Exploring the dynamics of finite-energy Airy beams: a trajectory analysis perspective

Abstract

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.