Coupled Integral equations for diffraction by profiled, anisotropic, periodic structures

Recently Popov and Neviere have reformulated harmonic Maxwell´s equations in Fourier space for periodic structures as a first-order system of differential equations. To ensure fast convergence of the Fourier series of the electromagnetic field, the authors utilized Li´s theorems of Fourier factorization in their derivation. In this paper, Popov´s and Neviere´s equations are slightly modified to facilitate the derivation of an equivalent system of Fredholm integral equations (IEs) of the second kind. This system of coupled IEs involves only transversal components of the electromagnetic field and corresponds to the volume-type electric field integral equation (EFIE) and magnetic field integral equation (MFIE) for the particular case of periodic structures. Therefore, the proposed, fast-converging IEs are herein after referred to as the TEFIE and TMFIE. The numerical solution of the TEFIE and TMFIE can be obtained with conventional direct or iterative solution methods.