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

Tuesday, December 13, 2016 - 10:30am - 11:30am
Keller 3-180
Maria Radosz (Rice University)
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.