单轴介质半空间电偶极源反射场的解析式

Analytical expression for reflected field of a vertical electric dipole over an uniaxial medium half-space

推导出单轴各向异性介质半空间上方垂直电偶极源电磁场的精确解析表达式.将场分量中的两类Somm erfeld型积分表达成绝对、快速收敛球面驻波函数级数展开式.应用超几何函数理论,将展开式中的展开系数表达成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分析和计算,是此类Somm erfeld半空间问题的精确、有效的解析解答.

An analytical expression was derived for the electromagnetic field of a vertical electric dipole over an uniaxial medium half-Space. The two Sommerfeld type integrals contained in the field components were expressed as a rapidly and absolutely convergent series of spherical standing wave functions; and these coefficients of the series were cast into the Legender polynomials with complex argument for the medium parameter by using the techniques of the hypergeometric functions. The obtained solution for the Sommerfeld half-Space problem has the advantage that it is accurate and efficient and can conveniently be employed to calculate and analyze the electromagnetic field.