On the Groundwave Excited by a Vertical Hertzian Dipole Over a Planar Conductor: Second-Order Asymptotic Expansion With Applications to Plasmonics

The surface electromagnetic fields radiated by a vertical electric dipole over a lossy conducting half-space are investigated. A simple derivation is presented of the second-order asymptotic groundwave expression, using a modified saddle-point method based on integration around vertical branch cuts. The method takes into account the influence of the Sommerfeld pole, which in the plasmonic case contributes a surface plasmon polariton. The proposed groundwave formulation is shown to be superior to the state-of-the-art Norton-Bannister theory for noble metals at optical wavelengths.