半空間電場型并矢格林函數(shù)及其數(shù)值計算

從均勻介質(zhì)中偶極子的輻射場出發(fā)，通過譜域展開，推導(dǎo)出半空間的電場型并矢格林函數(shù)譜域積分(索末菲爾德積分)形式的完整表達(dá)，包括場點(diǎn)與源點(diǎn)處于同側(cè)或異側(cè)時對應(yīng)的格林函數(shù)，重點(diǎn)討論了場點(diǎn)和源點(diǎn)在垂直方向重合時的結(jié)果及其物理解釋，排除了一般表達(dá)式在場源橫向距離為零時會出現(xiàn)奇異性的問題。通過嚴(yán)格的數(shù)值積分方法計算半空間分界面的場分布來對公式的正確性進(jìn)行了檢驗。
關(guān) 鍵 詞 平面分層介質(zhì)；并矢格林函數(shù)；索末菲爾德積分；奇異性

Abstract In this paper, complete spectral integral representations (Sommerfeld integrals) of the electric-field-type dyadic Green’s functions for half-space were derived via spectral-domain expansion of the radiation field of dipole located in free space. The Green’s functions of reflection or transmission electric field were given, corresponding to the case of source point and observation point located in the same side or the opposite side, respectively. Especially, the results and physical explains were given for source point and observation point overlapping in vertical direction, which eliminate the singularities arising in the general representations. Numerical computation results show the validity of the presented formulas.
Key words planar stratified media; dyadic Green’s functions; Sommerfeld integrals; singularity