Abstract
In this paper, we present new type of optical vortex called the squared Laguerre-Gaussian (LG)<sup>2</sup> vortex beam. It is theoretically and numerically proved 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)<sup>2</sup> beam. The presented beams are structurally stable in the case of one intensity ring. The considered beams supplement the basis of LG modes.
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