Spectrum created by line defects in periodic structures

DOI10.1002/mana.201300165zbMath1316.35215arXiv1306.6256OpenAlexW2962821476MaRDI QIDQ5175854

Michael Plum, B. Malcolm Brown, I. G. Wood, Vu Phuong Hoang

Publication date: 25 February 2015

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.6256

zbMATH Keywords

Laplace operatorFloquet-Bloch theoryline defectgap spectrumperturbations of periodic problems

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectrum, resolvent (47A10) Second-order elliptic equations (35J15) Antennas, waveguides in optics and electromagnetic theory (78A50) Waves and radiation in optics and electromagnetic theory (78A40) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (5)

Non-symmetric perturbations of self-adjoint operators ⋮ Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect ⋮ Gap localization of multiple TE‐Modes by arbitrarily weak defects ⋮ Asymptotics of eigenvalues in spectral gaps of periodic waveguides with small singular perturbations ⋮ Asymptotics of the eigenvalues and eigenfunctions of a thin square Dirichlet lattice with a curved ligament

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Theory of Bloch waves
• Mathematical analysis of the guided waves in photonic crystal fibers
• On guided waves created by line defects
• On guided electromagnetic waves in photonic crystal waveguides
• Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
• Guided Waves in a Photonic Bandgap Structure with a Line Defect
• On Spectral Bounds for Photonic Crystal Waveguides
• Partial Differential Equations with Periodic Coefficients and Bloch Waves in Crystals
• On the spectrum of waveguides in planar photonic bandgap structures

This page was built for publication: Spectrum created by line defects in periodic structures