Frequency-Domain Fields And Time-Domain Fields In Layered Media

The problem on the electromagnetic field from a dipole source in layered media has been visited by many investigators because of its useful applications in subsurface and closed-to-the-surface communication,radar,and geophysical prospecting and diagnostics. In the beginning of last century,Zenneck and Sommerfeld started to investigate the electromagnetic field along the planar ground.Lately,many investigators advanced great achievements in the study on this problem.In the end of 1990's,the debates on the trapped surface wave occurred between the two famous professors,R.W.P.King and J.R.Wait.In 1998,Wait wrote a comment on the 1994 King and Sandler's paper and claimed that the terms of the trapped surface wave,which varies asρ^-1/2in the far region,should be considered in the three-layered case.The new debates,naturally, rekindled the interest in the study on the electromagnetic field from a dipole source in the presence of a three-layered region.This problem had been solved from the works in the available recent works.In practical applications,the region of interest consists of a perfect conductor,coated with the two layer dielectrics under the air.For instance,both a forest circumstance consisting of air,trees,defoliations,and earth and a microstrip antenna on the silicon chip coated with dioxide silicon can be idealized as a problem of four-layered region.In the present study,we will investigate the electromagnetic field from vertical and horizontal dipoles in a four-layered region.From the analysis,it is seen that both the trapped surface wave and the lateral wave can be separated into the electric-type and magnetic-type terms.The trapped surface wave with its wave number being between k₀ and k₂,is determined by the sum of the residues of the poles.The lateral waves with its wave numbers k₀ and k₁ are determined by the integrations of the branch cuts.The computations and discussions show that the field components in far-field regions the terms of the trapped surface waves should be considered.Additionally,we will examine the approximate transient field of a horizontal electric dipole excited by a Gaussian pulse on the boundary between a homogeneous isotropic medium and one-dimensionally anisotropic medium in detail.The final formulas of the transient field are expressed in terms of several fundamental functions.The derivations and computations show that the three time-dependents electric field components consist of two lateral pulses which travel along the boundary with different velocities and different amplitudes.Especially,the Fresnel-integral terms do not completely cancel.