标题： 算子方法在色散介质中电磁波传播分析中的应用。 第一部分：一般性结果 显示英文标题

标题： An operator approach to the analysis of electromagnetic wave propagation in dispersive media. Part 1: general results

摘要： 本章研究了在色散各向同性的被动线性介质中电磁波传播的数学模型，其中介电常数$\varepsilon$和磁导率$\mu$随频率变化。我们强调物理要求与模型数学性质之间的联系。 特别关注因果性和被动性概念及其与赫尔戈茨函数存在的关联，这些函数决定了材料的色散特性。我们依次考虑一般被动介质和所谓的局部介质的情况，在这种情况下，$\varepsilon$和$\mu$是频率的有理函数。 这引导我们分析非耗散和耗散广义洛伦兹模型这一重要类。特别是，我们通过稳定性、能量守恒、色散及模式分析、群速度和相速度以及耗散系统中的能量衰减的概念讨论了模型的数学性质与物理性质之间的联系。 显示英文摘要

摘要： We investigate in this chapter the mathematical models for electromagnetic wave propagation in dispersive isotropic passive linear media for which the dielectric permittivity $\varepsilon$ and magnetic permeability $\mu$ depend on the frequency. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notions of causality and passivity and its connection to the existence of Herglotz functions that determine the dispersion of the material. We consider successively the cases of the general passive media and the so-called local media for which $\varepsilon$ and $\mu$ are rational functions of the frequency. This leads us to analyse the important class of non dissipative and dissipative generalized Lorentz models. In particular, we discuss the connection between mathematical and physical properties of models through the notions of stability, energy conservation, dispersion and modal analyses, group and phase velocities and energy decay in dissipative systems.