Poincaré sphere representation of partially polarized fields

The use of points on the surface of the poincaré sphere to represent the polarization state of fully polarized electromagnetic fields is extended to partially polarized fields by representing their polarization by points inside the sphere. The coordinates of a point <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W̄</tex> representing the polarization state are shown to be simply related to the Stokes parameters. The center of the sphere represents a completely unpolarized wave, and the degree of polarization is given by the distance of the point <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W̄</tex> from the center of the sphere. A simple formula is derived for calculating the power received by an antenna illuminated by a partially polarized wave. A method is described for measuring the polarization state by a number of intensity measurements.