Modal analysis of diffraction by snake gratings using a tensor product of pseudo-periodic functions and Legendre polynomials.

The problem of diffraction by snake gratings is presented and formulated as an eigenvalue eigenvector problem. A numerical solution is obtained thanks to the method of moments where a tensor product of pseudo-periodic functions and Legendre polynomials is used as expansion and test functions. The method is validated by comparison with the usual Fourier modal method (FMM) as applied to crossed gratings.

Scattering by cylinders with an arbitrary cross-section using domain decomposition and polynomial expansions.

In this paper, the electromagnetic field scattered by a cylinder with an arbitrary cross section is computed using a domain decomposition method in which the structure under consideration is enclosed with two fictitious circular cylinders. TE and TM polarizations are investigated. Our code is successfully validated by comparison with analytical results and with the finite element software COMSOL.

Modal spectral element method with modified Legendre polynomials to analyze binary crossed gratings.

In a previous paper, a modal spectral element method (SEM), the originality of which comes from the use of a hierarchical basis built with modified Legendre polynomials, was shown to be very powerful for the analysis of lamellar gratings. In this work, keeping the same ingredients, the method has been extended to the general case of binary crossed gratings. The geometric versatility of the SEM is illustrated with gratings whose patterns are not aligned with the boundaries of the elementary cell.

Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms.

We introduce a Domain Decomposition Spectral Method (DDSM) as a solution for Maxwell's equations in the frequency domain. It will be illustrated in the framework of the Aperiodic Fourier Modal Method (AFMM). This method may be applied to compute the electromagnetic field diffracted by a large-scale surface under any kind of incident excitation.

Matched coordinates for the analysis of 1D gratings.

The Fourier modal method (FMM) is certainly one of the most popular and general methods for the modeling of diffraction gratings. However, for non-lamellar gratings it is associated with a staircase approximation of the profile, leading to poor convergence rate for metallic gratings in TM polarization. One way to overcome this weakness of the FMM is the use of the fast Fourier factorization (FFF) first derived for the differential method.