Tight focusing of a double-ring-shaped, azimuthally polarized beam

We study the focusing properties of a double-ring-shaped azimuthally polarized beam through an annular high NA objective lens. It is shown that a subwavelength focal hole (～0.5λ) with a quite long depth of focus (～26λ) is achieved near the focus. This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.