Weierstrass solid immersion lens (SIL) has been used to obtain superresolution because a smaller focal size is desirable. In this paper, focus shaping of Weierstrass SIL illuminated by an axisymmetric Bessel-modulated Gaussian beam (QBG beam) is investigated. It has been found theoretically that the sharper focusing of Weierstrass SIL disappears for a certain beam order of QBG beam. For case of a smaller beam order, the focus still locates on the plane of Weierstrass SIL and Weierstrass SIL still plays a tighter focusing role. However, when the beam order increases continuously, the focus lefts the plane of Weierstrass SIL, and shifts along an optical axis considerably. In addition, under condition of the higher beam order, the dependence of the focal shift on the beam order is nearly linear, which may be used to alter a focal position conveniently.
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The focusing properties of radially polarized Bessel-modulated Gaussian (QBG) beam are theoretically investigated in detail by vector diffraction theory. The QBG beam contains an optical vortex. Calculation results show that the intensity distribution in focal region of radially polarized QBG beam can be altered considerably by changing beam parameter and the topological charge of the optical vortex. Beam parameter can induce remarkable focus evolution in axial direction. While topological charge adjusts intensity distribution more significantly in transverse direction, for instance, one focal spot changes into one ring pattern. And some novel focal patterns may occur, including two-peak focus, one ring focus, two-ring focus, three-ring focus, and even dark hollow focus, which is very important in optical tweezers technique.
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