Airy beam with a hyperbolic trajectory

The well-known Airy beams are generated when a transparency with a cubic phase put at the focal distance from a spherical lens is illuminated by a Gaussian beam. In this case, a diffraction-free Airy beam that propagates with acceleration on a parabolic path is generated behind the spherical lens's focus. We have shown that directly behind the cubic-phase transparency there is a path section on which the Airy beam is propagating with acceleration on a hyperbolic path. We refer to the Airy beam on the hyperbolic path section as a Hyperbolic Airy (HA) beam. The HA beams notably show the linear divergence, the nonuniform acceleration, rapidly decaying with distance, and the “center of gravity” shifting linearly with distance in the absence of the linear phase in the initial field, with the acceleration being by an order of magnitude higher than that of the Airy beam on the parabolic path section.