Two-vector representation of a nondepolarizing Mueller matrix

•A two-vector representation gives a simple view of a pure Mueller matrix.•An alternative plane representation is also studied and compared.•The polarimetric properties are visually and geometrically characterized.•Pure Mueller matrices are classified on the basis of both representations.•The new approaches provide a powerful tool for the analysis of measured M. matrices.

A geometric view of the polarimetric properties of a nondepolarizing medium is presented by means of a pair of vectors in the Poincaré sphere. An alternative representation constituted by a set of vectors contained in the equatorial plane of the Poincaré 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.