1301.0837 (Vincent Duchêne et al.)

Localized perturbations of periodic structures and the bifurcation of
defect modes    [PDF]

Vincent Duchêne, Iva Vukićević, Michael I. Weinstein

Waves in extended periodic structures are well-known to spatially disperse and decay in amplitude as time advances. This dispersion is associated with the continuous spectrum of the underlying differential operator and the absence of discrete eigenvalues. The introduction of localized perturbations, leads to defect modes, states in which energy remains trapped and spatially localized. In this paper we present results on the bifurcation of such defect modes, associated with the emergence of discrete eigenvalues from the continuous spectrum.

View original: http://arxiv.org/abs/1301.0837