Geometric approach to the degree of polarization for arbitrary fields

The eigenvalue decomposition of the polarization matrix is employed to find out the geometric interpretation of the traditional degree of polarization and, in particular, of the degree of polarization for arbitrary electromagnetic fields put forward recently by Setälä et al. [2002, Phys. Rev. Lett., 88, 123902]. It is shown that both measures have similar geometric meaning as a measure for the purity of the polarization state. Possible extensions to the analysis are discussed.