This paper is a continuation of Melenk et al., “Stability analysis for electromagnetic waveguides. Part 1: acoustic and homogeneous electromagnetic waveguides” (2023) [5], extending the stability results for homogeneous electromagnetic (EM) waveguides to the non-homogeneous case. The analysis is done using perturbation techniques for self-adjoint operators eigenproblems. We show that the non-homogeneous EM waveguide problem is well-posed with the stability constant scaling linearly with waveguide length L. The results provide a basis for proving convergence of a Discontinuous Petrov-Galerkin (DPG) discretization based on a full envelope ansatz, and the ultraweak variational formulation for the resulting modified system of Maxwell equations, see Part 1.

本文是 Melenk 等人“电磁波导稳定性分析”的延续。第 1 部分：声学和均匀电磁波导”(2023) [5]，将均匀电磁 (EM) 波导的稳定性结果扩展到非均匀情况。该分析是使用扰动技术来解决自伴算子本征问题。我们证明非均匀电磁波导问题是适定的，稳定性常数与波导长度L成线性比例。结果为证明基于全包络 ansatz 的不连续 Petrov-Galerkin (DPG) 离散化的收敛性以及由此产生的修改后的麦克斯韦方程组的超弱变分公式提供了基础，请参阅第 1 部分。