Structurally Stable Astigmatic Vortex Beams with Super-High Orbital Angular Momentum (ABCD Matrix Approach)

We have demonstrated efficiency of employing the ABCD matrix approach to transform higher-order structured Laguerre–Gaussian (sLG) beams into structurally stable astigmatic sLG (asLG) beams, highlighting their dynamics at propagating. Radical transformations beam structure by a cylindrical lens form not only orbital angular momentum (OAM) fast oscillations and bursts, but also make asLG unstable in propagation through spherical lenses when focusing paraxially. But, if performs Fourier after lens, symmetric emerges focal plane with sharp OAM dip; then, restores its former astigmatism, becoming far diffraction domain. By investigating area, we showed that dip is associated nothing less than process dividing vortex constitutes predicted Anan’ev Bekshaev.