Gap localization of TE-Modes by arbitrarily weak defects

TL;DR

This paper investigates how even very weak defects in photonic crystal waveguides can create localized TE-modes within spectral gaps, using a divergence equation model that accounts for discontinuous coefficients.

Contribution

It demonstrates that arbitrarily weak defects can induce spectrum in the spectral gaps of photonic crystals, extending understanding of defect-induced mode localization.

Findings

Weak defects introduce spectrum into spectral gaps.

Discontinuities in coefficients are incorporated into the model.

Analysis applies to a broad class of photonic crystals.

Abstract

This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. It is shown that arbitrarily weak perturbations introduce spectrum into the spectral gaps of the background operator.