Huge spikes and dips of the orbital angular momentum in structured Laguerre-Gaussian beams resistant to simple astigmatism

The article investigated conditions for shaping astigmatic-invariant structured Laguerre-Gaussian (LG) beams in the case of simple astigmatism. We have theoretically and experimentally confirmed that the conditions of astigmatic invariance are that the $\theta$-phase parameter of the structured LG (sLG) beam is equal to the arctangent of the ratio of the Rayleigh length $z_0$ to the focal length $f_{cyl}$ of a cylindrical lens for a single amplitude parameter of $\varepsilon=1$. For the rest amplitude parameter values, $\varepsilon\neq1$, the astigmatic invariance condition is set by the equality of the orbital angular momenta (OAM) of structured sLG and astigmatic-invariant sLG (asLG) beams. We have also found sharp spikes and dips of the OAM in astigmatic asLG beams in the region where OAM turns into zero. The height and depth of these spikes and dips significantly exceed the maximum and minimum OAM values in the conventional structured sLG beams. It has been shown that the occurrence of spikes and dips of the OAM is caused by a radical restructuring of the LG mode spectra in the form of their strong ordering. Theoretical calculations, accompanied by a computer simulation, and an experiment agree well with each other.