Optical doughnut for optical tweezers

We describe novel optical doughnuts for optical tweezers. With new phase functions, the proposed doughnut beams have dark cores in specified shapes. The technique can offer a simple method for creating a variety of beam shapes to match the trapped objects. One can rotate the beams directly by revolving their phase structures about their axes on the initial plane. The technique for generating the traditional Laguerre-Gaussian beam can be used to create these novel beams.