Forming of the thin light tube at sharp focusing of azimuthally-polarized radiation

The theoretical and numerical analysis of transmission function of focusing system with the high numerical aperture is spent with the purpose of formation in focal area of a thin light tube at azimuthally-polarized radiation. It is analytically shown, that due to a destructive interference of two beams, formed by two narrow rings, it is possible to overcome not only whole-aperture diffractive limit, but also a limit connected with the ring aperture. Thus, however, intensity in the center of a focal plane essentially decreases, that practically leads to break of a tube. It is numerically shown, that long thin tubes can be formed by means of aperture apodizing by phase function of diffractive axicon, and also by complex transmission function matched with Laguerre-Gaussian modes and radial Airy-Gaussian beams.