Geometric Polarimetry—Part I: Spinors and Wave States

A new formal approach for the representation of polarization states of coherent and partially coherent electromagnetic plane waves is presented. Its basis is a purely geometric construction for the normalized complex-analytic coherent wave as a generating line in the sphere of wave directions and whose Stokes vector is determined by the intersection with the conjugate generating line. The Poincaré sphere is now located in physical space, simply a coordination of the wave sphere, with its axis aligned with the wave vector. Algebraically, the generators representing coherent states are represented by spinors, and this is made consistent with the spinor-tensor representation of electromagnetic theory by means of an explicit reference spinor that we call the phase flag. As a faithful unified geometric representation, the new model provides improved formal tools for resolving many of the geometric difficulties and ambiguities that arise in the traditional formalism.