Numerical scattering analysis of TE plane waves by a metallic diffraction grating with local defects.

We consider the numerical scattering of plane waves by a metallic diffraction grating with a single defect. Besides different diffracted orders, a perturbed scattered field with arbitrary reflection direction is generated by the defect. We transform the diffraction grating into a closed waveguide by introducing a perfectly matched layer. The diffracted field is solved by applying pseudoperiodic boundary conditions on cell boundaries. Then we take two steps to resolve the perturbed scattered field. On the defect cell it is obtained by solving the governing wave equation with absorbing boundary conditions derived by a fast recursive doubling procedure. On the rest of the domain the perturbed scattered field is computed by using the recursive matrix operators efficiently. An optical theorem is employed to evaluate the proposed method.