Polarization ellipse and Stokes parameters in geometric algebra

Adler G. Santos, Quirino M. Sugon, Daniel J. McNamara

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

    Original languageEnglish
    Pages (from-to)89-98
    Number of pages10
    JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
    Volume29
    Issue number1
    DOIs
    Publication statusPublished - Jan 1 2012

    All Science Journal Classification (ASJC) codes

    • Electronic, Optical and Magnetic Materials
    • Atomic and Molecular Physics, and Optics
    • Computer Vision and Pattern Recognition

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