The Poincare sphere: isolated and real trajectories describing the state of polarization

Abstract

For a given crystal optics device with polarization properties there are two kinds of trajectories that can be drawn on the Poincare sphere, namely the isolated and real trajectories. Using Stokes vectors and Mueller matrices, the parametric equations that represent the evolution of the state of polarization due to the passage of light through polarizers and optical components exhibiting linear or circular birefringence are given. The geometrical trajectories given by these equations, are useful for analyzing or designing optical birefringent networks and they are easy to obtain with today's computer software. An example of their application in the analysis of a Solc filter is given.