Investigating the focus shaping of the TEM11* beam with radial varying polarization

In this article, based on vector diffraction theory the focusing properties of double ring shaped higher order Laguerre–Gauss beam with radial varying polarization are investigated numerically. The numerical simulations show that the evolution of some interesting focal spot, focal split and focal patterns in the focal region by changing polarization rotation angle under tight focusing through the high NA lens. It is also shown that a subwavelength focal hole with a quite long depth of focus, multiple focal holes are achieved near the focus, when tuning β (is the ratio of the pupil radius to the beam waist) in the focal plane for different modes under tight focusing through the high NA lens. We found that when tuning, beam parameter or the polarization rotation angle of the incident beam, it is possible to generate some interesting novel focal patterns, including multiple intensity rings, dark hollow focus and cylindrical crust focus. Such kind of beams plays an important role in optical trapping, laser cutting and optical manipulation applications.