  In practice, Airy beams can only be reproduced in an approximate manner, with
a limited spatial extension and hence a finite energy content. To this end,
different procedures have been reported in the literature, based on a
convenient tuning of the transmission properties of aperture functions. In
order to investigate the effects generated by the truncation and hence the
propagation properties displayed by the designed beams, here we resort to a new
perspective based on a trajectory methodology, complementary to the density
plots more commonly used to study the intensity distribution propagation. We
consider three different aperture functions, which are convoluted with an ideal
Airy beam. As it is shown, the corresponding trajectories reveals a deeper
physical insight about the propagation dynamics exhibited by the beams analyzed
due to their direct connection with the local phase variations undergone by the
beams, which is in contrast with the global information provided by the usual
standard tools. Furthermore, we introduce a new parameter, namely, the escape
rate, which allow us to perform piecewise analyses of the intensity
distribution without producing any change on it, e.g., determining
unambiguously how much energy flux contributes to the leading maximum at each
stage of the propagation, or for how long self-accelerating transverse
propagation survives. The analysis presented in this work thus provides an
insight into the behavior of finite-energy Airy beams, and therefore is
expected to contribute to the design and applications exploiting this singular
type of beams.
