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Resonance spectrum for one-dimensional layered media

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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 k→ ∞ . The bands of resonances in the complex lower half plane are localized below the band spectrum of the corresponding periodic problem (k=∞) with k – 1 or k resonances in each band. We prove that as k→ ∞ , the resonance spectrum converges to the real axis.

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Keywords: Layered; One-dimensional; Scattering resonances; Truncated periodic

Document Type: Research Article

Affiliations: Malmö University, School of Technology and Society, SE-205 06 Malmö, Sweden

Publication date: 2006-11-01

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