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Geometric phase of rotations and 3D coordinate transformations.

Luis Garza-Soto, Nathan Hagen

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |March 17, 2026
    PubMed
    Summary

    This study derives the spin-redirection phase using wave superposition, a novel approach. This method offers a new perspective on geometric phase phenomena in optics and physics.

    Area of Science:

    • Optics and Photonics
    • Geometric Phase Phenomena

    Background:

    • Previous research focused on the Pancharatnam-Berry phase using linearly polarized light.
    • The spin-redirection phase (Rytov-Vladimirsky-Berry phase) lacked a derivation from wave superposition.

    Purpose of the Study:

    • To derive the spin-redirection phase using the wave superposition model.
    • To demonstrate the applicability of wave superposition to different geometric phases.

    Main Methods:

    • Utilizing a wave superposition model.
    • Representing oscillations with rotating vectors.
    • Applying the model to geometric phase examples.

    Main Results:

    • The first derivation of the spin-redirection phase via wave superposition.

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  • Successful illustration using a three-fold mirror system.
  • Successful illustration using a helically coiled fiber.

    • Conclusions:

    • Wave superposition provides a unified framework for understanding geometric phases.
    • This approach offers new insights into the Rytov-Vladimirsky-Berry phase.
    • The model is applicable to various optical systems exhibiting geometric phase.