English

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

Quantum Physics 2016-07-26 v2 High Energy Physics - Theory Mathematical Physics math.MP Optics

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)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 zz axis.

Keywords

Cite

@article{arxiv.1602.03223,
  title  = {$SU(1,1)$ Approach to Stokes Parameters and the Theory of Light Polarization},
  author = {R. D. Mota and D. Ojeda-Guillén and M. Salazar-Ramírez and V. D. Granados},
  journal= {arXiv preprint arXiv:1602.03223},
  year   = {2016}
}