The combination of VIEs and the introduction of normal-vector fields in the periodic directions results in a similar convergence as compared to RCWA  for binary gratings.
Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," Journal of the Optical Society of America A, Vol.
In the spectral domain, the Green's function is directly and efficiently available per Fourier mode but now the field-material interactions need careful attention, in view of the Fourier factorization rules that have become so widespread in RCWA and the differential method.
This observation has been worked out in full detail for 2D and 3D field-material interactions and given a solid theoretical foundation by Li [2, 3], within the context of RCWA.
The most commonly employed field-material interaction formula used in the context of RCWA and the Differential Method is given by [4, Equation (15)]
The computational advantages for a binary grating can be transferred to more general gratings by following the approach taken in RCWA, in which a grating is approximated by a stack of binary gratings.
To compare our results with results obtained with RCWA , an array of cavities with square cross section of edge length 0.
Discussion starts by establishing the numerical framework for scattering matrices in semi-analytical methods and unifying the MOL and RCWA.
To demonstrate the utility and performance enhancement of the approach described in this paper, a three dimensional electromagnetic band gap (EBG) material was modeled using RCWA.
Other than the scattering matrix manipulations, the three versions of RCWA were kept identical.