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.

中文翻译：

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用于超薄多层光栅的 RCWA 的高效稳定实现：无需求解特征值的 T 矩阵方法

本文基于透射率矩阵（T-matrix）方法，提出了一种无需求解特征值的高效且稳定的超薄多层光栅严格耦合波分析（RCWA）方法。通过实施所提出的方法，解决了传统T矩阵方法中因病态矩阵求逆引起的数值不稳定问题。此外，与传统的RCWA方法相比，该方法不需要求解特征矩阵的特征值和特征向量，避免了这个过程带来的数值问题和耗时问题。一个数值例子表明，CST 模拟的结果与所提出的方法获得的结果是一致的。