Band-gap structure of spectra of periodic dielectric and acoustic media. I. Scalar model
Figotin, Alex Kuchment, Peter
Figotin, Alex
Kuchment, Peter
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1996
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Article
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Band-gap structure of the spectrum,Periodic acoustic media,Periodic dielectrics,Propagation of electromagnetic and acoustic waves
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Citation
Figotin, A., & Kuchment, P. (1996). Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model. SIAM Journal on Applied Mathematics, 56(1), 68-88.
Abstract
We investigate the band-gap structure of the spectrum of second-partial differential operators associated with the propagation of waves in a periodic two-component medium. The medium is characterized by a real-valued position-dependent periodic function ε(x) that is the dielectric constant for electromagnetic waves and mass density for acoustic waves. The imbedded component consists of a periodic lattice of cubes where ε(x) = 1. The value of ε(x) on the background is assumed to be greater than 1. We give the complete proof of existence of gaps in the spectra of the corresponding operators provided some simple conditions imposed on the parameters of the medium.
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Society for Industrial and Applied Mathematics Publications
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SIAM Journal on Applied Mathematics
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0036-1399