梁通过尖边界边界条件时的解析解
Analytical Solutions for Beams Passing Apertures with Sharp Boundaries
摘要：
详细阐述了一个近似的衍射光束的傍轴传播，与一维和二维截面，这是从尖锐的边界孔径释放。近似适用于任何梁的条件下，其边缘的厚度是远远小于任何其他长度尺度的梁的初始轮廓。这种近似可以很容易地推广到任何光束的初始轮廓有几个尖锐的功能。因此，该方法可以作为研究光束在复杂障碍物上衍射的一种工具。分析结果进行了比较，数值解和实验结果，这表明近似的高精度。对于由尖锐边界限制的初始均匀场，该解对于任何传播距离和任何边缘尖锐度都是精确的。因此，它可以作为一个有效的工具来表示的光束，由一系列的狭缝具有复杂的结构，由一个简单的，但精确的解析解。
英文摘要：
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
