作为因果函数类的Lorentzian叠加
Superpositions of Lorentzians as the class of causal functions
摘要：
我们证明了所有的函数服从Kramers-Kronig关系可以近似为叠加的洛伦兹函数，以任何精度。其结果是，典型的教科书分析的介电色散响应函数的洛伦兹方面可以被视为涵盖了整个类的因果函数。进一步的结果是，洛伦兹谐振可以被视为用于例如通过使用不同参数的开口环谐振器来设计任何期望的超材料响应的可能的构建块。两个例子的功能，远离典型的洛伦兹共振行为，表示在洛伦兹叠加：一个陡峭的色散介质，实现大的负极化率与任意低的损耗/增益，和一个最佳的实现完美的透镜在带宽。误差界推导出的近似。
英文摘要：
We prove that all functions obeying the Kramers-Kronig relations can be approximated as superpositions of Lorentzian functions, to any precision. As a result, the typical text-book analysis of dielectric dispersion response functions in terms of Lorentzians may be viewed as encompassing the whole class of causal functions. A further consequence is that Lorentzian resonances may be viewed as possible building blocks for engineering any desired metamaterial response, for example by use of split ring resonators of different parameters. Two example functions, far from typical Lorentzian resonance behavior, are expressed in terms of Lorentzian superpositions: A steep dispersion medium that achieves large negative susceptibility with arbitrarily low loss/gain, and an optimal realization of a perfect lens over a bandwidth. Error bounds are derived for the approximation.
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