The Fourier modal method (FMM) is certainly one of the most popular and general methods for the modeling of diffraction gratings. However, for non-lamellar gratings it is associated with a staircase approximation of the profile, leading to poor convergence rate for metallic gratings in TM polarization. One way to overcome this weakness of the FMM is the use of the fast Fourier factorization (FFF) first derived for the differential method. That approach relies on the definition of normal and tangential vectors to the profile. Instead, we introduce a coordinate system that matches laterally the profile and solve the covariant Maxwell’s equations in the new coordinate system, hence the name matched coordinate method (MCM). Comparison of efficiencies computed with MCM with other data from the literature validates the method.

中文翻译：

---

用于一维光栅分析的匹配坐标

傅里叶模态法 (FMM) 无疑是用于衍射光栅建模的最流行和通用的方法之一。然而，对于非层状光栅，它与轮廓的阶梯近似有关，导致 TM 偏振中金属光栅的收敛速度很差。克服 FMM 的这一弱点的一种方法是使用首先为微分方法推导的快速傅立叶分解 (FFF)。该方法依赖于轮廓的法向和切向矢量的定义。相反，我们引入了一个横向匹配轮廓的坐标系，并在新坐标系中求解协变麦克斯韦方程组，因此命名为匹配坐标法 (MCM)。将 MCM 计算的效率与文献中的其他数据进行比较验证了该方法。