Geometric Polarimetry - Part I: Spinors and Wave States

A new approach to polarization algebra is introduced. It exploits the geometric properties of spinors in order to represent wave states consistently in arbitrary directions in three dimensional space. In this first expository paper of an intended series the basic derivation of the spinorial wave state is seen to be geometrically related to the electromagnetic field tensor in the spatio-temporal Fourier domain. Extracting the polarization state from the electromagnetic field requires the introduction of a new element, which enters linearly into the defining relation. We call this element the phase flag and it is this that keeps track of the polarization reference when the coordinate system is changed and provides a phase origin for both wave components. In this way we are able to identify the sphere of three dimensional unit wave vectors with the Poincaré sphere. Index Terms state of polarization, geometry, covariant and contravariant spinors and tensors, bivectors, phase flag, Poincaré sphere.