Wave analysis of Airy beams

The Airy beams are analyzed in order to provide a cogent physical explanation to their intriguing features which include weak diffraction, curved propagation trajectories in freespace, and self healing. The asymptotically exact analysis utilizes the method of uniform geometrical optics (UGO), and it is also verified via a uniform asymptotic evaluation of the Kirchhoff-Huygens integral. Both formulations are shown to fully agree with the exact Airy beam solution in the paraxial zone where the latter is valid, but they are also valid outside this zone. Specifically it is shown that the beam along the curved propagation trajectory is not generated by contributions from the main lobe in the aperture, i.e., it is not described by a local wave-dynamics along this trajectory. Actually, this beam is identified as a caustic of rays that emerge sideways from points in the initial aperture that are located far away from the main lobe. The field of these focusing rays, described here by the UGO, fully agrees with the Airy beam solution. These observations explain that the "weakdiffraction" and the "self healing" properties are generated, in fact, by a continuum of sideways contributions to the field. The uniform ray representation provides a systematic framework to synthesize aperture sources for other beam solutions with similar properties in uniform or in non-uniform media.