Tight focusing of double ring shaped radially polarized multi gaussian beam with cosine phase plate is studied numerically based on vector diffraction theory. For higher-order, radially polarized mode beams as well as a fundamental mode (R-TEM01*) beam, the strong longitudinal component forms a sharper spot at the focal point under a high-NA focusing condition. In particular, double-ring-shaped radially polarized mode (R-TEM11*) beams can effectively reduce the focal spot size because of destructive interference between the inner and the outer rings. The mathematical expressions for the focused fields are derived. Simulation results show that the focused fields and phase distributions at focus are largely influenced by both the cosine parameter and beam diameter of the incident beams. Moreover, focal spot with flat-topped, two focal spots patterns can be flexibly achieved by carefully choosing the cosine parameter (C) and the ratios of the pupil diameter to the beam diameter (β) which confirms the potential of such beams in wide applications, such as optical tweezers, lithography, and material processing.
