各向异性介质的色散关系
Dispersion relation for anisotropic media
摘要：
研究了电磁波在各向异性介质中的传播问题，该介质具有介电常数和磁导率的两个通用矩阵$ε^{ij}$和$μ^{ij}$。这些矩阵不需要是对称的、正定的，甚至是可逆的。在无度规电动力学方法的框架下，导出了紧致的张量色散关系。所得公式可用于电磁波在经典介质和具有一般线性本构关系的现代类型介质（包括超材料）中传播的理论研究。
英文摘要：
The electromagnetic wave propagation in an anisotropic dielectric media with two generic matrices $ε^{ij}$ and $μ^{ij}$ of permittivity and permeability is studied. These matrices are not required to be symmetric, positive definite, and even invertible. In the framework of a metric-free electrodynamics approach, compact tensorial dispersion relation is derived. The resulted formula are useful for a theoretical study of electromagnetic wave propagation in a classical media and in a modern type of media with a generic linear constitutive relation including metamaterials.
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