  The propagation characteristics of Airy beams is investigated and fully
described under the traveling 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 . We show how
physical 3 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.
