论文标题
Kramers-Kronig关系以及电磁波与机械波之间的类比
Kramers-Kronig relations and the analogy between electromagnetic and mechanical waves
论文作者
论文摘要
Kramers-Kronig关系（KKRS）的重要结果是，材料介质中的耗散行为不可避免地意味着分散的存在，即构成方程中的频率依赖性。基本上，关系是因果关系的频域表达，并在数学上与希尔伯特变换对相对应。关系有多种形式，可以通过多种数学工具获得。在这里，在电磁案例中给出了两个不同的示例，说明了为此目的可用的折衷数学设备。然后，我们应用声学（机械） - 电磁类比来获得弹性版本。最后，我们讨论了稳定性和被动性的概念，并提供了一种新颖的算法来通过使用快速傅立叶变换来数值计算关系。
The important consequence of the Kramers-Kronig relations (KKrs) is that dissipative behavior in material media inevitably implies the existence of dispersion, i.e., a frequency dependence in the constitutive equations. Basically, the relations are the frequency-domain expression of causality and correspond mathematically to pairs of Hilbert transforms. The relations have many forms and can be obtained with diverse mathematical tools. Here, two different demonstrations are given in the electromagnetic case, illustrating the eclectic mathematical apparatus available for this purpose. Then, we apply the acoustic (mechanical)-electromagnetic analogy to obtain the elastic versions. Finally, we discuss the concepts of stability and passivity and provide a novel algorithm to compute the relations numerically by using the fast Fourier transform.
