Airy beams and waves

Abstract

The Airy functions were analyzed by Kalnins and Miller [1], and the Airy beams were introduced by Berry and Balazs [2] in the context of quantum mechanics. There are other investigations into the properties of the Airy wave packets [3,4]. The original Airy beam cannot be physically realized because infinite power is required to excite the beam. Siviloglou and Christodoulides [5] have introduced a physically realizable Airy beam, and the various properties of this beam have been investigated [6,7]. Bandres and Gutierrez-Vega [8] have analyzed the generalized Airy-Gauss beams that are also physically realizable. All these investigations pertain only to the beams that satisfy the paraxial wave equation. Yan, Yao, Lei, Dan, Yang, and Gao [9], using the virtual source method, have extended the analysis to full Airy waves governed by the exact Helmholtz equation. In this chapter, some aspects of Airy beams and waves are treated. The fundamental Airy beam and the “finite-energy”(modified) fundamental Airy beam are discussed. The fundamental Airy beam is generalized to obtain the full-wave solution, namely the fundamental Airy wave. For the fundamental Airy wave, the radiation intensity distribution is found to be the same as that for a point electric dipole situated at the origin and oriented normally to the propagation direction. A treatment of the basic full modified Airy wave by the use of the complex space source theory is provided. The propagation characteristics of the basic full modified Airy wave are found to be the same as those for the basic full Gaussian wave, provided that for the former an equivalent waist and an equivalent Rayleigh distance are introduced.