We report an advanced formulation of the Fourier modal method developed for two-dimensionally periodic multilayered structures containing materials with nonzero macroscopic magnetoelectric coefficients (also known as coefficients of chirality and bianisotropy) represented as arbitrary $3\times 3$ tensors. We consider two numerical schemes for this formulation: with and without generalized Fourier factorization rules. For both schemes, we provide explicit expressions for the Fourier tensors of macroscopic material parameters and demonstrate that, in the absence of magnetoelectric coupling, they reduce to the conventional factorization rules. We show that the scheme employing factorization rules facilitates improved convergence, even when the macroscopic chirality coefficient is large. The described formulation represents a fast and rigorous technique for theoretical studies of periodic structures with chiral, bianisotropic, or nonreciprocal materials in the widely used framework of the Fourier modal method.

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• Classical optics
• Light-matter interaction
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• Photonic crystals
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