Generation of an elliptic Bessel beam

TLDR: A technique is reported for the generation of elliptic hollow beams, which are actually scaled versions of higher-order Bessel beams, based on the fact that stretching coordinates in the space domain results in a contraction in the frequency domain, along with a change in the overall amplitude of the spectrum.

Abstract: In an elliptic coordinate system the solution for a diffraction-free beam is given by a Mathieu beam, which is mathematically complicated and therefore takes considerable computational time and a large memory space. A technique is reported for the generation of elliptic hollow beams, which are actually scaled versions of higher-order Bessel beams. The analysis is based on the fact that stretching coordinates in the space domain results in a contraction of the coordinates in the frequency domain, along with a change in the overall amplitude of the spectrum. The beam, produced holographically, is structurally stable and retains its shape up to approximately 1 m.