Skew ray tracing in a step-index optical fiber using geometric algebra

Angeleene S. Ang, Quirino M. Sugon, Daniel J. McNamara

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    We used geometric algebra to compute the paths of skew rays in a cylindrical, step-index multimode optical fiber. To do this, we used the vector addition form for the law of propagation, the exponential of an imaginary vector form for the law of refraction, and the juxtaposed vector product form for the law of reflection. In particular, the exponential forms of the vector rotations enables us to take advantage of the addition or subtraction of exponential arguments of two rotated vectors in the derivation of the ray tracing invariants in cylindrical and spherical coordinates. We showed that the light rays inside the optical fiber trace a polygonal helical path characterized by three invariants that relate successive reflections inside the fiber: the ray path distance, the difference in axial distances, and the difference in the azimuthal angles. We also rederived the known generalized formula for the numerical aperture for skew rays, which simplifies to the standard form for meridional rays.

    Original languageEnglish
    Pages (from-to)3764-3773
    Number of pages10
    JournalApplied Optics
    Volume54
    Issue number12
    DOIs
    Publication statusPublished - Apr 20 2015

    All Science Journal Classification (ASJC) codes

    • Atomic and Molecular Physics, and Optics
    • Engineering (miscellaneous)
    • Electrical and Electronic Engineering

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