Approximate Transient Field of Horizontal Electric Dipole on the Boundary Between a Homogeneous Isotropic Medium and One-Dimensionally Anisotropic Medium

Abstract

Approximate solutions are carried out for the transient field of a horizontal electric dipole with a delta function excitation and Gaussian excitation located on the planar boundary between a homogeneous isotropic medium and one-dimensionally anisotropic medium. The derivations and analysis show that the components of the electric field consist of two delta function lateral pulses which decrease with the amplitude factor \( 1/\rho ^2 \) and travel along the boundary with different velocities and different amplitudes. With the Gaussian excitation, the final formulas of the transient field are expressed in terms of several fundamental functions. In particular, the Fresnel-integral terms in those formulas do not completely cancel for the electric field components.