We study the photonic band structure of a metal–dielectric periodic structure. The metallic component is described by the Drude model; therefore, the electric permittivity is frequency dependent, i.e., dispersive. Rather than solving a nonlinear eigenvalue problem for the band structure of the material, we follow a time-dependent formulation described in Raman and Fan (Phys Rev Lett 104:087401, 2010) which leads to a linear eigenvalue problem. At issue is the question of completeness of the eigenfunctions, which is claimed but not proven in Raman and Fan (2010). We establish completeness in one dimension. We further describe the existence of accumulation points in the spectrum that lead to an infinite family of ‘zero group velocity’ waves. Numerical calculations illustrate some of the main ideas of this work.

中文翻译：

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金属-介电周期性结构中的光子带隙现象

我们研究了金属-电介质周期性结构的光子带结构。金属成分由Drude模型描述；因此，介电常数取决于频率，即色散。除了解决材料的能带结构的非线性特征值问题外，我们遵循拉曼和范（Phys Rev Lett 104：087401，2010）中描述的时间依赖公式，这会导致线性特征值问题。问题在于本征函数的完整性，这个问题在Raman and Fan（2010）中得到了主张，但没有得到证明。我们建立一维的完整性。我们进一步描述了频谱中积累点的存在，这些积累点导致了无限的“零组速度”波族。数值计算说明了这项工作的一些主要思想。