Efficient and Stable Implementation of RCWA for Ultrathin Multilayer Gratings: T-Matrix Approach Without Solving Eigenvalues

Based on the transmittance matrix (T-matrix) approach, an efficient and stable rigorous coupled-wave analysis (RCWA) method for ultrathin multilayer gratings without solving eigenvalues is proposed in this letter. The numerical instability caused by the inversion of an ill-conditioned matrix in the traditional T-matrix approach is solved by implementing the proposed method. Besides, compared with the traditional RCWA method, the proposed method does not need to solve the eigenvalues and eigenvectors of the eigenmatrix, which avoids the numerical problems and time-consuming problems caused by this process. A numerical example shows that the results of CST simulations are consistent with the results obtained by the proposed method.