Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2025

Fourier Finite-Difference method and Proper Orthogonal Decomposition for quick spectral study of 2D periodic photonic structures

Résumé

We present an original electromagnetic solver for three-dimensional photonic structures with a two-dimensional periodicity. It is based on Fourier expansions in the two periodic directions and an elegant yet efficient combination of finite-difference discretization and modal treatment in the propagation direction. The Fourier Finite Difference Method (FFDM) is cast into an easy-to-handle, agile, and efficient matrix formalism. Our approach uses matrix inversions instead of eigenmodes computations, a strategy that confers a clear advantage in terms of computation time for the large Fourier truncation orders that are typically used to deal with micro and nanophotonic structures of current interest. Therefore, it is particularly well suited for the analysis of generalized grating structures and metasurfaces. The computational gain increases with the Fourier truncation order. It is maximal (10-30) for coarse finite-difference steps, which are nevertheless sufficient to achieve a relative accuracy of approximately 1%. A second important advantage of the proposed method is the possibility of using model-order reduction techniques. We use Proper Orthogonal Decomposition (POD), in conjunction with the snapshot technique, to further speed up the computation of diffraction spectra as a function of the frequency, the incident angle, or any geometric parameter.

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Dates et versions

hal-05339190 , version 1 (30-10-2025)

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  • HAL Id : hal-05339190 , version 1

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Mondher Besbes, Yassine Ferhi, H. Benisty, Christophe Sauvan. Fourier Finite-Difference method and Proper Orthogonal Decomposition for quick spectral study of 2D periodic photonic structures. 2025. ⟨hal-05339190⟩
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