Analytical Formulas for Dipole Radiation Buried inside Planar Stratified Media

Document Type : Original Article

Authors

1 Corresponding Author: Prof. Dr. Samira T. Bishay, Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt.

2 Faculty of Science, Kafr El-Sheikh University, Egypt.

3 Canal High Institute of Engineering & Technology , Suez.

Abstract

In this paper, analytical formulas have been derived for the electromagnetic fields (EMFs) radiated from a vertical magnetic dipole (VMD) buried in planar stratified media. Three planar-layered conducting media model are adopted: air, seawater and ground. Expressions for the Hertz vector which are used to determine the electric and magnetic field
components of the dipole in the three planar-layered media are reduced to the integrals obtained by Sommerfeld previously. A simple technique with the aid of the complex image theory is used to obtain highly accurate analytical expressions for Sommerfeld integrals (SI) that arise in these calculations, which earlier were very tedious and complicated to evaluate. Closed-form expressions for the far field in the three regions due to a vertical magnetic dipole buried in second region (sea-water) are calculated and their physical meanings are discussed. The results are numerically evaluated and plotted. In addition, the results obtained in the three regions are compared with each other and with those mentioned elsewhere, and are proven that this method is very effective and simple. The formulas and computations can be applied
to the communication in lower frequencies region. The achieved results will also be useful for remote sensing of the ocean surface, especially when the transmitter is close to the surface.

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