Anomalous Propagation Characteristics of Airy Beam in Nonlinear Kerr Media

Li Shao,Yun-Long Wu,Qing Ye

doi:10.3390/cryst11080879

Abstract

The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Airy spatial solitons can also be formed, which are similar to the states formed in the interaction between two Airy beams in nonlinear media. This quasi-equilibrium state is formed by the interaction of the main soliton beam and side lobes of Airy beam due to their different propagation trajectories in the nonlinear media. Moreover, it has been shown the Airy spatial solitons in tree structure can be formed by adjusting the initial parameters in the interaction between the Airy beam and Kerr media.

Highlights

In 1979, Berry and Balazs first demonstrated that there existed a special solution to the Schrödinger equation which was called “Airy packet” in the context of quantum mechanics [1]
Due to the fact it is hard to acquire the accurate solution for Equation (1), we utilize the split-step Fourier method to investigate the propagation characteristics of a single Airy beam in nonlinear Kerr media with the initial condition of a 1D finite Airy beam, which can be expressed as φ(ξ = 0, s) = Ai(s) exp(as) where a is the decay factor, and the Ai(·) represents the Airy function [31]
By continuing to increase the initial amplitude of the Airy beam, as shown in Figure 1c, the diffraction effect and the nonlinear Kerr effect of an incident beam propagating in the media reach a preliminary balance, so the generation of breathing optical soliton and the formed spatial soliton propagating along the path of straight line can be observed

Summary

Introduction

In 1979, Berry and Balazs first demonstrated that there existed a special solution to the Schrödinger equation which was called “Airy packet” in the context of quantum mechanics [1]. Fascinating Airy beams, which had the characteristics of non-diffraction, self-acceleration and self-healing, were first realized by utilizing a liquid crystal spatial light modulator in the experiments [3]. It has been shown that the stable spatial solitons can be formed when the Airy beam propagates in the nonlinear media and interacts with the media. More and more works are being concentrated on the propagation characteristics of the Airy beam in different kinds of nonlinear media [20,21,22]. The study on the anomalous propagation characteristics of a single Airy beam in nonlinear Kerr media has barely been reported. The impacts of different initial parameters on the formation and evolution of Airy spatial solitons in the nonlinear Kerr media were investigated through numerical simulation. We hope our work can provide some theoretical groundwork for future experimental study on the propagation characteristics control of Airy beams in nonlinear media

Theoretical Model

Numerical Simulation and Results Analysis

Conclusions