Control of the orbital angular momentum via radial numbers of structured Laguerre-Gaussian beams

Fourier reciprocity between generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian beams carrying orbital angular momenta

We explore two distinct families of orbital angular momentum carrying light beams, which we refer to as generalized elliptical Gaussian and elegant elliptical Hermite-Gaussian vortex beams, respectively. We show that the fields of the two vortex families are related via a Fourier transform. Hence, one family can be viewed as a source of the far-field intensity distribution of the other and vice versa. We also examine the orbital angular momentum evolution of both beam families on their free space propagation and establish a relationship between the orbital angular momentum, TC, and beam ellipticity factors. Our results may find applications to optical communications and imaging with structured light.

Super bursts of the orbital angular momentum in astigmatic-invariant structured LG beams

A structured Laguerre-Gaussian (sLG) beam in an optical system with an astigmatic element acquires additional degrees of freedom in the form of changing the fine structure of the beam, its orbital angular momentum (OAM), and topological charge. We have theoretically and experimentally revealed that at a certain ratio between the beam waist radius and the focal length of the cylindrical lens, the beam turns into an astigmatic-invariant one, and such a transition does not depend on the beam radial and azimuthal numbers. Moreover, in the vicinity of the OAM zero, its sharp bursts occur, the magnitude of which significantly exceeds the initial beam OAM and grows rapidly as the radial number increases.