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 present a theoretical approach to generate a nondiffracting beam with extended depth of focus (DOF) and a smaller focal spot along the optical axis, by tight focusing of an azimuthally polarized beam with a circular symmetrical binary phase mask and an interference effect over a high-numerical-aperture (NA) lens axicon system. We find a general azimuthal diffraction integral for the circularly symmetric binary phase mask and examine it in two special cases: a high-NA lens and a high-NA lens axicon. The azimuthally polarized beam remains well behaved in both cases. We verify that the longitudinal component generated by azimuthally polarized illumination produces the narrowest spot size for a wide range of geometries. Finally, we discuss the effects of tight focusing on a dielectric interface and provide some ideas for circumventing the effects of the binary phase mask interface and even utilize them for spot size reduction.

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We propose to use a pure-phase filter in combination with a high NA lens axicon to achieve a sub-wavelength magnetic focal spot with large uniform magnetization depth when illuminated by a circularly polarized beam. The magnetization distributions are derived and evaluated based on the vector diffraction theory and the inverse Faraday effect of the isotropic and non-magnetically ordered material. With this kind of system, the longitudinal magnetization depth is increased to 12.82λ and the magnetic spot size has been reduced to 0.38λ. However, in the conventional lens with the same NA, the FWHM of the magnetic spot is found to be 0.43λ and its corresponding magnetization depth is only 0.89λ. We expect such a sub-wavelength strong longitudinal magnetic field with large magnetization depth can be widely used in high density magneto-optic recording and the scanning near-field magnetic microscope for studies of magnetic responses of sub-wavelength elementary cells of metamaterials.

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