Abstract
In previous studies, the trapped surface wave, which is defined by the residue sums, has been addressed in the evaluation of the Sommerfeld integrals describing electromagnetic field of a vertical dipole in the presence of three-layered or four-layered region. But unfortunately, the existing computational scheme cannot provide analytical solution of the field in the presence of the N-layered region when N > 4. The scope of this paper is to overcome the limitations in root finding algorithm implied by the previous approach and provide solution of poles in stratified media. A set of pole equations following with explicit expressions are derived based on the undetermined coefficient method, which enable a graphical approach to obtain initial values of real roots. Accordingly, the generated trapped surface wave components are computed when both the observation point and the electric dipole source are on or near the surface of a dielectric-coated conductor. Validity, efficiency, and accuracy of the proposed method are illustrated by numerical examples.
Highlights
It is known that the electromagnetic fields radiated by a vertical or horizontal electric dipole in stratified media are interesting and practically important in many cases [1,2,3]
E general integral representation of the electromagnetic field due to a dipole source has been addressed by King et al [6] in the presence of the N-layered region, which was developed from the original expressions firstly formulated by Sommerfeld in 1909 [7] in the presence of half-spaces
It is seen that the DR wave, lateral wave, and the trapped surface wave are combined in the total field to produce an interference pattern
Summary
It is known that the electromagnetic fields radiated by a vertical or horizontal electric dipole in stratified media are interesting and practically important in many cases [1,2,3]. Efforts have been made in a series of works [6,7,8] by investigators to derive analytical expressions for the Sommerfeld integrals, which leads to a better understanding of describing electromagnetic radiation from the dipole source than numerical solution, as well as time savings with respect to conventional techniques used to evaluate the integrals. In the comments by Wait and Mahoud et al in 1998 [9, 10], and studies by other pioneers, including Collin [11, 12] and Zhang and Pan [13], the three-layered structure was reconsidered by the use of asymptotic methods, contour integration, and branch cuts, where it is pointed out that the trapped surface wave, which is determined by residue sums of the poles, can be excited
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