  We present a method for the realization of radially and azimuthally polarized
nonparaxial Bessel beams in a rigorous but simple manner. This result is
achieved by using the concept of Hertz vector potential to generate exact
vector solutions of Maxwell's equations from scalar Bessel beams. The scalar
part of the Hertz potential is built by analogy with the paraxial case as a
linear combination of Bessel beams carrying a unit of orbital angular momentum.
In this way we are able to obtain spatial and polarization patterns analogous
to the ones exhibited by the standard cylindrically polarized paraxial beams.
Applications of these beams are discussed.
