Differential covariant formalism for solving Maxwell´s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces

A rigorous differential method describing the diffraction properties of lossy periodic surfaces is presented. A nonorthogonal coordinate system and a covariant formalism of Maxwell´s equation are used simplifying boundary conditions expression. Only one eigenvalue system, unique for the TE and TM polarizations even for an oblique incidence, needs to be solved. Thus the numerical treatment is very efficient and CPU requirements significantly reduced. Numerical results are successfully compared with those obtained by an integral method using the boundary element method (BEM) as a numerical procedure