The method of curvilinear coordinates applied to the problem of scattering from surface-relief gratings defined by parametric equations: application to scattering from a cycloidal grating

The method of curvilinear coordinates is formulated using the coordinate transformations given by parametric equations. As an illustration, a translation coordinate system and a relaxation coordinate system are used to calculate the reflectivities of various cycloidal profiles. We show, with this example, that parametric coordinate systems permit one to handle profiles that previously had been out of reach owing to their sharpness.