Comments on the problems in DCIM

For the rigorous analysis of multilayer printed geometries, numerical algorithms based on the method of moments (MoM) are widely favored. The application of the MoM in either the spectral or the spatial domain, requires knowledge of the Green´s functions in the corresponding domain. In the spatial domain, the Green´s functions for stratified media are traditionally represented by the Sommerfeld integral. However, this representation of the Green´s functions is not computationally efficient for use in conjunction with the MoM. To overcome this numerical inefficiency for obtaining the spatial-domain Green´s functions, they have been approximated by complex images using the Sommerfeld identity; hence, the method is named the discrete complex image method (DCIM). As is the case for most approximations, the closed-form Green´s functions have some limitations. Closed-form Green´s functions are accurate for small and moderate distances, but for distances larger than a few wavelengths, they deteriorate violently. Three possible sources of this problem are discussed and misunderstandings are clarified.