Orbital angular momentum burst control in astigmatic structured beams in ABCD-matrix transforms

We developed and experimentally implemented an ABCD matrix formalism for describing structural transformations and orbital angular momentum of structured Laguerre-Gaussian beams in an astigmatic optical system containing cylindrical and corrective spherical lenses. It was shown that the matrix formalism not only agrees well with the method of integral astigmatic transformations, but also significantly expands the scope of its application. It was found that a corrective spherical lens is capable of not only separating the vortex and astigmatic components of the orbital angular momentum, but also transforming a structurally unstable astigmatic Laguerre-Gaussian beam after a cylindrical lens into a structurally stable one, provided that the form of fast oscillations and bursts of the orbital angular momentum is preserved.