Mathematical reflections on the Fourier modal method in grating theory (Q2758023)

This paper surveys a computational method for diffraction gratings which is known as Fourier Modal Method, rigorous coupled wave analysis (RCWA), BKK method, Fourier expansion method among others. This method is very popular within the engineering community, but until recently it had serious problems with certain TM diffraction problems. The author points out that this is caused by an inadequate treatment of truncated Fourier series of discontinuous functions and their products. He investigates a so called inverse rule for the truncated Fourier sum of the product of discontinuous functions and demonstrates its correctness by numerical examples. On the other hand, up to now there is no convergence analysis for this method.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00050].