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We have demonstrated efficiency of employing the ABCD matrix approach to transform higher-order structured Laguerre–Gaussian (sLG) beams into structurally stable astigmatic sLG (asLG) beams, highlighting their dynamics at propagating. Radical transformations of the beam structure by a cylindrical lens form not only orbital angular momentum (OAM) fast oscillations and bursts, but also make the asLG beams structurally unstable in propagation through cylindrical and spherical lenses when focusing paraxially. But, if the spherical lens performs a Fourier transform of the asLG beam after a cylindrical lens, the symmetric beam emerges at the lens focal plane with a sharp OAM dip; then, the OAM restores its former astigmatism, becoming structurally stable at the far diffraction domain. By investigating the beam structure at the focal area, we have showed that the OAM sharp dip is associated with nothing less than the process of dividing the OAM into the vortex and astigmatic constitutes predicted by Anan'ev and Bekshaev. [ABSTRACT FROM AUTHOR]

We have developed a structured beams theory, computer simulation and experiment that have lost rotational symmetry and propagate in a medium with a general astigmatism. It transpires that the astigmatic medium brings to light such hidden properties of the structured beams as a sharp growing of the orbital angular momentum exceeding the sum of the radial and azimuth numbers, as well as the effect of the beam structure following the cylindrical lens rotation. [ABSTRACT FROM AUTHOR]