Hyperbolic Airy beams

We discuss finite-energy and infinite-energy Airy beams of the second kind. Similarly to the well-known paraxial Airy beams, these are accelerating beams that can be analytically described in the Fresnel diffraction zone but propagate along a hyperbolic rather than parabolic path over a certain length, with their “gravity center” shifting linearly with distance. The Airy beams of the second kind can be generated near a phase transparency with cubic phase modulation.