Treatment of nonconvergence of Fourier modal method arising from irregular field singularities at lossless metal-dielectric right-angle edges

Abstract

In a recent work [J. Opt. Soc. Am. A28, 738 (2011)], Lifeng Li and Gerard Granet investigate nonconvergence cases of the Fourier modal method (FMM). They demonstrate that the nonconvergence is due to the irregular field singularities at lossless metal-dielectric right-angle edges. Here we make further investigations on the problem and find that the FMM surprisingly converges for deep sub-wavelength gratings (grating period being much smaller than the illumination wavelength). To overcome the nonconvergence for gratings that are not deep sub-wavelength, we approximately replace the lossless metal-dielectric right-angle edges by a medium with a gradually varied refraction index, so as to remove the irregular field singularities. With such treatment, convergence is observed as the region of the approximate medium approaches vanishing.