Polygon-based unified Fourier-modal approach for diffractive optics simulations

In this article, we derive a theoretical formalism that unifies the rigorous coupled wave analysis and the dynamical diffraction theory. Based on this formalism, we design a computational approach for the diffraction calculation for the nanoscale lamellar gratings with an arbitrary line profile shape. In this approach, the gratings line profile is approximated as a polygon. This proves to be convenient since such an approach does not rely on the geometry model of the grating. We test the new approach against other computational theories and a synchrotron scattering experiment.