  We show that any pure, two-mode, $N$-photon state with $N$ odd or equal to
two can be transformed into an orthogonal state using only linear optics.
According to a recently suggested definition of polarization degree, this
implies that all such states are fully polarized. This is also found to be true
for any pure, two-mode, energy eigenstate belonging to a two-dimensional SU(2)
orbit. Complete two- and three-photon bases whose basis states are related by
only phase shifts or geometrical rotations are also derived.
