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A"],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>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 (\u223c30) 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.<\/jats:p>","DOI":"10.1364\/josaa.607379","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T14:00:09Z","timestamp":1783951209000},"page":"1380","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fourier finite-difference method and proper orthogonal decomposition for the quick spectral study of 2D periodic photonic structures"],"prefix":"10.1364","volume":"43","author":[{"given":"Mondher","family":"Besbes","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00d0rke27","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yassine","family":"Ferhi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00d0rke27","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7428-7196","authenticated-orcid":true,"given":"Henri","family":"Benisty","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00d0rke27","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8360-9254","authenticated-orcid":true,"given":"Christophe","family":"Sauvan","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00d0rke27","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,8,11]]},"reference":[{"key":"josaa-43-9-1380-R1","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s10043-003-0063-2","type":"journal-article","volume":"10","author":"Kikuta","year":"2003","journal-title":"Opt. 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