  We discuss the properties of pure multipole beams with well-defined
handedness or helicity, with the beam field a simultaneous eigenvector of the
squared total angular momentum and its projection along the propagation axis.
Under the condition of hemispherical illumination, we show that the only
possible propagating multipole beams are `sectoral' multipoles. The sectoral
dipole beam is shown to be equivalent to the non-singular time-reversed field
of an electric and a magnetic point dipole Huygens' source located at the beam
focus. Higher order multipolar beams are vortex beams vanishing on the
propagation axis. The simple analytical expressions of the electric field of
sectoral multipole beams, exact solutions of Maxwell's equations, and the
peculiar behaviour of the Poynting vector and spin and orbital angular momenta
in the focal volume could help to understand and model light-matter
interactions under strongly focused beams.
