Optical vortices with an infinite number of screw dislocations

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.