Product of Two Laguerre–Gaussian Beams

We show that a product of two Laguerre–Gaussian (pLG) beams can be expressed as finite superposition conventional LG with particular coefficients. Based on such an approach, explicit relationship is derived for the complex amplitude pLG in Fresnel diffraction zone. Two identical duet produce case “squared” Fourier-invariant beam, termed (LG)2 beam. For described by Laguerre polynomials azimuthal numbers n − m and + m, expression Fourier plane derived. Similar to beams, utilized information transmission, they are characterized orthogonal carry orbital angular momentum equal their topological charge.