The PML method for calculating the propagative wave numbers of electromagnetic wave in periodic structures

2025/06/08 by Lide Cai, Cai, Lide, Junqing Chen +2
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2506.07084

openalex publication_date 2025/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

When the electromagnetic wave is incident on the periodic structures, in addition to the scattering field, some guided modes that are traveling in the periodic medium could be generated. In the present paper, we study the calculation of guided modes. We formulate the problem as a nonlinear eigenvalue problem in an unbounded periodic domain. Then we use perfectly matched layers to truncate the unbounded domain, recast the problem to a quadratic eigenvalue problem, and prove the approximation property of the truncation. Finally, we formulate the quadratic eigenvalue problem to a general eigenvalue problem, use the finite element method to discrete the truncation problem, and show numerical examples to verify theoretical results.

Citations

• The PML-Method for a Scattering Problem for a Local Perturbation of an Open Periodic Waveguide
• PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface
• Exponential convergence of perfectly matched layers for scattering problems with periodic surfaces
• High order complex contour discretization methods to simulate scattering problems in locally perturbed periodic waveguides
• A Floquet-Bloch transform based numerical method for scattering from locally perturbed periodic surfaces
• A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides

Related

• The PML-Method for a Scattering Problem for a Local Perturbation of an Open Periodic Waveguide
• An adaptive finite element PML method for the elastic wave scattering problem in periodic structures
• PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface
• Simulation-Based Equations for Propagation Constant in Uniform or Periodic Transmission
• On generalized discrete PML optimized for propagative and evanescent waves