Axi-symmetrically polarized beams

1. What are axially symmetrically polarized laser beams?

Most laser beams are linearly polarized. Recently, however there has been growing interest in laser beams with axially symmetric polarizations.
These are referred to as axially symmetric beams or axially polarized laser beams.

What are the merits of axially polarized beams?
They relate to the polarization of the beam after focusing by a lens. When a linearly polarized beam is focused by a lens, rays along the axis of the incident polarization are focused in a direction parallel to the direction of polarization; orthogonal rays are focused in a direction perpendicular to their polarization.

When a radially polarized beam is focused the effect of the lens on the polarization is symmetric so that the focused beam is radially polarized (see left side of diagram below).

It is know that the focus of such a laser beam can cut materials efficiently and uniformly. The focus of an axially polarized beam has a component in the direction of propagation. This property is employed in high quality microscopes, because the power at the center of an axially polarized beam is zero. One of the applications of axially polarized beams is optical trapping or optical tweezing.
How can axially polarized beams be produced?