Propagation behavior of a modified anomalous vortex beam in fractional Fourier transform

Abstract

This paper presents a new investigation into the evolution properties of a modified anomalous vortex beam (MAVB) within a fractional Fourier transform (FRFT). Analytical formulas for the MAVB as it propagates through both apertured and unapertured FRFT are derived by applying the Collins formula and expanding the hard aperture function into a finite series of Gaussian functions. Numerical simulations produce graphical representations that show the variations in intensity at the receiving plane. These illustrations indicate that initial beam parameters, such as topological charge, beam order, modification parameters, and FRFT parameters like fractional order and truncation parameter, significantly impact the beam's intensity distribution. The intensity evolution of the beam within the FRFT system demonstrates a periodic dependence on the fractional order. Our findings offer a convenient method for laser beam shaping.