  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 Poincare' sphere.
