Discrete complex image approximation of periodic Green's functions in multilayer media

The periodic Green's function in layered media can be expressed as an infinite series in terms of the spectral domain Green's function which can be approximated by complex exponentials through the use of Discrete Complex Image Method (DCIM). During the application of the DCIM, two-level or three-level approximation schemes can be employed. In this work, the accuracy in approximating the periodic Green's function via two-level and three-level approximation schemes are studied and the accuracy improvement achieved by applying the 3-level approximation scheme along the real k_p axis is demonstrated through numerical examples.