Optimal phase element for generating a perfect optical vortex

We derived exact analytical relationships to describe the complex amplitude of a perfect optical vortex generated by means of three different optical elements, namely, (i) an amplitude-phase element with a transmission function proportional to a Bessel function, (ii) an optimal phase element with a transmission equal to the sign function of a Bessel function, and (iii) a spiral axicon. The doughnut intensity was shown to be highest when using an optimal phase element. The spiral-axicon-aided diffraction ring was found to be twice as wide as when generated using two other elements. Thus, the optimal filter was shown to be best suited for generating a perfect optical vortex. The simulation results were shown to corroborate theoretical predictions, with the experiment being in agreement with theory and simulation.