Modal expansion for the 2D Green's function in a non-orthogonal coordinates system

We present an efficient modal method to calculate the two-dimensional Green's function for electromagnetics in curvilinear coordinates. For this purpose the coordinate transformation based differential method, introduced for the numerical analysis of surface-relief gratings, is directly used with perfectly matched layers (PMLs). The covariant formalism Maxwell's equations, very convenient for the non-orthogonal coordinates formulation, also gives an unified analysis of PMLs. Numerical results for a line source placed above a perfectly conducting corrugated surface are presented.