Dense Sets and Far Field Patterns in Electromagnetic Wave Propagation
Dense Sets and Far Field Patterns in Electromagnetic Wave Propagation
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电磁波传播中的稠密集和远场模式
DOI：
10.1137/0516078
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发表时间：
1985
影响因子：
2
通讯作者：
R. Kress
中科院分区：
文献类型：
--
作者：
D. Colton;R. Kress
证明了在单位球边界上的平方可积切向矢量场空间中，有界理想导电障碍物对整个入射场的散射所对应的电远场图案是稠密的当且仅当不存在电磁Herglotz对的麦克斯韦本征函数，即解$\{ E，在所有空间中定义的麦克斯韦方程组的H\} $使得\[\mathop {\lim }\limits_{r \to \infty } \frac{1}{r}\iint\limits_{|X|\leqq r} {\left（{|E（x）|^2 +| H（x）|^2} \right）dx < \infty }.\]
It is shown that the electric far field patterns corresponding to the scattering of entire incident fields by a bounded perfectly conducting obstacle are dense in the space of square integrable tangential vector fields defined on the boundary of the unit ball if and only if there does not exist a Maxwell eigenfunction that is an electromagnetic Herglotz pair, i.e. a solution $\{ E,H\} $ of Maxwell’s equations defined in all of space such that \[\mathop {\lim }\limits_{r \to \infty } \frac{1}{r}\iint\limits_{|x| \leqq r} {\left( {|E(x)|^2 + |H(x)|^2 } \right)dx < \infty }.\]