A spectral volume integral equation method for arbitrary bi-periodic gratings with explicit fourier factorization

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Abstract

For dielectric periodic gratings, we propose the combination of a spectral-domain volume integral equation and Fourier factorization rules to address the Gibbs phenomenon caused by jumps in both the fields and the permittivity. From a theoretical point of view we discuss two ways to overcome the computational complexity caused by the inverse rule by changing the fundamental unknowns of the underlying electromagnetic problem. The resulting numerical system is solved iteratively and the corresponding matrix-vector product has an O(NMlogM) complexity, where M is the number of Fourier modes and N is the number of sample points in the longitudinal direction.
Original languageEnglish
Pages (from-to)133-149
JournalProgress In Electromagnetics Research B
Volume36
DOIs
Publication statusPublished - 2012

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