Abstract Starting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

中文翻译：

---

电磁散射和衍射经典理论教程

摘要 从麦克斯韦方程组出发，我们推导出了惠更斯-菲涅尔-基尔霍夫和瑞利-索末菲标量衍射和散射理论的基本结果。然后将这些结果扩展到涵盖矢量电磁场的情况。详细阐述了对完美导电半平面衍射问题的著名 Sommerfeld 解决方案。对来自障碍物的平面波的远场散射进行了一些详细的处理，并推导出了众所周知的光学截面定理，该定理将障碍物的散射截面与其前向散射幅度联系起来。还研究了在其他均质介质中由轻度不均匀性散射的情况，其中，在第一个 Born 近似中，发现一个相当简单的公式将远场散射幅度与主体介质的光学特性联系起来。铁磁材料中子散射的相关问题在论文的最后部分进行了讨论。