)|^2)).

“which after substitution of the appropriate LG functions can be shown to simplify down to [28] N = ∆ℓ 1 1 + |g(0)| 2 - 1 1 + |g(∞)| 2 ,(45)”

Plasmonic spin fields have been used to tailor merons with fractional topological charges, and a triplet-meron structure was designed and generated with nanometric and femtosecond space-time resolution.

“Plasmonic spin field has recently been also used to tailor more complex skyrmionic structures, such as the merons with fractional topological charges [51,52], whereby a novel quasiparticle triplet-meron structure were designed and generated (Fig. 4c), with nanometric and femtosecond space-time resolution [51].”

The spatial size of a spin-skyrmion feature can be realized on a deep-subwavelength scale because spin is not subject to diffraction.

“(i) ultrasmall-the spatial size of a spin-skyrmion features can be realized on a deep-subwavelength scale as the spin is not subject to diffraction [19,40,51]”

The skyrmion texture can be resolved on femtosecond scales and at optical single-cycle field level.

“(ii) ultrafast-the skyrmion texture can be resolved on femtosecond scales and at optical single-cycle field level [51,75]”