Highly Accurate and Fast Convergent Diffractive Interface Theory for Fast Analysis of Metasurfaces

Recently, an approximate formalism [Opt. Express 23, 2764, (2015)] called diffractive interface theory has been reported for the fast analysis of the optical response of metasurfaces, subwavelength two-dimensional periodic arrays. In this method, the electromagnetic boundary conditions are derived using the susceptibility distribution of the metasurface, such that the analysis of metasurface is possible without solving any eigenvalue equation inside the grating layer. In this paper, we modify the boundary conditions to achieve more accurate results. In addition, in this paper, correct Fourier factorization rules are also applied leading to faster convergence rate. The obtained results are compared with the former formalism and Fourier modal method (FMM). It is demonstrated that the accuracy of the results is far better than the previous formalism and very close to FMM, while it has less computational cost relative to FMM.