圆形波导有源区域DGF的特性研究(Ⅰ)
A CRITICAL STUDY ON DGF AT THE SOURCE REGION IN CIRCULAR WAVEGUIDES (Ⅰ)
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摘要: 本文是作者研究圆形波导有源区域并矢格林函数(DGF)的计算及其普遍性质的第Ⅰ部分,文中建立了有源区域DGF并矢运算的分布理论法,导出了圆形波导DGF并矢运算的完整表示式,纠正了文献中存在的一些错误和模糊之处。 本文的结论与基斯留克(Kisliuk)(1980,1983)的结论不同,它表明DGF的无散矢量本征函数展开式和无旋矢量本征函数展开式在有源区域不再是纯的无散和无旋场。此外,我们还指出戴(Tai,1973)通过互换并矢算子和有源区域DGF展开式中的积分号来进行并关运算是不恰当的。
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Abstract: This is the first part of our work on the dyadic Green s functions (DGF) at the souree region in circular waveguides. In this paper, a systematic and nevel approach is developed for the dyadic operation of DGF. The complete farms of the dyadie operation of DGF for circular waveguides are given. Ambiguities associated with the dyadic operation in the literature are clarified and the errors are redressed.Contrary to Kisliuk (1980, 1983), it is shown that the expansion of the longitudinal vector eigenfunctions L and the expansion ofthe transverse vector eigenfunctions M and N are not purely lognitudinal and transverse fields at the source region. In addition, it is also shown that the interchanging differential and integral operators to carry out the dyadic operation of DGF is invalid at the source region (Tai, 1973). -
C. T. Tai, Proc. IEEE,61(1973), 480.[2]C. T. Tai. Math. Note 28, Weapons Systems Laboratory,Kirtland,[3]Alb. NM, July 1973.[4]M. Kisliuk, Int. J. Electronics, 54(1983), 349.[5]M. Kisliuk, IEEE Trans. on MTT, MTT-28(1980), 894.[6]Y. Rahmat-Samii, ibid, MTT-23(1975), 762.[7]霍美瑜,科学通报,6(1981), 686.[8]范俊清,光学学报,1(1980), 357.[9]潘生根,电子科学学刊,6(1984), 181.[10]潘生根,电子科学学刊,7(1985), 171.[11]V. S. Vladimirow, Generalized Functions in Mathematical Physics, Mir Publishers, p. 31. [11] 郭敦仁,数学物理方法,人民教育出版社,1965,第102页. -
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