Introduction of a new vortex cosine-hyperbolic-Gaussian beam and the study of its propagation properties in fractional Fourier transform optical system

Based on the framework of the Huygens-Fresnel diffraction, we investigate theoretically the propagation properties of a new vortex beam, which is referred to as vortex-cosh-Gaussian beam (vChGB), through a paraxial ABCD optical system. A closed-form formula of vChGB passing through the above system is derived. We show by analytical and numerical calculations that the decentered parameter and the topological vortex charge affect strongly the characteristics of the considered beam upon propagating in free space. In a fractional Fourier transform system (FrFT), it is found that the intensity and the phase distributions of the propagating vChGB evolves gradually and periodically versus the order of the FrFT. The shape of the vChGB depends on the parameters of the beam and the fractional order of the FrFT system. The results obtained may be beneficial to applications in optical trapping, optical micromanipulation and beam shaping.