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

Angeleene S. Ang, Quirino Jr Mallorca Sugon, Daniel J. McNamara

Research output: Contribution to journalArticle

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

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Ray tracing
ray tracing
Algebra
Optical fibers
rays
algebra
optical fibers
cylindrical coordinates
Multimode fibers
spherical coordinates
numerical aperture
Refraction
subtraction
refraction
derivation
fibers
propagation
Fibers
products

All Science Journal Classification (ASJC) codes

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

Cite this

Skew ray tracing in a step-index optical fiber using geometric algebra. / Ang, Angeleene S.; Sugon, Quirino Jr Mallorca; McNamara, Daniel J.

In: Applied Optics, Vol. 54, No. 12, 20.04.2015, p. 3764-3773.

Research output: Contribution to journalArticle

Ang, Angeleene S. ; Sugon, Quirino Jr Mallorca ; McNamara, Daniel J. / Skew ray tracing in a step-index optical fiber using geometric algebra. In: Applied Optics. 2015 ; Vol. 54, No. 12. pp. 3764-3773.
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