Airy-like beams with parabolic accelerating trajectories in non-paraxial case

Abstract

Abstract We propose a new type of the Airy-like beams that can propagate along arbitrary parabolic accelerating trajectories without requiring the paraxial condition. Through the geometrical relation between predesigned parabolic caustic curve and local light rays emitting from initial plane, we derive the explicit expression of initial phase function of Airy-like beams and introduce an amplitude decay function to guarantee beams’ invariable intensity feature along accelerating trajectories. Furthermore, we compare the initial phase and complex amplitude distributions of the proposed beams with those of traditional Airy beams and numerically calculate the propagation of the two kinds of beams using Fourier angular spectrum formula. The results show that: (1) traditional paraxial Airy beams are the asymptotic approximation of Airy-like beams in paraxial condition, and that only propagate along parabolic accelerating trajectory in paraxial condition and ultimately lose their non-diffracting and accelerating features in the far field, (2) unlike the traditional Airy beams, our proposed Airy-like beams also possess these features even in non-paraxial condition and can maintain them up to the far field.