【摘要】 精确有效地计算索末菲尔德型积分是分析导电媒质半空间电磁波辐射和散射问题的关键.本文给出求解有限导电媒质平面上方垂直磁偶极源赫兹位函数的解析方法.利用圆柱波函数的球面波函数展开式和超几何函数理论,位函数中的索末菲尔德积分被表示成快速、绝对收敛的球面波展开式;展开系数是以物性参数为复宗量的勒让德多项式.该展开式易于电磁场的计算和分析,并且不受场点和源点的位置、媒质的物性参数和频率等条件的限制.更多还原

【Abstract】 An accurate and efficient method for computing Sommerfeld type integrals is crucial in the analysis of the electromagnetic waves for radiators and scatters in the presence of a conducting half-space.In this paper,an analytical approach is described for the evaluation of the Hertz potential of a vertical magnetic dipole over the finitely conducting medium plane.By using the expansion of spherical wave functions for a cylindrical wave function and the techniques of the hypergeometric functions,the Sommerfeld integral contained in the potential is expressed as a rapidly and absolutely convergent series of spherical wave functions;and the coefficients of the series are cast into the Legender polynomials with complex argument for the medium parameter.The obtained result has the advantage that it holds without the restrictions on the locations of dipole source and observation points,ranges of medium parameters and frequency and so on,and can conveniently be employed to calculate and analyze the electromagnetic fields.更多还原