因果性与无源性：从电磁学和网络理论到超材料
Causality and Passivity: from Electromagnetism and Network Theory to Metamaterials
摘要：
在这篇综述中，我们广泛地研究了因果性和被动性原理在物理学和工程学的各个领域中所发挥的作用，包括在现代超材料领域。其目的不是提供一份参考文献的全面清单，因为参考文献的数量将以千计，而是审查推动这些领域的主要成果和贡献，并提供一个统一的框架，从中了解不同领域的发展。为了实现这些目标，我们绘制了早期的历史领域通过其双重开始的分析Sellmeier方程和希尔伯特变换，从而产生了深远的色散关系的早期作品的Kramers，Kronig和Titchmarsh。然而，这些早期的关系构成了一个有限的结果，因为它们只适用于一类有限的传递函数。为了理解这个限制是如何被解除的，我们快速地绕到施瓦茨的分布分析中。这种方法扩展了分散分析的范围分布的传递函数，也表现出多项式增长特性的功能。为了将结果进一步推广到张量传递函数，我们考虑了无源性的概念-最初在电网络理论中研究。我们澄清了为什么被动性意味着因果关系。随后，作为特殊情况下，我们提出的例子色散关系从几个领域的物理学，包括电磁学，声学，地震学，反射测量，和散射理论。我们讨论和规则，衍生的解析关系，和近局部逼近。最后，我们回顾了从因果性和被动性到最近的超材料领域的思想的巧妙应用。这些想法已经对超材料性质设计和超材料器件性能中可以实现的东西提供了限制。
英文摘要：
In this review, we take an extensive look at the role that the principles of causality and passivity have played in various areas of physics and engineering, including in the modern field of metamaterials. The aim is not to provide a comprehensive list of references as that number would be in the thousands, but to review the major results and contributions which have animated these areas and to provide a unified framework from which to understand the developments in different fields. Towards these goals, we chart the early history of the field through its dual beginnings in the analysis of the Sellmeier equation and in Hilbert transforms, giving rise to the far reaching dispersion relations in the early works of Kramers, Kronig, and Titchmarsh. However, these early relations constitute a limited result as they only apply to a restricted class of transfer functions. To understand how this restriction can be lifted, we take a quick detour into the distributional analysis of Schwartz. This approach expands the reach of the dispersion analysis to distributional transfer functions and also to those functions which exhibit polynomial growth properties. To generalize the results even further to tensorial transfer functions, we consider the concept of passivity - originally studied in the theory of electrical networks. We clarify why passivity implies causality. Subsequently, as special cases, we present examples of dispersion relations from several areas of physics including electromagnetism, acoustics, seismology, reflectance measurements, and scattering theory. We discuss sum rules, derivative analyticity relations, and nearly local approximations. Finally we review the clever applications of ideas from causality and passivity to the recent field of metamaterials. These ideas have provided limits to what can be achieved in metamaterial property design and metamaterial device performance.
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