Structurally stable three-dimensional and two-dimensional laser half Pearcey beams

We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional structurally stable half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Opt. Express, 20, 18955 (2012), since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectrum of plane waves, which is non-zero at a half of parabola. For functions of HP-beams complex amplitudes, the orthogonality properties have been revealed. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.