Generalised quantised spiral beams

A generalisation is found of previously known quantised spiral beams in the form of closed non-self-intersecting plane curves. An analytic expression is obtained for the distributions of the complex amplitudes of the fields of these beams. It is shown that the intensity of such light fields can reach zeros on the generating curve and the generalisation allows the number of zeros to be controlled inside the closed curves, which is important for applied problems. The issue of the extremal properties of the orbital angular momentum of generalised quantised spiral beams is investigated.