We investigate the focusing properties of a double-ring-shaped azimuthally polarized beam by a high numerical aperture (NA) lens axicon based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal hole of having large uniform focal depth of without any annular aperture. We also observed that the distribution of the total intensity near the focus has little variation with the degree of truncation of the incident beam by the pupil. The authors expect such a super-long dark channel may find applications in optical, biological, and atmospheric sciences.
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