  It is shown that the two complex Cartesian components of the electric field
of a monochromatic electromagnetic plane wave, with a temporal and spatial
dependence of the form ${\rm e}^{{\rm i} (kz - \omega t)}$, form a SU(2) spinor
that corresponds to a tangent vector to the Poincar\'e sphere representing the
state of polarization and phase of the wave. The geometrical representation on
the Poincar\'e sphere of the effect of some optical filters is reviewed. It is
also shown that in the case of a partially polarized beam, the coherency matrix
defines two diametrically opposite points of the Poincar\'e sphere.
