Controllable two-dimensional diffraction-free polygon beams

This paper investigates diffraction-free Laguerre-Gaussian solutions of the two-dimensional paraxial wave equation in linear media, which are described by the radial and angular mode numbers, and constitute some diffraction-free polygon beams, constructed through the linear superposition principle. By selecting appropriate values of the two mode numbers and modulation depth, we generate triangular, quadrilateral, pentagonal and hexagonal structures at their center location. Depending on the nature of superposing beams, the central polygons could be bright or dark. We explore the influence of relevant parameters on the light field in detail and discuss some characteristics of their contour plots. Since the construction of polygon beams is realized by the superposition of Laguerre-Gaussian modes, which represent common forms of stable transmissions through optical fibers, this method could be of great significance for the practical realization of polygon beams in optical fibers, in the future. (C) 2022 Elsevier B.V. All rights reserved.