An application of complex analysis to polarization optics is given and it is shown that the Poincare sphere is nothing more than the Riemann sphere.
The approach of this paper is first to introduce the Poincare sphere by a stereographic projection of the plane representation of elliptically polarized light, where we use two orthogonal linear polarization as the basis. Then we choose two arbitrary orthogonal elliptically polarization as the basis to describe a general state of polarization and by using this general representation we define generalized Stokes parameters. The relationship between these plane representations is derived.
Next, generalized Malus' law describing the intensity of light after passage through an arbitrary analyser is obtained and it is represented by the generalized Stokes parameters.
Finally, complex analytical formulas of polarization calculus are given.
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