Partially coherent bottle beams

We theoretically investigate the three-dimensional intensity distribution of the partially coherent beams focused by a lens. It is shown that the intensity distribution in the neighborhood of the geometrical focus is not only dependent on the intensity distribution of the incident partially coherent beam, but also on its coherence. Based on this, a novel method is presented for achieving a dark focus surrounded by higher intensities. The method is to modulate the spectral degree of coherence of the incident partially coherent beam, and thereby we can change the three-dimensional intensity distribution in the neighborhood of the geometrical focus, and generate an adjustable three-dimensional dark focus.