A Study of Source Plane Mathieu Beams

Abstract

We derive the source field expressions of different Mathieu beams. In particular, Mathieu beams consisting of the infinite summations of J-type Bessel functions and their Gaussian counterparts are studied. Mathieu beams based on the summation of I-type Bessel functions are introduced as well. By plotting the source intensities of such beams, the variations of the related profiles are examined against the changes in the source parameters. It is found that, via the adjustment of these parameters, it is possible to obtain completely new beam configurations and also those similar to the existing beams of the present literature.