# Propagation Characteristics of High-Power Vortex Laguerre-Gaussian Laser Beams in Plasma
## 6 Conclusions  
In this article, the propagation characteristics of Laguerre-Gaussian vortex laser beams in plasma is modeled and simulated under the given parameters. By using the FDTD method, the numerical methodology for modeling the nonlinear permittivity and generating the LG beams is proposed. The simulation results about the 3D dynamic interaction of high-power LG beams with plasma are illustrated and discussed. The obtained simulation results verify the self-focusing and stochastic absorption phenomena of high-power laser beam propagation in plasma. Our work presents the methodology for the numerical simulations of the complex interaction of high-power Laguerre-Gaussian vortex laser beams with plasma by using the FDTD method. It provides detailed information about the dynamic 3D evolution of both the light field of the laser beam and the spatial distribution of electron density and many special laser beams can be simulated based on the TF/SF technique. This is much superior to the state-of-the-art studies [9; 10; 11] that were conducted only by solving the scalar wave equation based on the WKB method with complex eikonal function assumption and paraxial approximation, where only a simple laser beam of large beam size can be calculated and only the limited information such as the variation of beam size can be obtained. This research embraced the potential merits of theory models and simulation techniques for many research applications such as the laser machining and laser-driven inertial confined fusion.  
**Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/8/5/665/s1](http://www.mdpi.com/2076-3417/8/5/665/s1)]([http://www.mdpi.com/2076-3417/8/5/665/s1](http://www.mdpi.com/2076-3417/8/5/665/s1)). Video S1: Longitudinal views of high-power doughnut-shaped LG01 laser beam in plasma, Video S2: Cross-sectional views of high-power doughnut-shaped LG01 laser beam in plasma, Video S3: Longitudinal views of high-power doughnut-shaped LG01 laser beam in plasma, Video S4: Longitudinal views of high-power doughnut-shaped LG01 laser beam in plasma, Video S5: Longitudinal views of high-power doughnut-shaped LG01 laser beam in plasma, Video S6: Longitudinal  
double-ring-shaped LG12 laser beam in plasma, Video S4: Cross-sectional views of high-power double-ring -shaped LG12 laser beam in plasma.  
**Author Contributions:** [PERSON] provided the original ideas; [PERSON] proposed the physical models, [PERSON] designed the algorithms; [PERSON] performed the simulation experiments; [PERSON] processed the data of simulation results; [PERSON] wrote the article.  
**Acknowledgments:** The authors are grateful to the support by the Natural Science Foundation of China under grant Nos. 61575070, 61605049, 11774103, and 61101007; the Fujian Province Science Fund for Distinguished Young Scholars under grant No. 2015J06015; the Key Program of Natural Science Fund for Young Scholars of Fujian Provincial Universities under grant No. JZ160408; the Promotion Program for Young and Middle-Aged Teachers in Science and Technology Research of Huaqiao University under grant No. ZQN-YX203; the Research Fund of Huaqiao University under grant No. 13 BS408.  
**Conflicts of Interest:** The authors declare no conflict of interest.