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 Mo haram and Gaylord [J. Opt. Soc. Am. A 3, 1780 (1986)] converges slowly . (In some cases, for achieving a relative error of less than 1% in di ffraction efficiencies, the number of spatial harmonics retained in th e computation must be much greater than 100.) By classification of the modal methods for analyzing diffraction gratings into two distinct ca tegories, the cause for the slow convergence is analyzed and attribute d to the use of Fourier expansions to represent the permittivity and t he electromagnetic fields in the grating region. The eigenvalues and t he eigenfunctions of the modal fields in the grating region, whose acc urate determination is crucial to the success of the coupled-wave meth od, are shown to converge slowly as a result of the use of these Fouri er expansions. Despite its versatility and simplicity, the coupled-wav e method should be used with caution for metallic surface-relief grati ngs in TM polarization.