Tight focusing of radially polarized beams modulated by a fractal conical lens

A novel high numerical aperture (NA) focusing system with a fractal conical lens (FCL) is proposed, and tight focusing of radially polarized beams through the proposed optical system is investigated theoretically and numerically. The influence of several relevant factors, including the FCL's stage S, objective lens' NA, and truncation parameter β0, on the targeted beam's focusing characteristics in the focal region is discussed in detail. It is found that, when a FCL with S≥0 is employed, position of the major focal point would shift from the geometric focal point, and the focused intensity distributions cannot maintain symmetrical about the focus any more, although they present different profiles for various truncation parameters β0. When S≥2, multiple focal points can be generated, i.e., a single major focus and a series of subsidiary foci surrounding it along the optical axis, which form a focal region. These unique focusing characteristics with a FCL are remarkably different from that of without a FCL. The fascinating findings here may be taken advantage of when using radially polarized beams in exploiting new-type optical tweezers and making use of a FCL.