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Singular knot bundle in light.

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    As optical vortex knots shrink, nonparaxial effects create complex polarization structures. These "knot bundles" reveal new spin-orbit physics in tightly focused light.

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    Area of Science:

    • Optics and Photonics
    • Quantum Optics
    • Light-Matter Interactions

    Background:

    • Optical vortices exhibit topological properties in light beams.
    • Nonparaxial effects become significant as beam features approach the wavelength scale.
    • Understanding polarization behavior in tightly focused light is crucial for advanced optical applications.

    Purpose of the Study:

    • To investigate the structural changes in optical vortex knots under nonparaxial conditions.
    • To analyze the emergence of complex polarization singularities in reduced-scale optical vortices.
    • To explore the interplay of spin-orbit effects and polarization topology in tightly focused geometries.

    Main Methods:

    • Utilizing polynomial beam approximations to model optical vortex knot structures.
    • Employing numerical diffraction theory for detailed analysis.
    • Investigating the behavior of electric and magnetic fields at the nanoscale.

    Main Results:

    • Demonstrated that decreasing optical vortex knot size induces nonparaxial effects that alter singularity structure.
    • Identified intertwined knotted nodal structures in transverse and longitudinal polarization components, termed "knot bundles of polarization singularities."
    • Revealed unique spin-orbit effects and polarization topology features in tightly focused configurations.

    Conclusions:

    • Nonparaxial effects fundamentally change optical vortex knot structure at the wavelength scale.
    • The "knot bundle of polarization singularities" represents a novel topological structure arising from longitudinal field components.
    • Proposed an experimental method to observe and measure these nanoscale polarization phenomena.