Generation of on-demand quasi-Mathieu beams with a controlled generation of spatial spectrum of angular Mathieu-Gauss functions with a digital laser.

This study provided an intra-cavity method for the selective generation of all kinds of quasi-Mathieu beams. The method employed L-type digital lasers to selectively generate the Fourier spectrum of the gaussian-modulated angular Mathieu function. The lasing field then underwent a Fourier-transform with an extra-cavity lens, and was converted into quasi-Mathieu beams after passing through an axicon. The selection of the lasing quasi-Mathieu beams was controlled by the projection phase of the intra-cavity spatial light modulator (SLM) of digital lasers, which provided flexibility in dynamically generating on-demand quasi-Mathieu beams. The formalism of the resulting quasi-Mathieu beams is detailed in this paper. The nondiffracting characteristics of the resulting quasi-Mathieu beams were verified both numerically and experimentally. The capability of dynamically controlled generation and manipulation of lasing quasi-Mathieu beams by the proposed method is beneficial to practical applications of Mathieu beams.