Double doughnut-shaped focal spots with controllable position in axial direction

In order to generate double doughnut-shaped focal spots at adjustable positions along the axial direction, a vortex phase zone plate based on a formula of annular radius derived from vector diffraction integral was designed. The focusing properties of the modulated vortex phase zone plate were further investigated in a tightly focused system. First, integral formulas of linearly and circularly polarized vortex beams were calculated under high NA focusing conditions. Then, the intensity distributions of linearly and circularly polarized vortex beams in a high NA focusing system were simulated by integral formulas with various axial shifting distances and topological charges. Finally, the corresponding experimental results of linearly and circularly polarized light were also given, utilizing a spatial light modulator loaded on double doughnut-shaped phase patterns. The double doughnut-shaped focal spots with a topological charge of 1 and axial distances of +/- 10 mu m and +/- 15 mu m were produced when the incident light was linearly polarized. As well as the double doughnut-shaped focal spots with axial distances of +/- 20 mu m, topological charges of 1-4 were also produced when the incident light was circularly polarized. The simulated and experimental results demonstrated that two doughnut-shape focal spots with controllable axial shifting distances and dark spot sizes could be produced in the tight focusing region of a high NA objective when it is modulated by the vortex phase zone plate. This kind of vortex phase zone plate could be applied in the field of optical micromanipulation, two beam super-resolution nanolithography, and Stimulated-Emission-Depletion (STED) fluorescence microscopy.