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首页> 外文期刊>Physical review >Towards more general constitutive relations for metamaterials: A checklist for consistent formulations
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Towards more general constitutive relations for metamaterials: A checklist for consistent formulations

机译：对超材料的更一般构成关系：一致配方的清单

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摘要

When the period of unit cells constituting metamaterials is no longer much smaller than the wavelength but only smaller, local material laws fail to describe the propagation of light in such composite media when considered at the effective level. Instead, nonlocal material laws are required. They have to be derived by approximating a general response function of the electric field in the metamaterial at the effective level that is accurate but cannot be handled practically. But how to perform this approximation is not obvious at all. Indeed, many approximations can be perceived and one should be able to decide as quickly as possible which of these possible material laws are mathematically and physically meaningful at all. Here, at the example of a second order Pade approximation of the general response function of the electric field, we present a checklist of each possible constitutive relation that has to pass in order to be physically and mathematically liable. As will be shown, only two out of these nine Pade approximations pass the checklist. The work is meant to be a guideline applicable to decide which constitutive relation actually makes any sense at all. It is an essential ingredient for future research on composite media as any possible constitutive relation to be discussed should pass it.
机译：当构成超材料的单位细胞的时期不再小于波长而是仅小，但是当在有效水平考虑时，本地材料法未能描述这种复合介质中的光在这种复合介质中的传播。相反，需要非本体材料法律。它们必须通过近似在可以准确而是实际处理的有效水平的超材料中电场的一般响应函数来得出。但是如何执行这种近似并不明显。实际上，可以感知许多近似，并且应该能够尽可能快地决定这些可能的材料法在数学上以及物理上的内容。这里，在电场的一般响应函数的二阶梯队近似的示例中，我们呈现了必须通过的每个可能的本构思的核对表，以便物理和数学方式易于倾向。如将显示，这些九个曲线近似的两个出来了通过清单。这项工作意味着是一个适用于决定哪些本构体关系的指导方针实际上是任何意义。对于未来的复合介质研究，作为要讨论的任何可能的本构关系，这是一个必不可少的成分应该通过它。

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  • 来源
    《Physical review》 |2020年第19期|195411.1-195411.23|共23页
  • 作者

    Fatima Z. Goffi; Karim Mnasri; Michael Plum; Carsten Rockstuhl; Andrii Khrabustovskyi;

  • 作者单位

    Institute for Analysis Karlsruhe Institute of Technology Englerstrafie 2 76131 Karlsruhe Germany;

    Institute of Theoretical Solid State Physics Karlsruhe Institute of Technology Wolfgang-Gaede-Strasse 1 76131 Karlsruhe Germany;

    Institute for Analysis Karlsruhe Institute of Technology Englerstrafie 2 76131 Karlsruhe Germany;

    Institute of Theoretical Solid State Physics Karlsruhe Institute of Technology Wolfgang-Gaede-Strasse 1 76131 Karlsruhe Germany Institute of Nanotechnology Karlsruhe Institute of Technology P.O. Box 3640 76021 Karlsruhe Germany;

    Department of Physics Faculty of Science University of Hradec Kralove Rokitanskeho 62 500 03 Hradec Kralove Czech Republic Institute of Applied Mathematics Graz University of Technology Steyrergasse 30 8010 Graz Austria;

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