Pearcey beams carrying orbital angular momentum

We have obtained a new solution of the paraxial Helmholtz equation, which describes a two-parameter family of structurally stable three-dimensional vortex circular Pearcey beams with their complex amplitude expressed through a degenerate hypergeometric function. The vortex Pearcey beams have an orbital angular momentum and the auto-focusing property, and propagate along an accelerating trajectory toward their focus, where the intensity ring of the beam is "sharply" reduced in diameter. An explicit expression has been obtained for the complex amplitude of vortex circular Pearcey-Gaussian beams, which also have the auto-focusing property.