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

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 twomode 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.