We investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic (asLG) depends on quantum numbers (n,ℓ) and three parameters. Two them are control parameters initial sLG amplitude ϵ phase θ. third one is ratio Rayleigh length z0 focal f It was theoretically revealed experimentally confirmed that asLG beam ...