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SU(1,1) approach to Stokes parameters and the theory of light polarization

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Abstract

We introduce an alternative approach to the polarization theory of light. This theory is based on a set of quantum operators, constructed from two independent bosons, three of them being 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 the 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.

© 2016 Optical Society of America

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