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 0.5λ having large uniform focal depth of 48λ 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 β 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.

We investigated the focusing properties of a double-ring-shaped azimuthally polarized beam tightly focused with a high NA lens and a binary phase filter. We observe that by using 3 belts and 5 belts binary phase filters novel focal patterns including splitting of focal rings and multiring focus are obtained. We also found that a suitably designed phase structure can shift the focal rings along optical axis. The author expects such investigation is worthwhile for optical manipulation and material processing technologies.

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The intensity distributions near the focal point for tight focusing of azimuthally polarized Laguerre-Gaussian beam including higher order modes are calculated based on vector diffraction theory. For higher order as well as the fundamental lower order mode A-TEM 01 *, a small focal hole at the centre is obtained for the focusing under high NA lens. In a limit of NA = 0.95, the higher order A-TEM p1 * mode beams of p = 1, 2, 3, 4, 5 and 6 are established numerically in detail. It is observed that one of the higher order mode A-TEM 51 * generates some interesting results. And it is also observed that the intensity distribution of the different mode has little variation among the degree of truncation (b) of the input beam beside the pupil. This work is important for optical manipulation, optical data storage, micro-machines and optical trapping applications for low refractive index particles.