Image Solution for the 3-D Static Green’s Function of a Vertically Stratified Two-Layer Half-Space

The general form of 3-D static Green's function for a general structure consisting of N arbitrary adjacent dielectric wedges is derived using the Kontorovich-Lebedev and Fourier transforms. It consists of several point sources in physical space and a line image source in complex space for each region of the problem geometry. While the point sources can be treated conventionally, the line image distributions are obtained by extracting a proper asymptotic behavior of the solution, which can be numerically computed. As an example, the case of a vertically stratified two-layer half-space is investigated and the respective point and line image sources are obtained. The efficiency of the proposed solution method is demonstrated by comparing the computational time for a given structure with that required by a commercially available numerical code using the finite integration technique.