Properties of the squared Laguerre–Gaussian vortices

In this paper, a new type of optical vortex called the squared Laguerre–Gauss (LG)² vortex beam has been investigated. Theoretical conclusions and numerical experiment confirm that these beams are Fourier-invariant and retain their structure at the focus of a spherical lens. In the Fresnel diffraction zone, such a beam is transformed into a superposition of conventional LG beams, the number of which is equal to the number of rings in the (LG)² beam. The presented beams are structurally stable in the case of one intensity ring.