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. Using the Floquet–Bloch theory in negative‐order Sobolev spaces, we characterize the precise number of eigenvalues created by the line defect in terms of the band functions of the original periodic background medium for arbitrarily weak defects.

中文翻译：

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通过任意弱缺陷对多个TE模式进行间隙定位

本文考虑了TE模式在光子晶体波导中的传播。通过将线性缺陷引入周期性背景介质中来创建波导。周期本底问题和摄动问题都由发散型方程建模。我们分析的一个特点是我们允许算符系数的不连续性，这是对许多光子晶体进行建模所必需的。使用负序Sobolev空间中的Floquet-Bloch理论，我们根据任意弱缺陷的原始周期性背景介质的带函数，描述了由线缺陷产生的特征值的精确数量。