Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential

Abstract

We study periodic inversion and phase transition of normal, displaced, and chirped finite energy Airy beams propagating in a parabolic potential. This propagation leads to an unusual oscillation: for half of the oscillation period the Airy beam accelerates in one transverse direction, with the main Airy beam lobe leading the train of pulses, whereas in the other half of the period it accelerates in the opposite direction, with the main lobe still leading - but now the whole beam is inverted. The inversion happens at a critical point, at which the beam profile changes from an Airy profile to a Gaussian one. Thus, there are two distinct phases in the propagation of an Airy beam in the parabolic potential - the normal Airy and the single-peak Gaussian phase. The length of the single-peak phase is determined by the size of the decay parameter: the smaller the decay, the smaller the length. A linear chirp introduces a transverse displacement of the beam at the phase transition point, but does not change the location of the point. A quadratic chirp moves the phase transition point, but does not affect the beam profile. The two-dimensional case is discussed briefly, being equivalent to a product of two one-dimensional cases.

Guided Self-Accelerating Airy Beams—A Mini-Review

“…In the one-dimensional (1D) case, the paraxial propagation of a beam in a linear medium with an external harmonic potential is described by the following equation [58,59]:…”

“…(i) Find the Fourier transforms of ψ(x, 0) = Ai(x) exp(ax) and exp(ibx 2 ), which can be written as [2,4,58,59]:ψ…”

“…By the separation of variables, the 2D problem can be reduced to two 1D cases [59,72]. The result is displayed in Fig.…”

Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs

“…The first experimental demonstration of controling and using simple linear chirped laser pulses was carried by Melinger et al in the early 1990s [28] . In the optical field, a chirp carried by AiBs was introduced by Zhang et al, showing that a linear chirp introduces a transverse displacement of the beam at the phase transition point, but does not change the location of the point [29] . The propagation properties of the chirped Bessel waves were investigated successfully in 2015 [30] .…”

Two-dimensional χ^2 solitons generated by the downconversion of Airy waves

“…Realizations of AWs have been predicted and demonstrated in optics [3]- [9], plasmonics [10]- [12], electron beams [13], and gas discharge [14]. In linear media, the propagation of two-dimensional (2D) factorized AWs has been demonstrated too [1,3,4,15,16].…”