# Metamaterials with epsilon and/or mu < 0.

All known natural materials have epsilon and mu > 0. However, there is an intense effort to manufacture so-called metamaterials, where both of these are <0. In such a case, given n = sqrt[epsilon x mu], one would take the negative root and n is still a real number, but n <0 why do we take the negative?

What does this say about the propagation of v=c/n, does this mean light is going backwards?

n= √µϵ
n= √(-1) √-1
n= ί ί
n = -1

substances with negative µ and ϵ have some properties differnt from those with positve µ and ϵ and materials eith both µ & ϵ negative are not naturally found .

wavevector is in the direction of phase velocity, it means left handed materials have negative group velocity

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There is a paper about invisibility which mentioned metamaterials. You said these materials have an index of refraction -1, Does this really mean that light goes backward when it reaches the metamaterial?. Is this really possible?? How could someone create a material with such properties??

yes in microwave region , electromagnetic wave bends once it reaches to metamaterial .

Claude Bile

There is a paper about invisibility which mentioned metamaterials. You said these materials have an index of refraction -1, Does this really mean that light goes backward when it reaches the metamaterial?. Is this really possible?? How could someone create a material with such properties??

The phrase "light goes backwards" is somewhat arbitrary because light possesses two velocities, group velocity and phase velocity. A negative index means the group velocity is in the opposite direction to the phase velocity. It is entirely consistent with the laws of electromagnetism as far as I know.

The basic configuration for negative index materials is a layer of split-ring resonators (for negative mu) interspersed by layers of parallel conducting wires (for negative epsilon). The (narrow) wavelength range over which negative refraction is attained depends on the size of the resonators.

Claude.