ABSTRACT
The solution to the paraxial equation of propagation in the form of Airy functions was first offered by E.G. Kalnins and Jr Miller in 1974. Nonspreading wave packets in the context of quantum mechanics were analyzed by M.V. Berry and N.L. Balazs in 1979. The solution to the two-dimensional paraxial equation as a product of Airy functions was proposed by I.M. Besieris. The key peculiarity of the Airy beam is that its major lobe propagates along a curved trajectory, which has the form of a parabola. Because of this, the Airy beams are called accelerating or ballistic (a body moving only upon the force of gravity takes a parabolic trajectory referred to as ballistic). Non-paraxial accelerating Weber beams that retain their shape upon propagation on a parabolic path have been considered. Being similar to the "half-Bessel" beams, the Weber beams can be described analytically, which is not the case for the "half-Bessel" beams.
