Horizontal Dipole Excitation Field, High Lossy Dielectric Surface Coating Uniaxial Media

In the past many years, the electromagnetic field generated by a dipole source in the presence of three-layered regions has been visited by many investigators because of its wide useful applications, such as the propagation of the low frequency wave over the earth or sea covered by a layer, and the electromagnetic field generated by a microstrip antenna on the silicon chip with a conductive substrate.In early 1990's, R. W. P. King, et al. concluded that the dominant field in the far region generated by a electric dipole is the lateral-wave, which attenuates with ρ^-2. In 1998, J. R. Wait has claimed that under the case addressed by King and Sandier, the main field in the far region is the trapped surface wave, which attenuates with ρ^-1/2. Lately, Mahmoud also presented comments on King's works. The debates between King et al. and the commenters naturally rekindled the interest in the study on the old problem.Recently, Collin presented the exact field of a hertzian dipole in the air above a dielectric-coated lossy earth. From 2002 to 2005, Zhang et al. have investigated the electromagnetic field of vertical and horizontal electric dipoles in the three-layered medium. Along the researching line, Li has extended the investigation on the electromagnetic field in a three-layered region consisting of air, a uniaxial lay and a perfect conductor.Considering the actual situations, in which the substrate layer is always imperfect, it is needed to study the field from a horizontal electric dipole above a high lossy medium coated with a uniaxial layer. In this paper, the explicit formulas were derived for the six components of the electromagnetic field in air excited by a horizontal electric dipole over a planar high lossy dielectric coated with a uniaxial layer. Numerical results were also obtained.Similar to the perfect case addressed by Li, et al, the complete field in the present case is also composed of the direct wave, the ideal reflected wave, the trapped-surface wave, and the lateral wave. Both trapped-surface wave andlateral wave have two types - the electric type (TM) and the magnetic type (TE). The wave numbers in the ρ direction of the electric-type trapped surface wave, which are between k₀ and k_L, are different from those of the magnetic-type trapped surface wave, which are between k₀ and k_T. When the thickness l of the uniaxial layer satisfies nπ <[(k_T)/(K_L)]({k_L²— k)0²)^1/2 ? l < (n + 1)π, there are n + 1 modes of the electric-type trapped surface waves. When the thickness l satisfies (n — (1/2))π < (k_T² — k₀²)^1/2 ? l < (n + (1/2))π, there are n modes of the magnetic-type trapped waves. The wave number of the lateral wave is k₀ no matter how thick the uniaxial layer is.