The generalization of a two-dimensional spatial spectral volume integral equation to a three-dimensional spatial spectral integral equation formulation for electromagnetic scattering from dielectric objects in a stratified dielectric medium is explained. In the spectral domain, the Green function, contrast current density, and scattered electric field are represented on a complex integration manifold that evades the poles and branch cuts that are present in the Green function. In the spatial domain, the field-material interactions are reformulated by a normal-vector field approach, which obeys the Li factorization rules. Numerical evidence is shown that the computation time of this method scales as on the number of unknowns. The accuracy of the method for three numerical examples is compared to a finite element method reference.

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We propose a fast semi-analytical approach for solving Maxwell's equations in Born approximation based on the Fourier modal method (FMM). We show that, as a result of Born approximation, most matrices in the FMM algorithm become diagonal, thus allowing a reduction of computational complexity from cubic to linear. Moreover, due to the analytical representation of the solution in the vertical direction, the number of degrees of freedom in this direction is independent of the wavelength. The method is derived for planar illumination with two basic polarizations (TE/TM) and an arbitrary 2D geometry infinitely periodic in one horizontal direction.

A spectral-domain integral equation for scattering by periodic birefringent dielectric objects embedded in a birefringent layered medium. In