Revisiting Poincaré Sphere and Pauli Algebra in Polarization Optics

We present one of the main lines of development of Poincaré sphere representation in polarization optics, by using largely some of our contributions in the field. We refer to the action of deterministic devices, specifically the diattenuators, on the partial polarized light. On one hand, we emphasize the intimate connection between the Pauli algebraic analysis and the Poincaré ball representation of this interaction. On the other hand, we bring to the foreground the close similarity between the law of composition of the Poincaré vectors of the diattenuator and of polarized light and the law of composition of relativistic admissible velocities. These two kinds of vectors are isomorphic, and they are “imprisoned” in a sphere of finite radius, standardizable at a radius of one, i.e., Poincaré sphere.