Electromagnetic Fields of Hertzian Dipoles in Layered Media of Moderate Thickness Including the Effects of All Modes

Fast numerical methods are developed to compute the electromagnetic fields of Hertzian dipole of layered media (layered medium Green´s function) of moderate thickness for the entire distance range. The method consists of using a fast all modes (FAM) method of determining all mode locations in the complex plane. The modes include surface wave modes, leaky wave modes, and improper modes. For the case of layer thickness of one wavelength, it requires only 0.12 CPU seconds as preprocessing to determine 400 mode locations accurately in the complex plane using a Pentium IV 3.2 GHz PC with Matlab. The mode locations are required only to be computed once. The numerical modified steepest descent method (NMSP) is then used to compute the steepest descent integral with all the pole proximities extracted and accounted for by using incomplete error functions. With the extraction of the poles, the NMSP requires no more than six quadrature points to compute fields at distances larger than 0.02 wavelength. The CPU per distance point based on the FAM/NMSP method is less than 3 ms for all distance ranges. The accuracy of the method has been confirmed to within 0.2% from the benchmark calculations of the half-space extraction method.