Convergence performance of the coupled-wave and the differential methods for thin gratings

The new formulation of the coupled-wave analysis recently proposed by Lalanne and Morris [J. Opt. Sec. Am. A 13, 779 (1996)] and by Granet and Guizal [J. Opt. Sec. Am. A 13, 1019 (1996)] that drastically improves the convergence performance of the method for lamellar gratings and for TM polarization is shown to be badly conditioned for gratings with a small thickness. Numerical evidence obtained with the coupled-wave analysis and with the differential methods for several grating diffraction problems shows that, in some cases that we identify, the convergence of the conventional formulation can be faster than that of the new one. The discussion includes lamellar, multilevel binary, and continuous-profile geometries. (C) 1997 Optical Society of America.