SU(1,1) approach to Stokes parameters and the theory of light polarization
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 (Poincaré 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.
- Publication:
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Journal of the Optical Society of America B Optical Physics
- Pub Date:
- August 2016
- DOI:
- 10.1364/JOSAB.33.001696
- arXiv:
- arXiv:1602.03223
- Bibcode:
- 2016JOSAB..33.1696M
- Keywords:
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- Quantum Physics;
- High Energy Physics - Theory;
- Mathematical Physics;
- Physics - Optics
- E-Print:
- J.Opt.Soc.Am.B 33 (2016) 1696-1701