Zhou Junhe, Hu Qingsong
Opt Express. 2023 Nov 6;31(23):38334-38342. doi: 10.1364/OE.504905.
In this paper, what we believe to be a novel class of beams, which are referred to as the spherical Gauss-Laguerre beams, are proposed. The beams propagate stably in the anomalous dispersive media, within which the second order derivative with respect to t could be combined with the two-dimensional (2D) Laplacian operator in the transverse direction and forms a three-dimensional (3D) Laplacian operator, which describes the beam propagation in the z direction within the four-dimensional (4D) x-y-z-t space-time. The wave equation is solved by the variable separation method and the analytical expression for the spherical Gauss-Laguerre beams is derived. The beams have a 3D Gaussian field distribution with a variable beam waist with respect to the propagation distance. Unlike any 2D spatial vortex beams, the 3D beams could possess either the spatial vortex or the spatiotemporal optical vortex (STOV) by choosing the vortex plane in the 3D x-y-t space-time. The derived spherical Gauss-Laguerre beam expression in the 4D space-time is verified by the numerical simulations with excellent agreement.
在本文中，我们提出了一类我们认为是新颖的光束，即球面高斯 - 拉盖尔光束。这些光束在反常色散介质中稳定传播，在该介质中，关于时间(t)的二阶导数可以与横向的二维（2D）拉普拉斯算子相结合，形成三维（3D）拉普拉斯算子，它描述了光束在四维（4D）(x - y - z - t)时空内沿(z)方向的传播。通过变量分离法求解波动方程，并推导了球面高斯 - 拉盖尔光束的解析表达式。这些光束具有三维高斯场分布，其束腰随传播距离变化。与任何二维空间涡旋光束不同，通过在三维(x - y - t)时空中选择涡旋平面，三维光束可以具有空间涡旋或时空光学涡旋（STOV）。通过数值模拟验证了在四维时空中推导得到的球面高斯 - 拉盖尔光束表达式，结果吻合良好。
