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Towards more general constitutive relations for metamaterials: a checklist for consistent formulations

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


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 quick as possible which of these possible material laws are mathematically and physically meaningful at all. Here, at the example of a second order Padé approximation of the general response function of the electric field, we present a checklist each possible constitutive relation has to pass in order to be physically and mathematically liable. As will be shown, only one out of these nine Padé approximations passes the checklist. The work is meant to be a guideline applicable to decide which constitutive relation makes actually sense at all. ... mehr

Volltext §
DOI: 10.5445/IR/1000104493
Veröffentlicht am 02.01.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2019
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000104493
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 27 S.
Serie CRC 1173 ; 2019/24
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter metamaterials, electromagnetism, nonlocal homogenization, Padé expansion
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