On the far‐zone electromagnetic field of a vertical Hertzian dipole over an imperfectly conducting half‐space with extensions to plasmonics

Abstract

New asymptotic formulas for the electromagnetic fields of a vertical Hertzian dipole over an imperfectly conducting half‐space are derived using two variants of the modified saddle point method, referred to as subtractive and multiplicative. The accuracy of the two far‐zone formulations is assessed by comparisons with the state‐of‐the‐art Norton‐Bannister theory and with the rigorous results of numerical integration for problems involving seawater in the microwave range and gold in the visible range. It is found that the performance of the three approximate methods is similar, except at the surface of plasmonic media, where the saddle point methods are superior to the Norton‐Bannister formulation.

The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

“…For that purpose, in the future, we will insist on the investigation of special function X(k, α)and its properties as well as other special functions that could be used to describe the field behavior. Additionally, the obtained asymptotic solutions can be refined with any accuracy and presented in expanded form, according to known procedures [60] and a comparison with relevant recent research, e.g., [61][62][63][64], is to be made.…”

On the Far‐Zone Electromagnetic Field of a Horizontal Electric Dipole Over an Imperfectly Conducting Half‐Space With Extensions to Plasmonics

“…In either case, the smoothed G(s) in (A2) is expanded in a Maclaurin series about the origin, and each term is then integrated along the SDP in a closed form, resulting in an asymptotic series in Ω −1 . Typically, only the leading term of this expansion is employed, in which case the two methods lead to different expressions (Michalski & Lin, 2017), with the subtractive formula favored in the more recent literature (Collin, 2004).…”

“…where the two approximate formulas apply in the high-contrast case (| r | ≫ 1) and the second one further assumes that ≫ (z+h) (Michalski & Lin, 2017;Ott, 1943). Comparing (62) with the numerical distance expressions in the Norton and King formulations (see Appendices B and C), we note the absence of the notorious sin 2 2 factor in the denominator, whose effect would be to deemphasize the attenuation function contribution for small angles 2 , near the z axis.…”

“…A two-dimensional horizontal line dipole over a plasmonic half-space was recently considered by Ung and Sheng (2008). The HED problem is more complex than its vertical (VED) counterpart (Michalski & Nevels, 2017;Michalski & Lin, 2017), because all six components of the electromagnetic fields, rather than just three, are involved. Since the direct and image fields virtually cancel for an HED near the ground, the total fields are significantly weaker than those of a similar VED (King, 1992).…”

Human Exposure to Field Radiated by Vertical Dipole Antenna over a Lossy Half-Space using Analytical Approach

“…Thin wire radiation above a lossy half space was originally introduced by Sommerfeld in 1908 [3] and has been the subject of interest of many researches [3][4][5][6][7][8][9], mainly because of many applications, such as wireless telecommunications [7,10], bioelectromagnetic, or surface wave propagation [11]. Moreover, small and directional antennas are used in 5G networks [12].…”