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A Spectral Volume Integral Equation Method for Arbitrary BI-Periodic Gratings with Explicit Fourier Factorization

By Martijn C. van Beurden
Progress In Electromagnetics Research B, Vol. 36, 133-149, 2012


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.


Martijn C. van Beurden, "A Spectral Volume Integral Equation Method for Arbitrary BI-Periodic Gratings with Explicit Fourier Factorization," Progress In Electromagnetics Research B, Vol. 36, 133-149, 2012.


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