What is the role of negative refractive index and negative permittivity of Metamaterials?
Metamaterials can be designed to have negative permittivity or negative permeability, or a combination of both resulting in a negative refractive index. But can you be more specific with your question? It is rather unclear what you'd to know. Do you mean possible applications or do you mean the technical details of how these properties arise within metamaterials?
It can be happen based on left hand criteria, where it is applied instead of right hand of old transmission line . You can check papers about CRLH composite right/left hand transmission line 2006 itoh,
Negative permeability is obtained from Kramers–Kronig relations. These relations are obtained from the requirement that no resultant energy from an event can be detected before the event occurred. Namely, if one has a temporal event(t) then event(t)step(t)=event(t). Step(t) is 0 before the event and 1 in the event. The Fourier transform of this equation to the frequency domain yields the anomalous dispersion and negative permeability. Therefore, negative refractive index does not violate causality! It yields phase velocity that is higher than speed of light, which does not present a problem if the energy propagation does not exceed c.
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