Airy beam propagation: autofocusing, quasi-adiffractional propagation, and self-healing

Abstract

We study the propagation of superpositions of Airy beams and show that, by adequately choosing the parameters in the superposition, effects as opposite as autofocusing and quasi-adiffractional propagation may be obtained. We also give a simple analytical expression for free propagation of any initial field, based on so-called number states (eigenstates of the quantum harmonic oscillator), that allows us to study their self-healing properties.

Self-healing of structured light: a review

“…Instead, the self-healing could be simply modeled via geometric optics [61]. Often, self-healing modes encompass self-accelerating modes, such as Airy [42,62,63] (Fig. 2(c)), Pearcey [43] (Fig.…”

“…Instead, the self-healing could be simply modeled via geometric optics [61]. Often, self-healing modes encompass self-accelerating modes, such as Airy [43,62,63] (figure 2(c)), Pearcey [44] (figure 2(d)), accelerating parabolic [64], accelerating Weber and accelerating Mathieu beams [45,65] (figure 2(e)). The intensity pattern of such a mode does not evolve perfectly unchanged upon propagation, as in the case of a nondiffracting beam, but instead evolves unchanged along an accelerating trajectory.…”

Generation of Talbot-like fields

“…they remain propagation invariant for distances that are much longer than the usual diffraction length of Gaussian beams with the same beamwidth 16 , self-healing, i.e. they regenerate themselves when a part of the beam is obstructed 17 , and abrupt autofocusing 18,19 , i.e. their maximum intensity remains constant while propagating and close to a particular point they autofocus increasing its maximum intensity by orders of magnitude.…”