Worku Norman G, Gross Herbert
J Opt Soc Am A Opt Image Sci Vis. 2020 Feb 1;37(2):317-326. doi: 10.1364/JOSAA.382133.
A new kind of pulsed beam, which we call a spatially truncated Gaussian pulsed beam, is defined to represent a Gaussian pulsed beam that is diffracted from a semi-infinite hard aperture. The analytical equations for the propagation of the spatially truncated Gaussian pulsed beam through a nonrotationally symmetric paraxial system with second-order dispersion is derived starting from the generalized spatiotemporal Huygens integral. The spatially truncated Gaussian pulsed beam is then combined with the conventional Gaussian pulsed beam decomposition method to enable the modeling of diffraction of a general ultrashort pulse from an arbitrarily shaped hard aperture. The accuracy of the analytical propagation equation derived for the propagation of the truncated Gaussian pulsed beam is evaluated by a numerical comparison with diffraction results obtained using the conventional pulse propagation method based on the Fourier transform algorithm. The application of the modified Gaussian pulsed beam decomposition method is demonstrated by propagating an ultrashort pulse after a circular aperture through a dispersive medium and a focusing aspherical lens with large chromatic aberration.
一种新型的脉冲光束，我们称之为空间截断高斯脉冲光束，被定义为表示从半无限硬孔径衍射出的高斯脉冲光束。从广义时空惠更斯积分出发，推导了空间截断高斯脉冲光束通过具有二阶色散的非旋转对称傍轴系统传播的解析方程。然后将空间截断高斯脉冲光束与传统的高斯脉冲光束分解方法相结合，以实现对任意形状硬孔径的一般超短脉冲衍射的建模。通过与基于傅里叶变换算法的传统脉冲传播方法获得的衍射结果进行数值比较，评估了为截断高斯脉冲光束传播推导的解析传播方程的准确性。通过使圆形孔径后的超短脉冲通过色散介质和具有大色差的聚焦非球面透镜，展示了改进的高斯脉冲光束分解方法的应用。
