Three-dimensional scalar beam diffraction by a half plane
Three-dimensional scalar beam diffraction by a half plane
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半平面的三维标量光束衍射
DOI：
10.1016/0010-4655(91)90208-3
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发表时间：
1991
影响因子：
6.3
通讯作者：
E. Jull
中科院分区：
文献类型：
--
作者：
G. A. Suedan;E. Jull
复源点技术极大地简化了散射和衍射解中源指向性的包含。通过用适当的复坐标代替其坐标，全向源成为波束源。光源的任何衍射解都成为光束衍射的对应解。用这种方法最容易得到局部光束源的几何衍射理论解。本文将复源点技术应用于几何衍射理论中的正则解：半平面三维标量光束衍射。首先，回顾了标量点源的一般三维解及其向波束源的演化。然后给出了在三维任意入射情况下，经刚性或软半平面的点源和光束源衍射的精确一致渐近解。给出了衍射积分的一种数值计算方法。该方法将带复数参数的菲涅耳积分转换为带复数参数的互补误差函数，并提供了高效的计算机子程序。通过一个算例说明了这一过程，并给出了三维数值图。半平面的电磁（矢量）场三维光束衍射也会得到同样的结果。用均匀几何衍射理论计算三维光束的楔形衍射也是如此，但其表达式更为复杂。
The complex source point technique greatly simplifies the inclusion of source directivity in scattering and diffraction solutions. By replacing its coordinates by appropriate complex coordinates, an omnidirectional source becomes a beam source. Any diffraction solution for the source becomes the corresponding solution for beam diffraction. Geometrical diffraction theory solutions for local beam sources can be most easily obtained in this way. Here the complex source point technique is applied to a canonical solution in geometrical diffraction theory: three-dimensional scalar beam diffraction by a half plane.First, a general three-dimensional solution for a scalar point source and its evolution to a beam source is reviewed. An exact uniform asymptotic solution for point and beam source diffraction by a rigid or soft half plane is then given for arbitrary incidence in three dimensions. A method for numerical evaluation of the diffraction integrals is shown. In this method the Fresnel integrals with complex arguments are converted to complementary error functions with complex arguments, for which efficient computer subroutines are available. The procedure is illustrated by a numerical example and three-dimensional numerical plots are presented.Electromagnetic (vector) field three-dimensional beam diffraction by half planes will yield to the same approach. So also will three-dimensional beam diffraction by wedges using the uniform geometrical theory of diffraction but the resulting expressions are more complicated.