Half Pearcey laser beams

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