Convergence of the coupled-wave method for metallic lamellar diffraction gratings

Numerical evidence is presented that shows that, for metallic lamellar gratings in TM polarization, the coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am. A3, 1780 ( 1986)] converges slowly. (In some cases, for achieving a relative error of less than 1% in diffraction efficiencies, the number of spatial harmonics retained in the computation must be much greater than 100.) By classification of the modal methods for analyzing diffraction gratings into two distinct categories, the cause for the slow convergence is analyzed and attributed to the use of Fourier expansions to represent the permittivity and the electromagnetic fields in the grating region. The eigenvalues and the eigenfunctions of the modal fields in the grating region, whose accurate determination is crucial to the success of the coupled-wave method, are shown to converge slowly as a result of the use of these Fourier expansions. Despite its versatility and simplicity, the coupled-wave method should be used with caution for metallic surface-relief gratings in TM polarization.