Resonance spectrum for one-dimensional layered media
We consider the "weighted" operator Pk= – âˆ,x a(x)âˆ, x on the real line with a step-like coefficient which appears when propagation of waves through a finite slab of a periodic medium is studied. The medium is transparent at certain resonant frequencies which are related to the complex resonance spectrum of Pk. If the coefficient is periodic on a finite interval (locally periodic) with k identical cells, then the resonance spectrum of Pk has band structure. In the article, we study a transition to semi-infinite medium by taking the limit kâ†’ âˆž . The bands of resonances in the complex lower half plane are localized below the band spectrum of the corresponding periodic problem (k=âˆž) with k – 1 or k resonances in each band. We prove that as kâ†’ âˆž , the resonance spectrum converges to the real axis.
Document Type: Research Article
Affiliations: Malmö University, School of Technology and Society, SE-205 06 Malmö, Sweden
Publication date: 2006-11-01