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Santos AG, Sugon QM, McNamara DJ. Polarization ellipse and Stokes parameters in geometric algebra. J Opt Soc Am A Opt Image Sci Vis. 2012;29(1):89-98doi: 10.1364/JOSAA.29.000089.
Santos, A. G., Sugon, Q. M., & McNamara, D. J. (2012). Polarization ellipse and Stokes parameters in geometric algebra. Journal of the Optical Society of America. A, Optics, image science, and vision, 29(1), 89-98. https://doi.org/10.1364/JOSAA.29.000089
Santos, Adler G, et al. "Polarization ellipse and Stokes parameters in geometric algebra." Journal of the Optical Society of America. A, Optics, image science, and vision vol. 29,1 (2012): 89-98. doi: https://doi.org/10.1364/JOSAA.29.000089
Santos AG, Sugon QM, McNamara DJ. Polarization ellipse and Stokes parameters in geometric algebra. J Opt Soc Am A Opt Image Sci Vis. 2012 Jan 01;29(1):89-98. doi: 10.1364/JOSAA.29.000089. PMID: 22218355.
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J Opt Soc Am A Opt Image Sci Vis. 2012 Jan 01;29(1):89-98. doi: 10.1364/JOSAA.29.000089.

Polarization ellipse and Stokes parameters in geometric algebra.

Journal of the Optical Society of America. A, Optics, image science, and vision

Adler G Santos, Quirino M Sugon, Daniel J McNamara

Affiliations

  1. Manila Observatory, Ateneo de Manila University Campus, Loyola Heights, Quezon City, Philippines. [email protected]

PMID: 22218355 DOI: 10.1364/JOSAA.29.000089

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.

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