Airy laser beams with hyperbolic trajectory in near field

From our review of the papers on accelerating beams and Airy beams (AB) it follows that the well-known types of AB are propagating along parabolic trajectories, while accelerating beams, which propagate along nonparabolic trajectories, do not have an analytical description in the Fresnel zone. Further in the paper we consider the second kind of AB. These beams are also accelerating, have an analytic expression in the Fresnel zone, propagate along a hyperbolic trajectory and can be generated with a phase mask having a cubic dependence on the transverse coordinate.