Formulation of electromagnetic scattering from surface-relief grating with period modulation

This paper considers the electromagnetic scattering problem of surface-relief grating with period modulation, and presents a formulation based on the coordinate transformation method (C-method). The C-method is originally developed to analyze the plane-wave scattering from perfectly periodic structures, and uses the pseudo-periodic property of the fields. Since the structure under consideration is not perfectly periodic, the fields are not pseudo-periodic and the C-method cannot be directly applied. This paper introduces the pseudo-periodic Fourier transform to convert the fields in imperfectly periodic structures to pseudo-periodic ones, and the C-method becomes then applicable.