Rotating elegant Bessel-Gaussian beams

We considered a new three-parameter family of rotating asymmetric Bessel-Gaussian beams (aBG-beams) with integer and fractional orbital angular momentum (OAM). Complex amplitude of aBG-beams is proportional to a Gaussian function and to $n$-th order Bessel function with complex argument. These beams have finite energy. The asymmetry ratio of the aBG-beam depends on the real parameter c $\geq 0$. For $c = 0$, the aBG-beam coincides with the conventional radially symmetric Bessel-Gaussian beam, with increasing c intensity distribution of the aBG-beam takes the form of Crescent. At $c \gg 1$, the beam is widening along the vertical axis while shifting along the horizontal axis. In initial plane, the intensity distribution of asymmetric Bessel-Gaussian beams has a countable number of isolated zeros located on the horizontal axis. Locations of these zeros correspond to optical vortices with unit topological charges and opposite signs on different sides of the origin. During the beam propagation, centers of these vortices rotate around the optical axis along with the entire beam at a non-uniform rate (for large $c \gg 1$): they will rotate by $45$ degrees at a distance of the Rayleigh range, and then by another $45$ degrees during the rest distance. For different values of the parameter c zeros in the transverse intensity distribution of the beam change their location and change the OAM of the beam. Isolated intensity zero on the optical axis corresponds to an optical vortex with topological charge of $n$. Laser beam with the shape of rotating Crescent has been generated by using a spatial light modulator.