论文标题
Maxwell方程的频谱，用于均匀分散介质之间的平坦接口
Spectrum of the Maxwell Equations for a Flat Interface between Homogeneous Dispersive Media
论文作者
论文摘要
该论文确定并分类了由时谐波麦克斯韦问题生成的非自动辅助操作员铅笔的频谱，而非线性依赖于在平面接口处连接的两种均匀材料的情况。我们在整个空间中在空间上研究一维和二维减少，$ \ mathbb {r} $和$ \ mathbb {r}^2 $。对频谱参数（即频率）的依赖性在介电函数中，我们对其形式没有任何假设。这些函数值决定了光谱集。为了允许非保守介质，允许介电函数变得复杂，从而产生非自动参与的问题。整个频谱由特征值和基本频谱组成，但是在所有情况下，各种标准类型的必需光谱都不重合。确定必需光谱的主要工具是Weyl序列。
The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar interface. We study spatially one-dimensional and two-dimensional reductions in the whole space $\mathbb{R}$ and $\mathbb{R}^2$. The dependence on the spectral parameter, i.e. the frequency, is in the dielectric function and we make no assumptions on its form. These function values determine the spectral sets. In order to allow also for non-conservative media, the dielectric function is allowed to be complex, yielding a non-self-adjoint problem. The whole spectrum consists of eigenvalues and the essential spectrum, but the various standard types of essential spectra do not coincide in all cases. The main tool for determining the essential spectra are Weyl sequences.
