Abstract In this paper, the dynamic evolution of Gaussian beam governed by the two-dimensional fractional Schrodinger equation with variable coefficient is studied. The influences of the longitudinal modulation, the Levy index and the chirp parameters on the evolution of the Gaussian beam are discussed in detail. The results show that in the absence of the beam chirp, the unchirped Gaussian beam is axisymmetric and exhibits a ring-shaped structure, but due to the longitudinal modulation, the size of the ring will change. In the presence of the beam chirp, the axisymmetry is broken and optical beam in propagation exhibits a crescent structure. In the longitudinal periodic modulation, the chirped Gaussian beam oscillates periodically along a certain direction. The influence of the Levy index on the evolution of the Gaussian beam is also studied, and the result shows that the increasing of the Levy index will enhance the diffraction of the optical beam in propagation.

中文翻译：

---

基于二维分数阶薛定谔方程的高斯光束传播

摘要 本文研究了二维变系数分数阶薛定谔方程控制的高斯光束的动力学演化问题。详细讨论了纵向调制、Levy指数和chirp参数对高斯光束演化的影响。结果表明，在没有光束啁啾的情况下，未啁啾的高斯光束是轴对称的，呈现环形结构，但由于纵向调制，环的尺寸会发生变化。在光束啁啾的存在下，轴对称性被破坏，传播中的光束呈现出新月形结构。在纵向周期调制中，啁啾高斯光束沿某个方向周期性振荡。还研究了 Levy 指数对高斯光束演化的影响，