The tight focusing of a double ring-shaped radially polarized sinh Gaussian beam with a cosine phase plate is studied on the basis of the vector diffraction theory. Under a high-NA focusing condition, the strong longitudinal component forms a sharper spot at the focal point for both fundamental mode (R-TEM01*) beams and higher-order, radially polarized mode beams. Due to destructive interference between the inner and outer rings, double-ring-shaped radially polarized mode (R-TEM11*) beams in particular can significantly lower the focal spot size. Simulation results show that the focused fields and phase distributions at focus are largely influenced by both the cosine parameter and truncation coefficient of the incident beams. Moreover, shifted focal spot, and optical cage patterns can be flexibly achieved by carefully choosing the cosine parameter (C) and it is also observed that the intensity distribution of the different mode has little variation among the degree of truncation (?) of the input beam beside the pupil. This work is important for optical manipulation, particle limitation systems, laser surface modification, and laser direct writing techniques.
