Generation of Airy solitary-like wave beams by acceleration control in inhomogeneous media

Abstract

We investigate the propagation of Airy beams in linear gradient index inhomogeneous media. We demonstrate that by controlling the gradient strength of the medium it is possible to reduce to zero their acceleration. We show that the resulting Airy wave beam propagates in straight line due to the balance between two opposite effects, one due to the inhomogeneous medium and the other to the diffraction of the beam, in a similar way as a solitary wave in a nonlinear inhomogeneous medium. Going even further we were able to invert the sign of the acceleration of the beam.

Full characterization of Airy beams under physical principles

“…Thus, substituting s = 2λ in Eq. (26) and solving for l c , we can get the position s max (l c ), where the oscillations of the Airy profile must dampen.…”

“…However, the Airy functions also appear in the description of the propagating modes in inhomogeneous media, in particular in one-dimensional linear gradient-index media [24][25][26].…”

“…For the particular case of the linear potential [36], the standing Airy wave packet arises from considering a particle subject to a constant force, e.g., gravitational force, so that when it takes the value of zero, the particle wave packet is still described by the Airy function but is accelerating away from the infinite wall as a consequence of removing the stabilizing force [26].…”

Structure invariant wave packets

“…From Eqs. (15) and (16), it is also clear that different values of α must be considered if the zeroth order or the first order solutions are going to be used. In [16] we present a discussion on the election of this parameter in the realm of classical optics.…”

Airy beam induced optical routing

“…This so-called Airy beam has already been utilized for many different applications ranging from abruptly autofocusing waves [14] to optical snowblowers in micromanipulation experiments [15]. Moreover, recent works introduced further ideas for controlling the trajectory of accelerated beams [16][17][18][19] and some of them support even arbitrary paths [20,21]. In the following, we introduce an adaptive all-optical routing technique based on these beams.…”