Mathieu and Weber tightly autofocusing beams

Abstract

We theoretically investigate the propagation dynamics of vectorial Mathieu and Weber tightly autofocusing beams, which are constructed based on nonparaxial Weber and Mathieu accelerating beams, respectively. They can automatically focus along the paraboloid and ellipsoid, and the focal fields represent the tightly focusing properties resembling that generated with a high NA lens. We demonstrate the influence of the beam parameters on the spot size and energy proportion of longitudinal component of the focal fields. It reveals that Mathieu tightly autofocusing beam supports a more superior focusing performance, of which the longitudinal field component with superoscillatory feature could be enhanced by decreasing the order and selecting the suitable interfocal separation of the beam. These results are expected to provide new insights for the autofocusing beams and the tight focusing of the vector beams.