Trajectory analysis of phase effects associated with truncated Airy beams

Abstract

Airy wave packets constitute a very peculiar type of structured light: during their propagation, their transverse profile undergoes a self-accelerating displacement while it remains shape invariant. They are thus the only non-dispersive beam-type solution to the Helmholtz paraxial equation in free space. Such properties are possible by virtue of their infinite power content. However, experimentally, Airy beams can only be reproduced in an approximate manner, with a limited extension and hence a finite power content. To this end, differentcutoffprocedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In this Communication, we present and discuss our latest advances in the analysis of the effects that convolving an Airy beam with different aperture functions have on their propagation properties. More specifically, we make use of a trajectory-based methodology, which allows us to analyze and explain the beam propagation in terms of trajectories directly connected with the beam local phase variations.