Improvement of the coordinate transformation method for surface-relief gratings with sharp edges

Abstract

The coordinate transformation method for modeling surface-relief gratings is reformulated with use of the recent results [ J. Opt. Soc. Am. A13, 1870 ( 1996)] on the Fourier factorization of products that contain discontinuous periodic functions. The matrix operator of the eigenvalue problem in the traditional formulation is modified following the correct Fourier factorization procedures. In addition, a new and simpler matrix operator is derived. Both the modified old operator and the new operator greatly improve the convergence of the coordinate transformation method for gratings whose profiles have sharp edges.