This paper is a continuation of Melenk et al., "Stability analysis for electromagnetic waveguides. Part 1: acoustic and homogeneous electromagnetic waveguides" (2023), 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.
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Coupling Light in Ion-Exchanged Waveguides by Silver Nanoparticle-Based Nanogratings: Manipulating the Refractive Index of Waveguides
- Award ID(s):
- 2110603
- PAR ID:
- 10374294
- Date Published:
- Journal Name:
- ACS Applied Nano Materials
- Volume:
- 5
- Issue:
- 4
- ISSN:
- 2574-0970
- Page Range / eLocation ID:
- 5439 to 5447
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In a time-harmonic setting, we show for heterogeneous acoustic and homogeneous electromagnetic wavesguides stability estimates with the stability constant depending linearly on the length L of the waveguide. These stability estimates are used for the analysis of the (ideal) ultraweak (UW) variant of the discontinuous Petrov--Galerkin (DPG) method. For this UW DPG, we show that the stability deterioration with L can be countered by suitably scaling the test norm of the method. We present the "full envelope approximation," a UW DPG method based on nonpolynomial ansatz functions that allows for treating long waveguides.more » « less
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