Perfect vortex beam: Fourier transformation of a Bessel beam

Abstract

We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel-Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel-Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber.

Optimal focusing of a beam in a ring vortex

“…Our discussion and results are connected with previous works dealing with the so called perfect vortex [13][14][15][16], which is an infinitely narrow RV with arbitrary integer topological charge. It is clear that this ideal field cannot be generated in practice.…”

“…In this case, the last two factors in the plate transmittance, Eq. (12), corresponds to the helical axicon (HA) [16]. This phase plate generates RVs with smaller peak intensities and wider bright annuli in comparison to optimal RVs.…”

“…As occurs in conventional focusing, the generation of an infinitely narrow RV [13][14][15][16] is impossible. Therefore, it is important to establish the optimal approximation to this field that can be physically implemented.…”

3.36-Tbit/s OAM and Wavelength Multiplexed Transmission over an Inverse-Parabolic Graded Index Fiber

“…The second branch is collimated, polarized with a linear polarizer (LP) and reflected by a phase-only spatial light modulator (SLM) for conversion to OAM mode of l = +2. On SLM-1, the technique of 'perfect' optical vortex generation is applied [8]. The generated mode of l = +2 is again equally divided into two portions with a beam splitter (BS): one of the beams is reflected with an odd number of mirrors (MR) to reverse the OAM order as l = -2, and the polarization of the other is rotated by π/2 with a half-wave plate (HWP).…”

High-directional vortex beam emitter based on Archimedean spiral adiabatic waveguides

“…In the design presented in this letter, the Archimedean spiral replaces the closed cavity of the micro-ring, enabling the spatial modulation of the source in the radial direction, in order to concentrate the emitted power into a ring of stronger intensity with far less pronounced side lobes. This principle is similar to the approach used for generating the so-called perfect vortex beam [18], which is usually realized by adding a radial modulation function to the conventional phase mask implemented with spatial light modulator [19,20].…”