Mathematical Theory of Diffraction
Mathematical Theory of Diffraction
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衍射的数学理论
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
A. Sommerfeld
中科院分区：
文献类型：
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作者：
A. Sommerfeld
由于种种原因，菲涅尔创立的绕射理论和基尔霍夫在解析上更精确的绕射理论，已不能满足数学严谨性的要求。我之前已经表达了一些这种类型的反对意见(†)。这一理论之所以与经验有较好的一致性，仅仅是因为光的波长很小这一情况。对于赫兹振荡和声波的治疗，其中的波长明显更大，它必然被证明是完全不可用的。在光学上也存在着旧的衍射理论不再适用的情况。相反，我在这里给出一个严格的数学处理，它完全基于在电磁理论中已经建立的微分方程和边界条件。然而，我必须把自己限制在最简单的情况下，因为似乎从一开始就没有希望以数学上令人满意的方式解决普通光学中异常复杂的问题。稍后我将谈到庞加莱先生**的一项工作，它也打破了旧的理论。
The theory of diffraction, as it was founded by Fresnel and made more precise analytically by Kirchhoff, does not satisfy the requirements of mathematical rigor for various reasons. I have already expressed some objections of this type previously†). This theory owes its relatively good agreement with experience merely to the circumstance that the wavelength of light is a very small quantity. For the treatment of Hertzian oscillations and acoustic waves, in which the wavelength is significantly larger, it necessarily proves to be completely unusable. There also exist conditions in optics under which the older diffraction theory is no longer sufficient. In contrast, I give here a mathematically rigorous treatment which is based solely on the differential equations and boundary conditions that have been established in electromagnetic theory. I must, however, limit myself to the very simplest cases, since it seems hopeless from the start to solve the exceptionally complicated problems of ordinary optics in a mathematically satisfactory way. I will speak later of a work by Mr. Poincare**) that also breaks with the older theory.