Fourier Finite-Difference method and Proper Orthogonal Decomposition for quick spectral study of 2D periodic photonic structures
Abstract
We present an original rigorous numerical method for calculating light diffraction by 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. It 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. The computational gain increases with the Fourier truncation order. It is maximal (~30) for structures with subwavelength thicknesses, since a small number of finite-difference steps is sufficient to achieve a relative accuracy of approximately 1%. Our approach is particularly well suited for the analysis of generalized grating structures and metasurfaces. A second advantage of the proposed method is the possibility of using model-order reduction techniques. We use proper orthogonal decomposition (POD) to further speed up the computation of diffraction spectra as a function of the frequency, the incident angle, or a geometric parameter.
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BibTeX
@article{besbes2026fourier,
title = {{Fourier Finite-Difference method and Proper Orthogonal Decomposition for quick spectral study of 2D periodic photonic structures}},
author = {Mondher Besbes and Yassine Ferhi and Henri Benisty and Christophe Sauvan},
journal = {Journal of the Optical Society of America. A Optics, Image Science, and Vision},
year = {2026},
month = aug,
doi = {10.1364/josaa.607379},
url = {https://iogs.hal.science/hal-05339190v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Fourier Finite-Difference method and Proper Orthogonal Decomposition for quick spectral study of 2D periodic photonic structures
AU - Mondher Besbes
AU - Yassine Ferhi
AU - Henri Benisty
AU - Christophe Sauvan
PY - 2026
DA - 2026/08/11
JO - Journal of the Optical Society of America. A Optics, Image Science, and Vision
DO - 10.1364/josaa.607379
UR - https://iogs.hal.science/hal-05339190v2
AB - We present an original rigorous numerical method for calculating light diffraction by 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. It 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. The computational gain increases with the Fourier truncation order. It is maximal (~30) for structures with subwavelength thicknesses, since a small number of finite-difference steps is sufficient to achieve a relative accuracy of approximately 1%. Our approach is particularly well suited for the analysis of generalized grating structures and metasurfaces. A second advantage of the proposed method is the possibility of using model-order reduction techniques. We use proper orthogonal decomposition (POD) to further speed up the computation of diffraction spectra as a function of the frequency, the incident angle, or a geometric parameter.
SN - 1084-7529
SN - 1520-8532
ER -