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Guided Waves in a Photonic Bandgap Structure with a Line Defect

Summary: Guided Waves in a Photonic Bandgap Structure
with a Line Defect
Habib Ammari  Fadil Santosa y
Numerical simulations have shown that when a line of defects is
introduced into a photonic bandgap structure, waves can be guided
along the line. It has been conjectured that the mechanism respon-
sible for the guidance phenomenon is the introduction of a spectrum
in the bandgap by the defect. The purpose of this work is to give
a mathematical framework for understanding this phenomenon. We
show that there exist solutions of the scalar wave equation which is
localized near the line defects which behave like guided modes. More-
over, these solutions can be parameterized by a frequency spectrum
which is continuous, and can cover parts of the original bandgap. The
frequency of the guided modes depend on a wave number parameter
and can be interpreted as a dispersion relation. We illustrate the main
ndings of the investigation in a numerical example.
1 Introduction
The purpose of this work is the study of wave propagation in an in nite
periodic structure with a line defect. The medium under consideration is


Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique


Collections: Mathematics