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Explicit algebraic characterization of Mueller matrices.

José J Gil, Ignacio San José

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    Summary
    This summary is machine-generated.

    This study provides an algebraic characterization of Mueller matrices using the coherency matrix and its principal minors. These findings are also expressed using characteristic Stokes vectors for analyzing polarized light.

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    Area of Science:

    • * Optics and Photonics
    • * Polarimetry
    • * Mathematical Physics

    Background:

    • * Mueller matrices are fundamental in describing the polarization properties of light-matter interactions.
    • * Algebraic characterizations provide deeper insights into the structure and constraints of these matrices.
    • * Understanding Mueller matrix properties is crucial for applications in various optical fields.

    Purpose of the Study:

    • * To present a general explicit algebraic characterization of Mueller matrices.
    • * To relate this characterization to the non-negativity of leading principal minors of the coherency matrix.
    • * To explore specific cases, including matrices with zero polarizance and symmetric matrices.

    Main Methods:

    • * Derivation of an algebraic characterization based on the coherency matrix C(A) and its arrow form M(A).
    • * Analysis of the non-negativity of leading principal minors of C(A).
    • * Formulation of the results using a set of four characteristic Stokes vectors.

    Main Results:

    • * An explicit algebraic condition for Mueller matrices is established via the coherency matrix's principal minors.
    • * The characterization is equivalently expressed through four specific Stokes vectors.
    • * Analysis of special cases reveals distinct properties for Mueller matrices with zero polarizance and symmetric matrices.

    Conclusions:

    • * The presented algebraic characterization offers a novel perspective on Mueller matrix properties.
    • * The connection to principal minors and characteristic Stokes vectors provides a robust framework for analysis.
    • * The study contributes to a more comprehensive understanding of polarized light interactions.