Nonlinear propagation dynamics of finite-energy Airy beams

Abstract

The nonlinear dynamics of intense truncated Airy beams in Kerr ionizing media are investigated from numerical simulations and experiments. We show numerically that a competition between the linear and nonlinear effects takes place and may be modified by tuning the width of the main lobe of the Airy beam and the size of the truncating diaphragm. Our analysis shows that the acceleration of the Airy peak, an inherent feature of linear Airy beam propagation, is preserved only for powers in the main Airy lobe below a certain threshold. Nonlinear propagation of intense Airy beams with low power in the main lobe is sustained by a continuous energy flux from its neighbors, similarly to the mechanism sustaining nonlinear Bessel beam propagation. Airy beams with higher powers in the main lobe are reshaped into a multifilamentary pattern induced by Kerr and multiphoton nonlinearities. The nucleation of new filaments and their interaction affect the acceleration of the main Airy lobes. We finally show that the size of the truncation constitutes a control parameter for the energy flux that features the Airy beam acceleration. Experiments performed in water corroborate the existence of these two distinct nonlinear propagation regimes.

Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets

“…In addition, the Airy beam proves very resilient to perturbations, as it is able to linearly reconstruct (self-heal) itself 5 . Further research activity on Airy beams in the non-linear regime has revealed stationary non-linear 1D solutions 6 , (3 þ 1)D non-linear light bullets 7 , solitons in self-defocusing media 8 and other newly observed spatial mechanisms 9,10 . Recently, the Airy wavepacket concept has also been demonstrated for electron packets 11 .…”

Guided Self-Accelerating Airy Beams—A Mini-Review

“…One can see that the beam profiles are the same except for the inversion, which is in accordance with the theoretical result presented in Eq. (32). This way of generating SF beams is universal, it does not depend on the form of the initial beam.…”

“…This novel nonlinear generation method not only produced an Airy beam at a new wavelength and a higher energy, but also provided new possibilities for manipulating the dynamics of Airy beams in NL media [26][27][28][29][30]. According to the nonlinear Schrödinger equation, the nonlinearity plays a nontrivial role in controlling the persistence as well as the breakdown of Airy beams [31][32][33]. It has been demonstrated that the main lobe of an Airy beam experiences self-phase modulation in NL media that results in the self-focusing or trapping of the beam [28].…”

Semiconductor laser beam bending

“…Nonlinear behaviors [41,42], Helmholtz beams [43], convex trajectories [44], and optical routing [45] have also been discussed. Several studies have been conducted on nonspreading wave packets for the cubic Schrodinger equation with a bounded potential [46], asymptotic expansions for Riesz fractional derivatives of Airy functions and applications [47], stationary nonlinear Airy beams [48], and the dynamic control of the collapse of a vortex Airy beam [49].…”