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 astigmatic invariance are q-phase parameter LG (sLG) beam is equal to arctangent ratio Rayleigh length z0 focal fcyl a cylindrical lens single amplitude epsilon;=1. For rest values, epsilon;NotEqual;1, condition set by equality orbital angular momenta (OAM) sLG (asLG) beams. also found sharp spikes dips OAM asLG region where turns into zero. height depth these significantly exceed maximum minimum values conventional It has been shown occurrence caused radical restructuring mode spectra form their strong ordering. Theoretical calculations, accompanied computer simulation, an experiment agree well with each other.