The Spatial Mapping of Interconversion Between Laguerre-Gaussian and Hermite-Gaussian Beams Array With an Astigmatism Phase

The Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modes can be interconverted with an astigmatism phase. In this paper, based on the single beam, the interconversion of LG and HG beams array with the astigmatism phase is analyzed theoretically and the spatial mapping relationship is derived. In the experiment, 1 x 3, 2 x 2, 3 x 3 LG beams arrays are generated and converted into HG beams array via employing a spatial light modulator loaded with 0 degrees, 90 degrees, 45 degrees, -45 degrees astigmatism phases. The experimental results are in great agreement with the theoretical analyses. Moreover, from the number and direction of the dark fringe of converted HG beams array, the orbital angular momentum information of LG beams array can be obtained. This work theoretically perfects the theoretical model of the interconversion between LG and HG beams based on an astigmatism phase, and also provides a theoretical support for measuring the LG beams array.