Asymptotic solution for the electromagnetic scattering of a vertical dipole over plasmonic and non‐plasmonic half‐spaces

Abstract

Abstract A new asymptotic solution for the scattered electromagnetic fields of a vertical Hertzian dipole antenna in the presence of an imperfectly conducting half‐plane for ordinary and plasmonic media is proposed. The scattered electric and magnetic field components are calculated from the intermediate Hertz potential expressed in terms of the Fourier‐Bessel transforms associated with the Sommerfeld‐type integral, which is difficult to evaluate due to the singularities of the integrand near the integration path and its oscillatory and slowly decaying integrand. Using the modified saddle point method, an approximate closed‐form solution of the far‐zone scattered electromagnetic fields including surface waves is presented. The new formulations are applied to calculate radiation patterns of different impedance half‐planes for both ordinary and plasmonic media, that is, seawater, silty clay soil, silty loam soil and lake water as ordinary, and silver and gold as plasmonic media. Furthermore, a numerical evaluation of the proposed solution at various frequencies and comparisons with two alternative state of the art solutions shows that the proposed solution has higher accuracy in terms of the normalised root‐mean‐square error and the normalised maximum absolute error for plasmonic and non‐plasmonic structures.

Keywords

• antenna radiation patterns
• Bessel functions
• dipole antennas
• electromagnetic wave scattering
• Fourier transforms
• integral equations