Interaction of light with the polarization devices: a vectorial Pauli algebraic approach

A theoretical approach to the interaction between polarized light and polarization devices, based on the vectorial and pure operatorial form of the Pauli algebra, is presented. Unlike the standard (Jones and Mueller) approaches, this formalism is coordinate-free, i.e. it does not appeal to any matrix representation of the involved operators. This vectorial approach establishes a mathematical bridge between the Hilbert space of the density operators of the polarization states and the Poincaré space of their geometric representations and gives a rigorous justification of the handling of the interactions between the polarization states and polarization systems on the Poincaré sphere (in the Poincaré ball). In such an approach, unlike the standard ones, the three relevant quantities that characterize the interaction—the gain, the Poincaré vector of the outgoing light and its degree of polarization—result straightforwardly, in block, in the Pauli vectorial expressions of the density operator of the output state. The final equations are symmetric, compact and physically expressive. A generalized form of Malus' law, for any dichroic device and partially polarized light is obtained this way.