Control of giant orbital angular momentum bursts of structured Laguerre-Gaussian beams in a medium with general astigmatism

We examined theoretically and experimentally the influence of astigmatic elements (for exam-ple, a cylindrical lens) on a structured Laguerre-Gaussian beam (sLG) when the lens axes are di-rected at an arbitrary angle to the laboratory coordinate axes (a general astigmatism). Although a structurally stable Laguerre-Gaussian (LG) beam contains a great number of axisymmetric modes (in the LG basis) with matching phases and amplitudes, their superposition already loses its origi-nal axial symmetry, but acquires new properties (for example, fast oscillations of the orbital angu-lar momentum (OAM)), while the beam OAM cannot exceed the azimuthal number $\ell$ of the original LG mode. The loss of axial symmetry occurs due to bringing phase and amplitude perturbations into each mode of the sLG beam, which destroy the ring dislocations. Since degenerate ring dislocations are formed by optical vortices with opposite topological charges, but with equal weights, their destruction is accompanied by appearing of vortex pairs in the form of topological dipoles (their number is equal to the radial number $n$). As a result, the mode spectrum of the sLG is extended to the value $\pm(2n+\ell)$. The astigmatic element (cylindrical lens) violates the equality of vortex weights in the dipoles, which leads to a sharp growing the OAM of the sLG beam. Moreover, the OAM can be controlled by changing the rotation of the cylindrical lens axes and the control parameters of the sLG beam. It is these processes that are discussed in detail in our article, both in theoretical and experimental aspects. We show that with a certain orientation of the cylindrical lens axes, the beam OAM can exceed the sum of the orbital and azimuthal numbers $(OAM>n+\ell)$. Besides, we reveal that the intensity pattern of the astigmatic sLG beam can follow the rotation of the astigmatic element axes (the effect of the beam structure following the cylindrical lens axes) at certain relations between control parameters of the sLG beam and the astigmatic element.