2002/07/03 by Julian Edward, Edward, Julian
Computer Science · Mathematics · Physics and Astronomy · #35J05 #76Q05 #Advanced Mathematical Modeling in Engineering #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35J05 #msc:76Q05
paper · pdf · doi:10.48550/arxiv.math-ph/0207007
11 pages, Latex
arxiv created 2002/07/03 · openalex publication_date 2002/07/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions on the guide walls. It is proven that there are at least N (resp. N-1) trapped modes in the Neumann case (resp. Dirichlet case) under fairly general hypotheses, including the special case where the obstacles consist of line segments placed parallel to the waveguide walls. This work should be viewed as an extension of "Periodic structures on waveguides" by Linton and McIvor.