Asymmetric and astigmatic laser beams with orbital angular momentum : (Invited)

Here we study three different types of astigmatic laser beams (ALB), whose complex amplitude in the Fresnel diffraction zone is described by the complex argument Hermite polynomial of the order (n, 0). The first type is a circularly symmetric optical vortex with a topological charge n after passing through a cylindrical lens. On propagation, the optical vortex "splits" into n first-order optical vortices. Its orbital angular momentum (OAM) per photon is equal to n. The second type is the ALB of order (n, 0), which is generated when an elliptical laser beam passes through a cylindrical lens. The third type is an elliptical optical vortex with a topological charge n after passing through a cylindrical lens. With a special choice of the ellipticity degree (1:3), such a beam retains its structure upon propagation and the degenerate intensity null on the optical axis does not "split" into n optical vortices. Such a beam has fractional OAM not equal to n.