On the fast approximation of Green´s functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green´s function of a mixed-potential integral-equation formulation is examined and is found to be limited to low values of κ_oρ (in this context κ₀ρ = 2πρ/λ₀, where ρ is the distance between the source and the field points of the Green´s function and λ₀ is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large κ₀ρ is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green´s functions. In this paper, the method developed for the computation of the Green´s function is used for planar structures containing both lossless and lossy media