A Complete Nonuniform Asymptotic Expansion of the Dyadic Green’s Function for Dielectric Half-Space

The dyadic Green’s function (DGF) for a dielectric half-space is crucial to many electromagnetic applications. Several analytical approximations of Green’s function have been proposed, among which the first-order uniform asymptotic expansion (AE) has been extensively adopted. However, the mathematical formulation of a closed-form expression of a higher-order asymptotic series is challenging. Recently, the complete nonuniform AE of Sommerfeld integral (SI) for the half-space has been formulated. Consequently, based on the identical expansion procedure, this study formulates the complete nonuniform expansion of the DGF into a closed-form expression. Subsequently, its accuracy is investigated compared with that of the numerical integration and the first-order uniform expansion of the function. In addition, the higher-order derivative of the reflection coefficient is analytically derived into a closed-form expression, which is necessary for computing the proposed expansion up to any order.