A closed-form expression of the dyadic Green's function is formulated for an impedance half-plane, which is written in terms of the incomplete cylindrical function of Poisson form. Due to the branch-cut of the logarithm function that is required to calculate the input argument of the incomplete cylindrical function, the closed-form representation consists of two formulations. Since the closed-form expression contains a singularity at ρ =0, the small argument expansion of the expression is also derived to rigorously characterize the behavior of the function at ρ 0. The previously-reported complete asymptotic expansion for the Sommerfeld integral for an impedance half-plane is not accurate for practically important cases such as near-earth propagation and/or when the surface is highly conductive. Hence, in this paper, a new complete asymptotic series of the Sommerfeld integral are derived for the case that the existing asymptotic series is not accurate. The two asymptotic series not only allow efficient numerical computation but also provide more accurate results for virtually all propagation scenarios. Based on the two asymptotic series, the complete asymptotic series of the dyadic Green's function is derived. All derived formulations are numerically verified, and their accuracies are investigated.
Bibliographical noteFunding Information:
Manuscript received May 24, 2011; revised January 26, 2012; accepted February 25, 2012. Date of publication June 08, 2012; date of current version July 31, 2012. This work was supported by Defense Acquisition Program Administration and Agency for Defense Development under Contracts UD100002KD and UD110011GD. I.-S. Koh is with Department of Electronic Engineering, Inha University, Incheon 402-751, Korea (e-mail: firstname.lastname@example.org). Y. Lee is with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749, Korea (e-mail: email@example.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2012.2201086
All Science Journal Classification (ASJC) codes
- Electrical and Electronic Engineering