Polygonal Laguerre-Gauss beams

We demonstrate that Laguerre-Gauss (LG) beams can have a polygonal distribution with the radial and azimuthal components, the so-called polygonal Laguerre-Gauss beams. These light beams are generated with a linear and trigonometric phase function of the angular coordinate which transform the Perfect LG beams with a lens. The polygonal Laguerre-Gauss beams preserve their distribution within a maximum propagation distance without diffraction similar to that used in the propagation-invariant light fields. We expect that these polygonal Laguerre-Gauss beams will be a method for creating any distribution controlling the radial and azimuthal components; moreover, they can be a proposal to control the number of the ring structures of the light beams.