To study the tight focusing characteristics of azimuthally polarized Airy beams, the Richards-Wolf vector diffraction theory was adopt. The influences of the exponential attenuation factor, the radius of the main ring, and the proportional factor of the airy beams on the incident field patterns were respectively studied. The focal field distributions of the azimuthally polarized airy beams and the azimuthally polarized airy beams modulated by a vortex phase filter were studied, from which a sub-wavelength azimuthally polarized doughnut field and a transversally polarized bright field were garnered. The experimental results are basically consistent with the theoretical simulations. Furthermore, the multi-ring vortex phase filter was designed to modulate the azimuthally polarized airy beams according to the particle swarm algorithm, and an ultra-long and non-diffracting super-resolution transversally polarized light needle was produced on tight focusing. It turns out that the full width at half maximum and the depth of focus of the light needle are 0.395λ and 37.432λ respectively, which corresponds to an aspect ratio of 94.788. The polarization patterns of the focal fields are analyzed by calculating the Stokes polarization parameters. It is found that the focal field alternates between the radial polarization and azimuthal polarization and the singularity at the center of the beam disappears, which testify that the transversally polarized bright field distribution is realized. The research holds broad applications in high-density magneto-optical storage, super-resolution optical imaging, nanolithography and particle manipulation.