Theory of diffraction by small holes
Theory of diffraction by small holes
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DOI：
10.1103/physrev.66.163
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发表时间：
1944-10-01
期刊：
影响因子：
--
通讯作者：
Bethe, HA
中科院分区：
文献类型：
--
作者：
Bethe, HA
理论上处理了与波长相比较小的孔对电磁辐射的衍射。找到了满足麦克斯韦方程组和各处边界条件的完整解（第 4 节）。该解决方案适用于完美导电平面屏幕中的圆孔，但相信该方法将适用于更普遍的问题（第 8 节）。该方法基于衍射孔中虚拟磁荷和电流的使用，其优点是自动满足导电屏上的边界条件。调整电荷和电流，以便在孔中产生正确的切向磁场和法向电场。结果（第 5 节）与基尔霍夫方法的结果完全不同，给出的衍射电场和磁场值的比率（孔半径/波长）较小（第 6 节）。衍射场可以被认为是由孔平面中的磁矩和垂直于它的电矩引起的（第 6 节）。该理论应用于小孔耦合的空腔互激励问题（第 9 节）。这导致方程与普通耦合电路的方程非常相似。两个耦合腔的相位和幅度关系不是唯一确定的，但有两种频率略有不同的振荡模式，这些关系是相反的（第 10 节）。解决了从一个腔到另一个腔增强激励的问题（第 11 节）。
The diffraction of electromagnetic radiation by a hole small compared with the wave-length is treated theoretically. A complete solution is found satisfying Maxwell's equations and the boundary conditions everywhere (Section 4). The solution holds for a circular hole in a perfectly conducting plane screen, but it is believed that the method will be applicable to much more general problems (Section 8). The method is based on the use of fictitious magnetic charges and currents in the diffracting hole which has the advantage of automatically satisfying the boundary conditions on the conducting screen. The charges and currents are adjusted so as to give the correct tangential magnetic, and normal electric, field in the hole. The result (Section 5) is completely different from that of Kirchhoff's method, giving for the diffracted electric and magnetic field values which are smaller in the ratio (radius of the hole/wave-length)(Section 6). The diffracted field can be considered as caused by a magnetic moment in the plane of the hole, and an electric moment perpendicular to it (Section 6). The theory is applied to the problem of mutual excitation of cavities coupled by small holes (Section 9). This leads to equations very similar to those for ordinary coupled circuits. The phase and amplitude relations of two coupled cavities are not uniquely determined, but there are two modes of oscillation, of slightly different frequency, for which these relations are opposite (Section 10). The problem of stepping up the excitation from one cavity to another is treated (Section 11).