Absence of bound states for waveguides in 2D periodic structures

Details Absence of bound states for waveguides in 2D periodic structures Absence of bound states for waveguides in 2D periodic structures

2011-11-19

arxiv.org/abs/1111.4578v1

Mathematics

Spectral Theory

Scientific paper

We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a 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 as a consequence of the perturbation, no eigenvalues can arise in the band gaps of the unperturbed, fully periodic problem.

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