Abstract
<jats:p>The traditional mathematical instrument to track the evolution of the polarization of a plane wave traversing an optical medium, is the Poincaré sphere. In this paper, we follow an alternative strategy which does not rely on plane wave analysis, spherical trigonometry or geodesic trajectories on the Poincaré sphere. We show how a rigorous first order differential equation can be implemented as wave equation for polarized light. Its derivation is inspired by the Dirac treatment of the relativistic quantum wave equation of the electron. As generic example, we will derive the polarization transport of a monochromatic beam pointing along the optical axis of a gyrotropic medium. The Jones differential N-matrix is thereby identified as major constituent term in the transport equation</jats:p>