Two-vector representation of a nondepolarizing Mueller matrix

A geometric view of the polarimetric properties of a nondepolarizing medium is presented by means of a pair of vectors in the Poincar\'e sphere. An alternative representation constituted by a set of vectors contained in the equatorial plane of the Poincar\'e sphere is also defined and interpreted. The analyses of the magnitudes and relative orientations of the constitutive vectors of such simple representations allow for a classification of nondepolarizing media.