Abstract
Group theory provides a method for a unified treatment of the Poincaré sphere, the Jones matrix and the Mueller matrix. We first introduce the Poincaré sphere by a stereographic projection of the plane representation of elliptically polarized light. Next we consider the unitary group and the rotation group by interpreting the stereographic projection through group theory. By extending these two groups, we finally consider the unimodular group and the Lorentz group. The unitary group and the rotation group are related to the Jones and Mueller matrices of totally transparent systems, while the unimodular group and the Lorentz group are related to the Jones and Mueller matrices of most general systems including partially transparent systems. By this approach we can grasp the unified treatment of these three methods and understand clearly their relationship and structure.
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