Analytical Expressions For Electromagnetic Waves In Stratified Medium Including One-Dimensionally Anisotropic Medium

The electromagnetic(EM) fields from electric dipole sources in layered media have been a classical and vigor problem. It is also an important topic studied by many investigators. Pan and King had investigated the EM fields in two layered medium(isotropic and one-dimensionally anisotropic medium) when the horizontal dipole and observation point both located in the isotropic medium, and the analytical expressions for EM fields were given, the results for every part of the fields can also be decomposed into three parts: the direct wave, the reflected wave and the lateral wave. The value of the expressions fitted with the experimental results very well. In reality, two layered medium usually correspond to earth and air, or sea and earth, for the long wave length, the earth can be approximated by a one-dimensionally anisotropic half space, so it is valuable to study the propagation of the EM waves in the layered medium composed by one-dimensionally anisotropic medium.(1)The EM waves from a horizontal dipole in the three layered region consisting one-dimensionally anisotropic medium are investigated. The upper is air; isotropic medium is in the middle; one-dimensionally anisotropic medium is at the bottom; the three layered medium representing the practical case is “air-sea-ground”. The analytical expressions and the results of computation are given. 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 wave number of the air and that of the earth is determined by the sum of the residues of the poles. The lateral waves are determined by the integrations of the branch cuts. The computations and discussions show that, in far-field regions, the terms of the trapped surface waves should be considered.(2)EM fields in one-dimensionally anisotropic medium due to a horizontal electric dipole situated in isotropic region are investigated. The analytical expressions for the EM fields in the one-dimensionally anisotropic medium are given, and the expressions are more complex than the isotropic case, and the complete fields also include the direct field terms and the lateral wave terms. The results can be reduced to the corresponding isotropic results and proved to satisfy the boundary conditions by using the results of the EM fields in isotropic medium. The propagation of the EM waves in one-dimensionally anisotropic earth or sediments is also investigated.(3) Following the work by Margetis in 2001, the integrated formulas for the EM fields in the planar boundary between isotropic and one-dimensionally anisotropic media due to a horizontal electric dipole situated on the interface are treated in detail. The calculable field components are given in terms of series that involve confluent hyper-geometric functions, namely, the Fresnel and exponential integrals, and the expressions are more complex than the isotropic case. The exact expressions and simplified formulas can be easily reduced to the corresponding isotropic case.