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摘要

本文针对平面电磁波对无限大导体平板上周期孔阵的透射问题, 首先用Bethe小孔理论将孔阵表示成偶极子阵列, 然后用平均化处理得到均匀的等效磁化/极化强度, 进而引入等效面源导出透射电磁波表达式, 最终给出了孔阵对平面电磁波屏蔽效能的解析公式. 该公式分别针对横电和横磁两种极化方式, 将屏蔽效能表示成孔阵周期面积、孔的极化系数、波长和入射角的简单函数, 其计算结果与全波仿真结果一致性好. 结果表明, 透射场强的幅值与孔极化系数和波频率成正比, 与周期面积成反比; 在横电极化方式, 波频率和周期面积不变的情况下, 透射场强的幅值与入射角的余弦值成正比, 入射角越大屏蔽效能越高; 在横磁极化方式下，透射场强幅值与入射角的关系相对复杂, 但在入射角较小时与入射角的余弦值近似成反比, 总体上入射角越大屏蔽效果越低.

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Abstract

Penetration of a plane electromagnetic wave through the apertures on a perfectly conducting flat plate is a classical electromagnetic problem. In some practical applications like electromagnetic shielding, where only the fields far from the apertures are concerned and the aperture sizes are small compared with a wavelength, the role of apertures can be represented by the equivalent electric and magnetic dipoles located in the centers of the apertures. In principle, the penetration field can be expressed as the superposition of the radiation fields of the dipoles. However, the direct superposition leads to a double series with complex form and poor convergence. On the other hand, this problem may also be solved by full wave numerical simulations. Even so, finding analytical solutions is still desirable considering that it is clear in physical significance and easy to implement. In this paper, the analytical formula of the penetration fields are derived for both TE and TM polarization mode with different angles of incidence. The derivation is carried out firstly by averagely distributing each dipole moment within each periodic unit. As a result, the dipole array is replaced with a flat sheet with uniform magnetization and polarization intensity. Then, the equivalent surface current and charge distributions are obtained directly from the polarization intensity. Finally, the penetration fields are treated as the radiation fields of the surface sources. It is shown that the amplitude of the penetration field is proportional to aperture magnetic polarization coefficient and wave frequency, and it is inversely proportional to the area of a periodic unit. In regard to the effect of the incidence angle, the amplitude of the penetration field is proportional to the cosine of the incidence angle for TE polarization. However, for the TM polarization, the relationship is a little complicated due to the coexistence of electric and magnetic dipoles: the field is not rigorously inversely proportional to the cosine of the incidence angle due to the existence of a correction term involving both the polarization coefficient and the sine of the angle. The formula is used to calculate the shielding effectiveness for several different aperture shapes and different incidence angles. The results are in good agreement with those from the full wave simulation software.

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作者及机构信息

通信作者:焦重庆,cqjiao@ncepu.edu.cn

基金项目:国家重点研发计划（批准号：2017YFB0902400）和中央高校基本科研业务费专项资金(批准号：2019MS003)资助的课题.

Authors and contacts

Corresponding author:Jiao Chong-Qing,cqjiao@ncepu.edu.cn

Funds:Project supported by the National Key R&D Program of China (Grant No. 2017YFB0902400) and the Fundamental Research Funds for the Central Universities, China （Grant No. 2019MS003）.

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参考文献

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施引文献

下载: 全尺寸图片幻灯片

孔形状	${\alpha _{\rm{e}}}$	${\alpha _{{\rm{m}}x}}$	${\alpha _{{\rm{m}}y}}$
圆形（r为半径）	$\frac{{2{r^3}}}{3}$	$\frac{{4{r^3}}}{3}$	$\frac{{4{r^3}}}{3}$
椭圆（l为长轴，沿x方向，w为短轴）	$\frac{{\text{π}}}{{24}} \cdot \frac{{{w^2}l}}{{{\rm{E}}(e)}}$	$\frac{{\text{π}}}{{24}} \cdot \frac{{{e^2}{l^3}}}{{K(e) - E(e)}}$	$\frac{{\text{π}}}{{24}} \cdot \frac{{{e^2}{l^3}}}{{{{(l/w)}^2}E(e) - K(e)}}$

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