Résumé
We present a simplification of the well-known Fourier Modal Method (FMM) equipped with Adaptive Spatial Resolution (ASR) concept for gratings with subwavelength heights. We show that in this case it is possible to compute the scattering matrix of the structure by solving only one eigenvalue problem (instead of three) which reduces the most expensive computational part of the FMMASR algorithm. This approach is very efficient and thus suitable for periodic metasurfaces.The Fourier Modal Method1 is one of the most versatile and efficient methods for modeling diffraction from gratings. This is why it is suitable for modeling metasurfaces based on binary gratings. The problem with this approach is that for metallic structures, it is necessary to truncate the Fourier series representing the fields to a high order implying the use of large matrices (especially in the case of crossed gratings). This situation can be improved by using the ASR concept2 to accelerate the convergence rate and thus reduce the size of the matrices in play. Still, this remains demanding from the computational point of view, for certain applications, because the heart of the FMM is based on the solution of an eigenvalue problem. This later has a cost scaling with the third power of the dimension of the matrices involved. This can be a severe limitation and hinder the use of the FMM.On the other hand, an interesting class of metasurfaces is made of gratings with subwavelength thicknesses. In this special case, it is possible (via a Taylor series expansion of the phase propagation matrix) to simplify the FMMASR is such a way that it is no longer needed to solve any eigenvalue problem3. This proves to be very efficient in reducing the computational cost.After recalling the principle of the FMMASR and the details of the corresponding algorithm, I will show how the assumption of subwavelength height leads to a simplified scattering matrix where it is sufficient to solve one eigenvalue problem. Numerical examples will be presented to support this new algorithm.References1. L. Li, “New formulation of the Fourier Modal Method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758-2767, 1997.2. B. Guizal, et al., “Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution,” Opt. Lett. 34, 2790-2792, 2009.3. J. Li, et al., “Efficient Rigorous Coupled-Wave Analysis Without Solving Eigenvalues for Analyzing One-Dimensional Ultrathin Periodic Structures,” IEEE Access, Vol. 8, 198131-198138, 2020.