Propagating parabolic rotational beams, new family of accelerated beams

Abstract

A novel class of structured propagating waves with parabolic rotational symmetry is introduced for the first time. These are described by exact solutions of the non-paraxial Helmholtz equation. As a result of the separability of the Helmholtz equation, the intensity of these wavefields remains invariant while propagating along parabolic trajectories, thus exhibiting apparent acceleration. We will show that superposition of the fundamental traveling waves can present parabolic, spherical or even rectilinear propagation.