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.