Redefining topological robustness in optical polarization fields through a generalized skyrmion number

Area of Science:

• Theoretical Physics
• Topology
• Optics

Background:

• Skyrmions are topologically non-trivial fields crucial across various scales.
• Current skyrmion number definitions require specific boundary conditions, limiting broader applications.

Purpose of the Study:

• To generalize the concept of skyrmions and their topological numbers.
• To overcome boundary condition limitations in defining skyrmion numbers.
• To explore applications in optical polarization fields for data storage.

Main Methods:

• Utilized de Rham cohomology of compactly supported forms to generalize skyrmions.
• Defined a new ${\coprod }_{i=1}^{\infty }{Z}^i$-valued topological number.
• Investigated optical polarization fields for theoretical and experimental validation.

Main Results:

• Introduced a generalized skyrmion number assigning a tuple of integers $\left(a_1,\dots ,a_k\right)\in Z^k$ without boundary restrictions.
• Demonstrated significantly increased data storage capacity in optical polarization fields.
• Showcased strong robustness of the generalized skyrmion number.

Conclusions:

• The novel topological number expands the definition and applicability of skyrmions.
• Optical skyrmions, in this generalized context, are robust, topologically protected states.
• This formalism addresses key challenges in optical skyrmion applications for communications and computing.