1111.4578 (Vu Hoang et al.)

Absolute continuity for waveguides in 2D periodic structures    [PDF]

Vu Hoang, Maria Radosz

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 there are no bound states, i.e. the whole spectrum of the corresponding operator self-adjoint operator is absolutely continuous.

View original: http://arxiv.org/abs/1111.4578