On the location of proper and improper surface wave poles for the grounded dielectric slab [microstrip antennas]

A recently obtained closed-form asymptotic representation due to S. Barkeshli (1988) of the microstrip surface Green´s function is known to provide an efficient moment method analysis of microstrip problems. However, in order to make this closed-form expression accurate even for very small separation of source and field points (to within a few tenths of a wavelength), both the proper and improper surface wave transition effects must be included in the solution. This requires finding the location of the corresponding proper and improper poles. A good initial estimate that allows the poles to be located rapidly by using an iterative procedure is presented. The number of proper and improper surface wave poles that have to be considered and their values are tabulated