The influence of circular aperture on the focusing properties of partially coherent controllable dark-hollow beams

Based on the generalized Huygens-Fresnel integral, the focusing properties of partially coherent controllable dark-hollow beams(CDHBs) through a thin lens with circular aperture are studied in detail. Our main attention is focused on the influence of circular aperture on the focusing properties of partially coherent controllable dark-hollow beams. Numerical calculation results are shown that the circular aperture leads to the increase of the relative focal shift and the decrease of the effective beam width in the actual focal plane, and changes the dependences of the relative focal shift and the effective beam width on p (dark-size adjusting parameter), N(the order of the CDHBs), δg (initial transverse coherence width) and the effective Fresnel number Nw. Some physical explanations are also given.