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arXiv · 1602.03223

$SU(1,1)$ Approach to Stokes Parameters and the Theory of Light Polarization

R. D. Mota·D. Ojeda-Guillén·M. Salazar-Ramírez·V. D. Granados
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Abstract

We introduce an alternative approach to the polarization theory of light. This is based on a set of quantum operators, constructed from two independent bosons, being three of them the $su(1,1)$ Lie algebra generators, and the other one, the Casimir operator of this algebra. By taking the expectation value of these generators in a two-mode coherent state, their classical limit is obtained. We use these classical quantities to define the new Stokes-like parameters. We show that the light polarization ellipse can be written in terms of the Stokes-like parameters. Also, we write these parameters in terms of other two quantities, and show that they define a one-sheet (Poincar\'e hyperboloid) of a two-sheet hyperboloid. Our study is restricted to the case of a monochromatic plane electromagnetic wave which propagates along the $z$ axis.

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R. D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez, V. D. Granados. 2016-02-10. $SU(1,1)$ Approach to Stokes Parameters and the Theory of Light Polarization. https://doi.org/10.1364/josab.33.001696

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