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Related Experiment Video

Updated: Jan 25, 2026

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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Quaternion algebra for Stokes-Mueller formalism.

Ertan Kuntman, Mehmet Ali Kuntman, Adolf Canillas

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |May 3, 2019
    PubMed
    Summary

    This study reformulates the Stokes-Mueller formalism using quaternion algebra, offering a new perspective on Mueller-Jones states and polarization effects in optical systems.

    Area of Science:

    • * Optics and Photonics
    • * Mathematical Physics

    Background:

    • * The Stokes-Mueller formalism is a standard method for describing optical polarization phenomena.
    • * Mueller-Jones states provide a framework for analyzing nondepolarizing optical systems.

    Purpose of the Study:

    • * To reformulate the Stokes-Mueller formalism using quaternion algebra.
    • * To explore the properties and applications of quaternion states in polarization optics.
    • * To demonstrate the applicability of quaternion states to depolarization phenomena.

    Main Methods:

    • * Reformulation of the Stokes-Mueller formalism in terms of quaternion algebra.
    • * Analysis of vector and matrix states associated with Mueller matrices.
    • * Investigation of quaternion states as rotators of Stokes quaternions.

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    Main Results:

    • * Quaternion algebra provides a suitable alternative representation for Mueller-Jones states.
    • * Vector and matrix states are isomorphic representations of a single quaternion state.
    • * The general quaternion state acts as a rotator for Stokes quaternions.
    • * Coherent linear combinations and depolarization phenomena can be described using quaternion states.

    Conclusions:

    • * Quaternion algebra offers a unified and elegant framework for polarization optics.
    • * This reformulation simplifies the analysis of polarization effects in optical systems.
    • * The quaternion approach provides new insights into depolarization phenomena.