Reformulation of the Fourier modal method for surface-relief anisotropic gratings

Surface-relief gratings made with anisotropic materials are finding more applications. An example is grooved magneto-optic disks as data storage media. The present work is a reformulation of the couple-wave method, for solving the anisotropic grating problem, that is described in Refs. 1-3. [Since the method essentially is a modal method relying on expanding both the electromagnetic fields and the permittivity function into Fourier series, here it is referred to as the Fourier modal method (FMM).] It originated from the work documented in Refs. 4-7. Recently Lalanne and Morris4, and Granet and Guizal5 simultaneously reformulated the conventional FMM for isotropic gratings in TM polarization. As a result, the convergence of the method for highly conducting metallic gratings was greatly improved. Auslender and Hava6 also reported the same reformulation. The findings of these authors were mathematically justified and summarized in the form of three Fourier factorization rules7. The use of these factorization rules has led to improvement of convergence in two other cases: the C method for gratings with sharp edges8 and the FMM for crossed gratings.9 This conference paper briefly reports yet another successful application of the factorization rules. A detailed exposition will soon appear elsewhere.10