## 1. Introduction

[2] Transient analysis of thin-wire radiating structures in the presence of dissipative half-spaces has been a matter of interest during recent decades, with applications in different fields such as ground penetrating radar (GPR) [*Peters et al.*, 1994], bioelectromagnetics [*Iskander*, 1991], electromagnetic compatibility [*Poljak*, 2007], etc.

[3] Numerical techniques for the simulation of these problems can been developed with different approaches. One is to apply a inverse Fourier transform (IFT) to the well known solution of the thin-wire antenna problem in the frequency domain [*Rahmat-Samii et al.*, 1978; *Lestari et al.*, 2004]. Two different approaches constitute the basis of these frequency domain numerical algorithms. On the one hand, there are algorithms based on the solution of the Sommerfeld problem for horizontal or vertical dipoles over lossy half-spaces, which turn out to be accurate but require intensive computational resources [*Miller et al.*, 1972a, 1972b; *Sarkar*, 1977; *Parhami and Mittra*, 1980; *Burke and Poggio*, 1981; *Burke et al.*, 1981; *Burke and Miller*, 1984; *Cui and Chew*, 2000a, 2000b]. On the other hand, there are solutions based on approximations such as the reflection-coefficient method [*Miller et al.*, 1972a, 1972b; *Sarkar*, 1977; *Burke and Poggio*, 1981], which is computationally faster but, as it assumes that the waves incident on the ground are plane waves, it presents losses of accuracy when the approximation is not valid [*Karwoski and Michalski*, 1987]. In any case, for wideband or ultrawideband systems the use of IFT is computationally inefficient, and numerical algorithms obtained directly in the time domain are advantageous compared with the aforementioned frequency domain techniques [*Miller and Landt*, 1980]. Therefore, additional efforts were devoted to the development of new methods of solution in the time domain. In this context, several authors [*Rubio Bretones and Tijhuis*, 1995, 1997; *Tijhuis and Rubio Bretones*, 2000; *Vossen*, 2003] have presented an extension of the Hallen's time domain electric field integral equation (TD-EFIE) to include lossy half-spaces, based on the transient solution of the Sommerfeld problems presented by *De Hoop and Frankena* [1960] and *Frankena* [1960]. This approach, as its counterpart in the frequency domain, leads to accurate solutions but with an intensive use of computational resources. To overcome this disadvantage, time domain solutions under the RC approximation have been implemented by *Poljak* [2007], by employing the time domain RC inferred by *Barnes and Tesche* [1991], and satisfactory results have been showed for particular cases of two coupled horizontal wires over dielectric half-spaces [*Poljak*, 2007; *Poljak et al.*, 2000].

[4] Moreover, parallel studies have recently been devoted to find improved numerical expressions for the direct time domain calculation of RC [*Rothwell and Suk*, 2003, 2005]. The main advantages of these expressions are in their range of applicability, being useful for reflections produced over all kind of soils, in contrast to those from *Barnes and Tesche* [1991], which are restricted to specific conditions over the constitutive parameters of the half-space. Given that those restrictive conditions are not always fulfilled, the use of the more general approach given by *Rothwell and Suk* [2003, 2005] is advisable for general purpose electromagnetic codes.

[5] An important drawback of using the time domain techniques developed so far is the poor efficiency in the treatment of strongly conductive soils. In the RC approximation the calculation of the transient response of conductive soils is performed by a convolution operator [*Poljak et al.*, 2000] between the incident electric field and the impulsive response of the soil. In cases where the late-time responses are of interest, this convolution is particularly intensive in terms of computational costs, and a bottleneck arises in terms of computational time in the simulations.

[6] In the present paper, we present a new algorithm for time domain simulation of arbitrarily oriented thin-wire antennas over lossy ground, by applying a RC approximation for the Pocklington's EFIE [*Miller and Landt*, 1980; *Miller*, 1994]. The main contributions of this work are: (1) wider applicability of the algorithm, by using recently proposed RC equations [*Rothwell and Suk*, 2003, 2005], (2) efficient treatment of all kind of conductive soils, by employing approximations derived from the analysis of impulsive response of the soil which drastically reduces the computational time for lossy grounds, and (3) ability to simulate arbitrarily oriented thin wires, by decomposing the interactions between different parts of the structures due to reflections on the ground, into those corresponding to waves polarized with the electric field parallel or perpendicular to the interface. The results are validated by using IFT to accurate frequency domain solutions.

[7] The paper is organized as follows, in section 2, an extension of Pocklington EFIE equation to include wires over lossy ground using the TD-RC method is described. Time domain reflection coefficients (TD-RC) needed for the formulation of the EFIE are presented in section 3, and a numerical approximation to decrease the computational burden of the calculation for the case of conductive soils is proposed. Section 4 formulates the numerical procedure of solution of the EFIE, by applying a point-matching method of moments and lagrangian interpolation basis functions both in the time and space domain, and takes into account the numerical decomposition of the electric field incident on the ground into its components polarized either parallel or perpendicular to the interface (TE or TM polarization). Finally, section 5 shows results for simulations in different lossy grounds.