Vortex sensing diffraction gratings

Abstract

We demonstrate a specially designed vortex sensing diffraction grating that generates multiple vortex patterns in the different diffracted orders. When this grating is illuminated with a separate vortex beam, the sign and order of the topological charge of the incident beam can be easily detected. Experimental results are shown for a variety of vortex beams including fractional values of the topological charge, and where both the diffraction grating and incident vortex illumination beam are generated by two different liquid crystal displays (LCDs). The programmability offered by the LCDs offers extremely convenient flexibility.

Vortex sensing analysis of radially and pseudo-radially polarized beams

“…1 because intensity measurements are insensitive to the additional phase terms. In previous work, 12 we proposed a vortex sensing diffraction grating that, as we show here, is well suited for the identification of these two polarization states.…”

“…12,13 We first form the product V l ðϕÞG γ ðxÞ of a two-dimensional (2-D) vortex producing phase pattern V l ðϕÞ ¼ expðilϕÞ with a linear phase diffraction grating pattern G γ ðxÞ ¼ expðiγxÞ. Here x is the horizontal spatial coordinate, γ ¼ 2π∕d where d is the period of the grating and the variable l represents the topological charge of the vortex producing phase pattern.…”

“…First, we employed binary π phase gratings (i.e., with values AE1) where we varied the width (w) of the þ1 region compared with the grating period (d). 12 In a second approach, we obtained equal values for the coefficients by using a Dammann grating approach. 15 Finally, we utilized a new approach where the coefficients could be varied such that the higher charges had a greater coefficient 16 by applying the theory for the optimal phase beam splitters.…”

Techniques to measure complex-plane fields

“…In many investigations into the quantum nature of these beams, it is necessary to be able to detect the amount of OAM carried by the beam. There already exists a number of methods used in determining the topological charge of an optical vortex such as computer-generated holograms [14], interferometers [15,16] and SLMs [17,18].…”

Measuring the topological charge of vortex beams by using an annular ellipse aperture

“…Recently, Hickmann et al [11] observed the generation of a truncated triangular optical lattice when a vortex beam passed through an equilateral triangular aperture. Moreno and Davis [12] introduced a technique to characterize the topological charge of an optical vortex through its diffraction intensity pattern after a fork-shaped grating. Guo et al [13] found that the far-field diffraction intensity pattern of an optical vortex passing through a circular annular aperture comprises some bright and dark rings, and the number of the bright rings is just equal to the topological charge value of the measured optical vortex.…”