计算索末菲尔德型积分的新方法--球面波级数展开法

江滨浩; 刘永坦

计算索末菲尔德型积分的新方法--球面波级数展开法

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出版历程
- 收稿日期: 2001-07-29
- 修回日期: 2002-06-17
- 刊出日期: 2003-02-19

A new technique for computating sommerfeld type integrals-expantion of spherical wave functions

摘要

摘要: 利用广义阻抗边界条件模拟和简化地球表面对电磁场的影响。应用圆柱波函数的球面波展开表达式,地平面上方水平电偶极子电磁场中的索末菲尔德型积分可表达成快速、绝对收敛的球面波展开式,利用积分路径的变换和超几何函数理论,展开式中的展开系数可表达成以大地表面复阻抗为宗量的第二类勒让德函数。该展开式数学物理意义明显,并且十分便于数值计算,该文给出的方法是求解下索末菲尔德半空间问题的精确、有效解析方法。
- 电磁场理论; 索末菲尔德型积分; 广义阻抗边界条件; 球面波展开
Abstract: Generalized impedance boundary conditions are employed to simulate the effect of the earths surface on electromagnetic fields. The Sommerfeld type integrals contained in the electromagnetic fields of a horizontal electric dipole over the ground plane are expressed as a rapidly and absolutely convergent expansion of spherical wave functions; and the coefficients of the series are cast into the Legendre functions with argument for the complex surface impedance of the ground with the help of the techniques of the transformation of integration path and the hypergeometric functions. The obtained results have explicit mathematical and physical interpretation and can conveniently be used to calculate the fields. The technique described here is an accurate and efficient computation for the Sommerfeld type integrals.

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参考文献(1)

P. Giuseppe, L. V. John, The centennial of Sommerfelds diffraction problem, and short biography of Arnola Sommerfeld(1868-1951), Electromagnetics, 1998, 18(2), 103-116.[2]江滨浩,刘永坦,有限导电平面上电偶极子电磁场的解析公式,电波科学学报,1999,14(1),13-18.[3]江滨浩,刘永坦,Sommerfeld型积分的解析表达式,微波学报,2000,16(1),38-43.[4]胡俊,聂在平,索末菲尔德积分新方法-快速汉克尔变换,电子学报,1992,6(3),126-131.[5]S.O. Park, C. A. Balanis, Analytical technique to evaluate asymptotic part of the impedance matrix of Sommerfeld type integrals, IEEE Trans. on Antennas Propagat., 1997, 45(3), 798-805.[6]K.A. Michalski, Extrapolation methods for Sommerfeld integral tails[J].IEEE Trans. on Antennas Propagat.1998, 46(10):1405-1418[7]J.R. Wait.[J].Electromagnetic Wave Theory, New York, Harper Row.1985,:-[8]T.B.A. Senior, J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, Stevenage,UK, IEE press, 1995, Ch3.[9]T.B.A. Senior, J. L. Volakis, Higher order impedance and absorbing boundary conditions, IEEE Trans. on Antennas Propagat., 1997, 45(1), 107-114.[10]M.A. Ricoy, J. L. Volavis, Derivation of generalized transition/boundary conditions for planar multiple-layer structures, Radio Science, 1990, 25(4), 391-405.[11]J.A. Stratton, Electromagnetic Theory, New York, McGraw-Hill, 1941, 412-413.[12]数学手册,北京,人民教育出版社,1979.[13]W. Magnus, F. Oberhettinger, R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Third Edition, New York, Chelsea Publishing, 1966.[14]I. S. Gradshteyn, I. M. Ryzhik, Table of Integral, Series, and Products, New York, Academic Press, 1980, 860.

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