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 in the framework of polynomial modal methods for complex metasurface modeling.

The polynomial modal method (PMM) is one of the most powerful methods for modeling diffraction from lamellar gratings. In the present work, we show that applying it to the so-called matched coordinates leads to important improvement of convergence for crossed lamellar gratings with patterns that are not parallel to the coordinates' axes. After giving the new formulation of the PMM under matched coordinates in the general framework of biperiodic structures, we provide numerical examples to demonstrate the effectiveness of the proposed approach.

Numerical scheme for the modal method based on subsectional Gegenbauer polynomial expansion: application to biperiodic binary grating.

The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system.

Perturbation method for the Rigorous Coupled Wave Analysis of grating diffraction.

The perturbation method is combined with the Rigorous CoupledWave Analysis (RCWA) to enhance its computational speed. In the original RCWA, a grating is approximated by a stack of lamellar gratings and the number of eigenvalue systems to be solved is equal to the number of subgratings. The perturbation method allows to derive the eigensolutions in many layers from the computed eigensolutions of a reference layer provided that the optical and geometrical parameters of these layers differ only slightly.

Rigorous and efficient grating-analysis method made easy for optical engineers.

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt.