Vectorial Pauli algebraic approach in polarization optics. I. Device and state operators

This paper inscribes on the line of the efforts (sketched in the Introduction) in elaborating theoretical approaches alternative to the traditional Jones and Mueller matrix calculi in polarization optics. The more abstract, compact and elevated forms of linear algebra are not fully exploited yet in the polarization optics. A vectorial and pure operatorial Pauli algebraic approach to the interaction between the polarized light and the polarization optical systems is given. This is the most compact, adequate and elegant calculus corresponding to the well-known geometric handling of the polarization states and their interaction with the polarization devices on the Poincaré sphere. In this first paper, we deduce the Pauli algebraic vectorial forms of the operators corresponding to the orthogonal and nonorthogonal polarization devices and to all the states of light polarization. In the next paper we shall give the vectorial Pauli algebraic analysis of the interaction between the whole hierarchy of these devices and the various forms of polarized light.