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    Area of Science:

    • Optics and Photonics
    • Electromagnetism
    • Mathematical Physics

    Background:

    • Understanding the polarization of light is crucial in optics.
    • Three-dimensional (3D) light fields exhibit complex polarimetric structures.
    • Previous studies often focused on paraxial or lower-dimensional polarization properties.

    Purpose of the Study:

    • To investigate the intrinsic polarimetric structure of 3D light fields.
    • To determine the influence of optical system geometry on polarization states.
    • To analyze the characteristic decomposition of polarization matrices in 3D.

    Main Methods:

    • Analysis of 3D light fields generated from random 2D paraxial waves.
    • Mathematical investigation of polarization matrix decomposition.
    • Application of theoretical results to tightly focused optical fields.

    Main Results:

    • Identified geometric factors determining central 3D polarimetric properties.
    • Demonstrated that polarization state (regular/nonregular) depends solely on geometry.
    • Characterized the structure of the polarization matrix decomposition.

    Conclusions:

    • The geometry of an optical system fundamentally governs the 3D polarimetric structure of light fields.
    • These geometric dependencies are independent of the specific wave properties beyond initial conditions.
    • The findings provide a new perspective on polarization control in focused optical systems.