Yeo Joel, Li Hao
J Opt Soc Am A Opt Image Sci Vis. 2020 Mar 1;37(3):368-373. doi: 10.1364/JOSAA.382205.
Research in laser-plasma interaction, high harmonic generation, and filamentation involves Gaussian beams propagating through inhomogeneous media, where the refractive index varies spatially in both the transverse and longitudinal directions. However, most analytical Gaussian beam solutions to the paraxial wave equation for inhomogeneous media are limited to media with the refractive index only varying quadratically in the transverse direction. In this paper, we present a new class of Gaussian beam solutions for a longitudinally varying medium with a transverse quadratic-index profile. We also highlight a few examples from this class of solutions, which include features such as a one-parameter generalization of the free-space Gaussian beam, beam "collimation," beam self-focusing, and the existence of multiple beam waists.
激光与等离子体相互作用、高次谐波产生和丝状化方面的研究涉及高斯光束在非均匀介质中传播，其中折射率在横向和纵向都随空间变化。然而，大多数针对非均匀介质的傍轴波动方程的解析高斯光束解仅限于折射率仅在横向呈二次方变化的介质。在本文中，我们给出了一类新的适用于具有横向二次折射率分布的纵向变化介质的高斯光束解。我们还强调了这类解中的几个例子，其中包括自由空间高斯光束的单参数推广、光束“准直”、光束自聚焦以及多个光束腰的存在等特征。
