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Title: Absence of bound states for waveguides in two-dimensional periodic structures

We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a perturbation in form of a line defect. The defect is aligned along one of the coordinate axes, periodic in that direction (with the same periodicity as the background), and bounded in the other direction. This setting models a so-called “soft-wall” waveguide problem. We show that there are no bound states, i.e., the spectrum of the operator under study contains no point spectrum.
Authors:
 [1] ;  [2] ;  [1]
  1. Institute for Analysis, Karlsruhe Institute for Technology (KIT), Kaiserstrasse 89, 76133 Karlsruhe (Germany)
  2. (United States)
Publication Date:
OSTI Identifier:
22251036
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; COORDINATES; LINE DEFECTS; PERIODICITY; PERTURBATION THEORY; SPECTRA; WAVEGUIDES