Concise Complete Uniform Asymptotic Expansion of Dyadic Green's Function for Dielectric Half-Space Including Low-Loss and Lossless Media

초록

The first-order uniform asymptotic expansion (UAE) of the dyadic Green's function for a dielectric half-space has been used for a long time, but its applicability is limited for a large contrast case between the permittivities of two media. The complete UAE of the Green's function has been formulated, which shows that it can be applied to any propagation scenario except for the small distance between the source and the observation point and for very low-loss ground. The uniform expansion was derived by subtracting the pole of the integrand for the half-space from that for the impedance plane. Here, a new UAE is formulated by modifying the subtraction. Then, the conventional branch-cut contribution is incorporated into the final formulation to extend its valid region. The performance of the new formulation is compared with that of the original expansion for both ordinary and plasmonic media.

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