Abstract

In a recent study, we have reported a simple, efficient, and robust method that is based on diffraction in an amplitude parabolic-line linear grating for determination of the topological charge (TC), $l$, of an optical vortex beam [J. Opt. Soc. Am. B 37, 2668 (2020) [CrossRef]  ]. Here, we present a demonstration of the application of that method for characterization of a pair of superposed vortex beams having different winding numbers. It is shown that, when two vortex beams, described by Laguerre–Gaussian beams with winding numbers ${l_1}$ and ${l_2}$ and radial index $p = 0$, impinge on-axis and collinearly on a diffraction grating having a quadratic curvature on its lines, with a simple analysis of the resulted diffraction patterns at the zero and first order, the TCs and their signs can be determined. The zero-order diffraction pattern shows an interference pattern of the beams. For close values of ${l_1}$ and ${l_2}$, it has a petal-like pattern in which the number of spots is equal to $|{l_1}{ -} {l_2}|$. It is also found that the first-order diffraction pattern depending to the signs of the beams’ TCs shows two different forms. If ${l_1}$ and ${l_2}$ have the same signs, the first-order diffraction pattern is only a set of elongated intensity spots. When the signs of ${l_1}$ and ${l_2}$ are opposite, the resulted pattern is a $({l_1} + 1)$ by $({l_2} + 1)$ slanted checkered-like matrix of bright spots. In addition, in this work, we use a simple, novel, and initiative method to generate and combine on-axis and collinearly a pair of vortex beams. Finally, a supporting theoretical study is presented that fully confirms the experimental results and simulation of propagation.

© 2021 Optical Society of America

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