Nonlinear dynamics and self-healing properties of elliptical Airy beams in Kerr media

TL;DR

This paper theoretically investigates how elliptical Airy beams propagate in Kerr media, revealing their enhanced stability, extended propagation, and improved self-healing properties under nonlinear conditions, with implications for long-distance laser transmission.

Contribution

It provides a comprehensive theoretical analysis of the nonlinear propagation and self-healing of elliptical Airy beams in Kerr media, identifying optimal input power for maximum stability and distance.

Findings

EABs exhibit longer propagation distances in nonlinear media.

Moderate power EABs show improved self-healing after obstruction.

Optimal input power enhances stability and propagation length.

Abstract

By numerically solving the nonlinear Schr\"odinger equation, we theoretically study the nonlinear propagation dynamics and self-healing properties of elliptical Airy beams (EABs) propagating in water under Kerr nonlinearity. Compared to linear propagation, EABs exhibit extended propagation distances and enhanced stability in nonlinear media. Furthermore, particular emphasis is placed on the impact of Kerr nonlinearity strength on the propagation and self-healing properties of EABs. By varying the input power, it is found that EABs within a moderate power range can propagate longer distances while maintaining higher intensity and exhibit improved robustness after being blocked, indicating better self-healing performance. Based on this analysis, we propose an optimal input power for EABs through a quantitative analysis of the impact of Kerr nonlinearity, enabling them to achieve the greatest propagation distance and maintain the highest stability. Our work provides a comprehensive theoretical understanding of the nonlinear propagation dynamics and self-healing properties of EABs, with their superior characteristics potentially applicable to long-distance laser transmission.