Full characterisation of Airy beams under physical principles

The propagation characteristics of Airy beams is investigated and fully described under the trav-eling waves approach analogous to that used for non-diffracting Bessel beams. This is possible when noticing that Airy functions are in fact Bessel functions of fractional order 1 3. We show how physical principles impose restrictions such that the non-diffracting Airy beams cannot be of infinite extent as has been argued, and introduce for the first time quantitative expressions for the maximum transverse and longitudinal extent of Airy beams. We show that under the appropriate physical conditions it is possible to obtain higher-order Airy beams. Bessel beams are known to belong to a class of optical beams described by the (2 + 1)-dimensional Helmholtz equation, and they have the property of being non-diffracting [1, 2] and self-healing [3, 4] on propagation. Originally, Bessel beam properties have been studied using the diffraction Rayleigh-Sommerfeld or Fresnel-Kirchhoff integrals. Implicitly, this approach consider