Spectrum created by line defects in periodic structures. Issue 17 (7th May 2014)

• Record Type: Journal Article
• Authors: Brown, B. M.; Hoang, V.; Plum, M.; Wood, I.
• Is Part Of: Mathematische Nachrichten. Volume 287:Issue 17/18(2014)
• Page Start: 1972
• Page End: 1985
• Publication Date: 2014-05-07
• Subjects: Perturbations of periodic problems -- line defect -- gap spectrum -- Floquet‐Bloch theory -- 35B27 -- 35J15 -- 35P05 -- 47A10 -- 78A50 -- 78A40; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201300165
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : We study a Helmholtz‐type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a three‐dimensional periodic medium; the defect is infinitely extended in one direction, but compactly supported in the remaining two. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. We will show that even small perturbations lead to additional spectrum in the spectral gaps of the unperturbed operator and investigate some properties of the spectrum that is created.