A reformulation of the differential theory associated with fast Fourier factorization used for periodic diffractive structures is presented. The incorporation of a complex coordinate transformation in the propagation equations allows the modeling of semi-infinite open problems through an artificially periodized space. Hence, the outgoing wave conditions of an open structure must be satisfied. On the other hand, the excitation technique must be adjusted to adapt with guided structures. These modifications turn the differential theory into an aperiodic tool used with guided optical structure. Our method is verified through numerical results and comparisons with the aperiodic Fourier modal method showing enhanced convergence and accuracy, especially when complex-shaped photonic guided devices are considered.

中文翻译：

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与FFF相关的非周期性微分方法：一种用于集成光波导建模的高效电磁计算工具。

提出了与用于周期性衍射结构的快速傅立叶因式分解相关的微分理论的重新表述。在传播方程中包含复杂的坐标变换，可以通过人工周期化的空间对半无限开放问题进行建模。因此，必须满足开放结构的出波条件。另一方面，必须调整激励技术以适应导向结构。这些修改将微分理论转变为与导向光学结构一起使用的非周期性工具。我们的方法通过数值结果进行了验证，并与非周期性傅立叶模态方法进行了比较，这种方法显示出增强的收敛性和准确性，尤其是在考虑了复杂形状的光子制导设备时。