Modified Fresnel Coefficients for Huygens' Sources in FDTD

Abstract

Scattering of electromagnetic fields from objects on or beneath the ground can be analyzed with the Finite-Difference Time-Domain (FDTD) method. The equivalence principle can be utilized for generation of incident plane waves where the Fresnel reflection and refraction coefficients are multiplied by the pulse spectrum in the frequency domain and the result is transformed into the time-domain. Errors will appear in the Huygens' sources due to numerical dispersion where the main errors come from the use of analytical reflection and refraction coefficients. Their influence on the accuracy is generally negligible for applications where the scattered field from the object is greater than the numerical errors introduced. However, if weak scattering events are considered, such as for objects buried in ground, the dispersion errors can be of the same order of magnitude as the scattered field. In this paper we derive the modified Fresnel coefficients for a homogeneous lossy ground which are consistent with the FDTD algorithm and can be used in the Huygens' sources for suppressing numerical errors. It is shown that the modified Fresnel coefficients reduces the noise level for an empty FDTD volume with 30 to 60 dB. As an application example, the far-zone scattering of a buried dipole is considered.