Internal perturbations of structured vortex beams: Controlling OAM by radial numbers

We analyzed the mode composition and the orbital angular momentum of structured Laguerre-Gaussian beams, whose HG modes were subjected to harmonic perturbations with multiple phases and equal amplitudes, which is similar to the input of big data arrays into a structured beam in two-parametric regime. It was shown that, at large values of the amplitude parameter and a variation of the phase parameter, a structured beam can change from a standard LG beam to an HG beam, while at low values of the amplitude parameter, the range of beam transformations sharply decreases, capturing only its transition from a vortex state to states with degenerate edge dislocations. We revealed that variations of the radial number of the structured Laguerre-Gaussian beam which is accompanied the orbital angular momentum oscillations, in both the negative and positive areas, over the entire range of changing the phase parameter. As the amplitude parameter increases, the amplitudes of the oscillations smooth out and, in the limit of large values of the amplitude parameter, tend to a smooth cosine form.