In this paper, a general methodology to study rigorous discontinuities in open waveguides is presented. It relies on a full vector description given by Maxwell’s equations in the framework of the finite element method. The discontinuities are not necessarily small perturbations of the initial waveguide and can be very general, such as plasmonic inclusions of arbitrary shapes. The leaky modes of the invariant structure are first computed and then injected as incident fields in the full structure with obstacles using a scattered field approach. The resulting scattered field is finally projected on the modes of the invariant structure making use of their bi-orthogonality. The energy balance is discussed. Finally, the modes of open waveguides periodically structured along the propagation direction are computed. The relevant complex propagation constants are compared to the transmission obtained for a finite number of identical cells. The relevance and complementarity of the two approaches are highlighted on a numerical example encountered in infrared sensing. Open source models allowing us to retrieve most of the results of this paper are provided.

中文翻译：

---

光子波导中的不连续性：采用有限元方法的基于Maxwell的严格3D建模。

在本文中，提出了一种研究开放波导中严格不连续性的通用方法。它依赖于有限元方法框架中Maxwell方程给出的完整矢量描述。不连续点不一定是初始波导的小扰动，而可能非常普遍，例如任意形状的等离子体包裹体。首先计算不变结构的泄漏模式，然后使用散射场方法将其作为具有障碍物的完整结构的入射场注入。最后，利用它们的正交性将最终的散射场投影到不变结构的模式上。讨论了能量平衡。最后，计算沿传播方向周期性构造的开放波导的模式。将相关的复数传播常数与有限数量的相同小区获得的传输进行比较。在红外传感中遇到的一个数值示例中，突出了这两种方法的相关性和互补性。提供了开放源代码模型，使我们能够检索本文的大部分结果。