  Classical beams of light with non-uniform polarization patterns (e.g.
radially and azimuthally polarized doughnut beams) may exhibit quantum-like
features as, for instance, inseparability. We establish an exact correspondence
between radially and azimuthally polarized classical modes of the
electromagnetic field and the two-qubit quantum Bell states. We demonstrate the
existence of a special representation for such classical modes by means of a
pair of Poincar\'e spheres. Points on these spheres are described by Stokes
parameters associated with such modes, and their explicit expressions are
given.
