Fast convergence with spectral volume integral equation for crossed block-shaped gratings with improved material interface conditions

For block-shaped dielectric gratings with two-dimensional periodicity, a spectral-domain volume integral equation is derived in which explicit Fourier factorization rules are employed. The Fourier factorization rules are derived from a projection-operator framework and enhance the numerical accuracy of the method, while maintaining a low computational complexity of O(NlogN) or better and a low memory demand of O(N).