Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media

Abstract

Abstract:We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, the higher the intensities of interacting beams, the easier to form solitons; when the intensities are small enough, no solitons are generated. Upon adjusting the interval between the launched beams, their interaction exhibits different properties. If the interval is large relative to the width of the first lobes, the generated soliton pairs just propagate individually and do not interact much. However, if the interval is comparable to the widths of the maximum lobes, the pairs strongly interact and display varied behavior.

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

“…Airy beams which are regarded as the zeroth-order Olver beams attract the attention of a lot of scientists of the laser community [24]- [30]. These zeroth-order Olver (Airy) beams have been the subject of many other studies in various optical systems, be it aligned, misaligned, turbulence, crystal, Kerr media [31]- [36] or others. More recently, Liu et al [37] have obtained an approximate analytical expression for the propagation of an Airy-Gaussian beams passing through an ABCD optical system with a rectangular annular aperture.…”

Guided Self-Accelerating Airy Beams—A Mini-Review

“…Indeed, it has been confirmed that Airy beams can exist in photonic lattices and give rise to interesting phenomena, such as accelerating lattice solitons [48]. And we have investigated the interactions of Airy beams in different NL media [29,30]. The governing nonlinear Schrödinger equation (NLSE) can now be written as…”

“…In 2009, Ellenbogen et al produced an Airy beam in an asymmetrically modulated quadratic optical NL medium by the three-wave mixing process [25]. 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].…”

On the dynamics of Airy beams in nonlinear media with nonlinear losses

“…We are interested in an intensity regime where the effects of NLLs are significant, being comparable to, or even dominant over other nonlinear effects (Kerr nonlinearity in our case). This means in particular that the possible solitary structures emerging from the Airy beam due to the Kerr nonlinearity, as described in [10], are significantly affected by NLLs. This condition is fulfilled if the intensity n 0 /(k 2 0 n 2 x 2 0 ) required for soliton formation is higher than, or of the order of the typical intensity (2/β (M) kx 2 0 ) 1/(M−1) at which NLLs are significant.…”

“…It was indeed in Optics where the land was prepared thanks to the re-discovery in the eighties of non-diffracting Bessel beams [4]. Since then huge amount of work has been made on self-accelerating Airy beams, including their properties [5,6], propagation dynamics in different nonlinear media [7][8][9][10][11][12], nonparaxial [13], vectorial [14] and fully nonlinear [15] generalizations, and applications as diverse as particle clearing [16] or creation of curved plasma channels [17]. It seems that this amount of work was necessary to close the circle with the recent creation of genuine quantum Airy wave packets of free electrons [18].…”