Comparing the Fourier modal method with the C method: analysis of conducting multilevel gratings in TM polarization

The coordinate transformation method (C method) with adaptive spatial resolution and the Fourier modal method (FMM) are compared in the case of conducting discontinuous multilevel gratings in TM polarization. A procedure permitting analysis of such gratings more efficiently with the C method than with the FMM is presented. The C method is observed to converge more rapidly than the FMM, whose instabilities are shown to harm the convergence in the aforementioned case.