Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model Academic Article uri icon

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 (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 (x) = 1. The value of (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.

published proceedings

  • SIAM Journal on Applied Mathematics

author list (cited authors)

  • Figotin, A., & Kuchment, P.

citation count

  • 107

complete list of authors

  • Figotin, Alex||Kuchment, Peter

publication date

  • February 1996