Algorithm for the rigorous coupled-wave analysis of grating diffraction

Diffraction of light by periodic gratings is analyzed with a characteristic-matrix formalism based on a rigorous coupled-wave approach. This formalism is particularly convenient for modeling the diffraction by nonuniform periodic structures. In order to overcome numerical difficulties that are due to inhomogeneous eigenmodes, we propose a new algorithm that remains stable for gratings of any thickness. We obtain the stability by distinguishing in the computation the growing and the decaying inhomogeneous modes. Numerical examples and comparisons with previous results are given.