Comparison of Mainardi, cos-Mainardi and cosh-Mainardi beams with and without optical vortex in FT and FrFT systems

In this paper, we investigated the propagation of the Mainardi, cos-Mainardi and cosh-Mainardi beams under the Fractional Fourier transforms (FrFT) and Fourier transforms (FT). The results show that with the change of b, q, p, and z, which are the hyperbolic parameter, the fractional order of Mittag-Leffler function, the fractional Fourier transform order, and the distance propagation, respectively, the properties of the Mainardi beam with and without optical vortex can be controlled. The results show that with changing b and q parameters, the beam size, number, width and direction of the beam changes. These results can be useful in signal processing and beam manipulation. Mainardi beam similar to AiB holds promise for wide applications because of its unique features of being diffraction-free, self-accelerating, and self-healing.