Circular Mathieu and Weber autofocusing beams

In this Letter, the new classes of non-paraxial autofocusing beams are introduced for the first time, to the best of our knowledge. We investigate both numerically and experimentally non-paraxial circular Mathieu and Weber autofocusing beams based on the solutions of the Helmholtz equation in elliptical and parabolic coordinates, respectively. The results show that such beams can significantly shorten the focus distance, and eliminate the intense oscillation effectively after the focusing point. The focal length and the peak intensity can be controlled by tunable parameters. In addition, we further experimentally realize their application of such beams in optical trapping.