A dipole in the presence of the earth´s surface: Analytic solutions and realization with HFSS

This paper revisits the classic Sommerfeld problem of determining the fields radiated from a dipole placed on a half-space. The approach to solving this problem has a wide range of applications from microstrip antenna design to VLF radio wave propagation. A brief overview of the analytic field expressions, which are asymptotically evaluated in the spectral domain using the modified saddlepoint method, are presented for 1) a vertical dipole above the earth, 2) a vertical dipole in the earth, and 3) a horizontal dipole at the interface between the earth and air. A significant advantage of using an analytical approach to analyze this problem set is the physical insight gained from separating surface and lateral wave terms from radiated field expressions. While analytical solutions enable analysis with minimal computational overhead, developing expressions for antenna design and rapid prototyping is often impractical due to the complexity required for realizable antenna topologies. In order to simulate the performance of an arbitrary dipole antenna design in the presence of a half-space, it is valuable to utilize a three-dimensional (3D) full-wave computer-aided design (CAD) solver, which is readily available in academia and industry, such as ANSYS HFSS. However, because HFSS is not routinely used to solve the general half-space problem, the setup and subsequent analysis must be approached carefully in order to provide satisfactory results. Therefore, the objective of this paper is to review the analytic expressions for an infinitesimal dipole in the presence of a dielectric half-space, and to present the development and results of a set of complimentary HFSS models to include both ideal and realized dipole antennas.