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Related Experiment Video

Updated: Aug 23, 2025

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature
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Topological flowers and spider webs in 3D vector fields.

Xiaoyan Pang, Bujinlkham Nyamdorj, Xinying Zhao

    Optics Express
    |October 27, 2022
    PubMed
    Summary

    This study investigates topological flowers and spider webs in 3D vector fields, revealing novel topological reactions and characterization parameters for spin density vectors. These findings advance topological photonics and singular optics.

    Area of Science:

    • Optics and Photonics
    • Topological Physics
    • Vector Field Theory

    Background:

    • Topological structures are crucial in singular optics and topological photonics.
    • Existing research has focused on lemon and star structures, with less attention on flowers and spider webs.
    • The rapid growth of topological photonics necessitates the development of new theoretical frameworks.

    Purpose of the Study:

    • To investigate topological flowers and spider webs in 3D vector fields.
    • To analyze the topological reactions of spin density (SD) singularity loops.
    • To propose new parameters for characterizing topological patterns in 3D vector fields.

    Main Methods:

    • Strong focusing of higher-order singular beams.
    • Analysis of spin density (SD) vectors and transverse field polarization states.

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  • Definition of a 'relative topological charge' to study loop reactions.
  • Proposal and verification of 'radial index' and 'azimuthal index' for characterization.

    • Main Results:

    • Flowers and spider webs structures observed in SD vectors and polarization states with 2|m-1| folds/sectors.
    • Topological structures of SD vectors exhibit a 90°/|m-1| rotation.
    • Observation and analysis of topological reactions involving SD singularity loops.
    • The 'radial index' is unique to 3D vector fields and generally proportional to 1/|m-1|.

    Conclusions:

    • The study provides a method to describe topological behaviors of singularity groups in 3D vector fields.
    • New parameters ('radial index', 'azimuthal index') are introduced for measuring topological patterns.
    • This work enriches topological theory and offers potential applications in topological photonics.