Generation of a sub-wavelength focal spot with a long transversally polarized optical needle using a double-ring-shaped azimuthally polarized beam

•We investigate the tight focusing of double-ring-shaped azimuthally polarized beam.•A seven-belt complex filter modulated spiral phase hologram is used to improve the focusability.•We remove the focal shift and reduce the strong side lobe by using the SCF-SPH.•A sub-wavelength focal spot size with a long depth of focus is generated.•The creation of transversally polarized beam is validated by calculating the Stokes parameters.

Based on the vector diffraction theory, we study the tight focusing performance of a double-ring-shaped azimuthally polarized beam through a high numerical aperture objective using a spiral phase plate or a seven-belt complex filter modulated spiral phase hologram (SCF-SPH). The effect of truncation parameters on the tight focusing is demonstrated. The dependence of various polarizations on the intensity, focal shift and side lobe are also investigated. It is shown that the focal shift can be removed successfully and the side lobe can be reduced effectively by introducing a SCF-SPH into the imaging system. Also, a sub-wavelength focal spot along with a long transversally polarized optical needle is achieved. The polarization evolution of the wavefront near the focal plane is analyzed by calculating the Stokes polarization parameters. It is revealed that the annihilation of the polarization singularity at the beam center makes a bright focal spot possible.