Nonparaxial airy pulses at a dielectric layer

Intensive theoretical and experimental investigations of paraxial Airy beams are motivated by their unusual features, such as non-diffractive propagation, parabolic trajectory and self-healing [1–2]. These seminal publications with theoretical formulations based on the paraxial approximation of the wave equation and experimental confirmation were followed by many works on the accelerated Airy beam properties that generate very interesting applications, some of which are already realized [3]. A fundamental remark concerning the causality effects of the phenomenon is made in [4]. It is noted that the spatial and temporal accelerations are physically qualitatively different. According to the authors´ mathematical formulation of the problem, if the accelerated motion is considered in time, the solution requires the backward flow of time. Some physical ideas for overcoming this problem are proposed.