We propose a new method for band structure calculation of photonic crystals. It can treat arbitrarily frequency-dependent, lossy or lossless materials. The band structure problem is first formulated as the eigenvalue problem of an operator function. Finite elements are then used for discretization. Finally, the spectral indicator method is employed to compute the eigenvalues. Numerical examples in both TE and TM cases are presented to show the effectiveness. There exist very few examples in literature for the TM case, and the examples in this paper can serve as benchmarks.

中文翻译：

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具有频率相关介电常数的光子晶体的能带结构计算

我们提出了一种计算光子晶体能带结构的新方法。它可以任意处理频率相关的，有损耗的或无损耗的材料。首先将能带结构问题表述为算子函数的特征值问题。然后将有限元用于离散化。最后，采用光谱指标方法计算特征值。给出了TE和TM情况下的数值示例，以证明其有效性。文献中有关TM案例的例子很少，本文中的例子可以作为基准。