Nonparaxial shape-preserving Airy beams with Bessel signature
  Spatially accelerating beams that are solutions to the Maxwell equations may propagate along incomplete circular trajectories, after which diffraction broadening takes over and the beams spread out. Taking these truncated Bessel wave fields to the paraxial limit, some authors sustained that it is recovered the known Airy beams (AiBs). Based on the angular spectrum representation of optical fields, we demonstrated that the paraxial approximation rigorously leads to off-axis focused beams instead of finite-energy AiBs. The latter will arise under the umbrella of a nonparaxial approach following elliptical trajectories in place of parabolas. Deviations from full-wave simulations appear more severely in beam positioning rather than its local profile. 
Carlos J. Zapata-Rodriguez and Mahin Naserpour
physics.optics