Accurate evaluation of Green＇s functions in a layered medium by SDP-FLAM

Based on local Taylor expansions on the complex plane, a method for fast locating all modes （FLAM） of spectral-domain Green＇s Functions in a planar layered medium is developed in this paper. SDP-FLAM, a combination of FLAM with the steepest descent path algorithm （SDP）, is employed to accurately evaluate the spatial-domain Green＇s functions in a layered medium. According to the theory of complex analysis, the relationship among the poles, branch points and Riemann sheets is also analyzed rigorously. To inverse the Green＇s functions from spectral to spatial domain, SDP-FLAM method and discrete complex image method （DCIM） are applied to the non-near field region and the near filed region, respectively. The significant advantage of SDP-FLAM lies in its capability of calculating Green＇s functions in a layered medium of moderate thickness with loss or without loss. Some numerical examples are presented to validate SDP-FLAM method.