What exactly does negative permittivity mean?

[spikethecake]

Hi, this is my first time posting on these forums but I've been reading them for a while.

I was having a look at metamaterials and it mentioned that metamaterials had negative permittivity and negative permeability. I also found that metals naturally had negative permittivity; though I am still unsure whether this is always the case or just at certain frequencies.

I'd also like to ask why this occurs and what it means exactly; by being negative, is the field refracted in the opposite direction?

Thanks :)

 

[zrek]

Good question, may I join to you, I wonder too what is the answer

 

[zixue]

i am wondering too. following the equation C=dQ/dV, is the charge repelled or the field? what is the phenomena happened in most metals?
Some may response with the collision frequency, i guess. help, please?

 

[DrDu]

Negative pemittivity means that the electric displacement vector D and electric field are180 degrees out of phase, i.e. antiparallel.
This occurs in some region above a resonance. In a metal, the resonance frequency is formally zero and the region of negative permittivity extends up to the so-called plasma frequency.
You can get an easy picture of what is going on if you model the electric polarization P (~D) as a collection of harmonic oscillators of frequency $\omega_0$ which are driven via a coupling to the electric field $\sim E_0 \sin(\omega t)$, i.e.
$1/2m \frac{d^2 x}{dt^2}+\gamma \frac{dx}{dt} +k/2 x^2 =e E_0 \sin(\omega t)$
here,x is the coordinate, m is the mass, e the charge of an electron, and k the spring constant, $\gamma$ the damping.
You can solve this equation analytically and obtain x(t) as a function of frequency.

 

[UltrafastPED]

You may find this article of interest: "Physics of negative refractive index materials" (2005)

http://muri.lci.kent.edu/References/NIM_Papers/nim_overview/2005_ramakrishna_physics_nim.pdf

 

[zixue]

Negative permeability means that the electric displacement vector D and electric field are180 degrees out of phase, i.e. antiparallel.
This occurs in some region above a resonance. In a metal, the resonance frequency is formally zero and the region of negative permeability extends up to the so-called plasma frequency.
You can get an easy picture of what is going on if you model the electric polarization P (~D) as a collection of harmonic oscillators of frequency $\omega_0$ which are driven via a coupling to the electric field $\sim E_0 \sin(\omega t)$, i.e.
$1/2m \frac{d^2 x}{dt^2}+\gamma \frac{dx}{dt} +k/2 x^2 =e E_0 \sin(\omega t)$
here,x is the coordinate, m is the mass, e the charge of an electron, and k the spring constant, $\gamma$ the damping.
You can solve this equation analytically and obtain x(t) as a function of frequency.

Thanks DrDu. So what happen at even lower frequency region in the metal that cause an increase in negative permittivity followed by a decrease in negative permittivity e.g. well-shaped pattern of e' as a function of frequency? i guess i'd figured out the decrease in negative permittivity as the frequency approaching the plasma frequency. just that I don't understand why is it having an increase negative permittivity at lower frequency.

 

[zixue]

You may find this article of interest: "Physics of negative refractive index materials" (2005)

http://muri.lci.kent.edu/References/NIM_Papers/nim_overview/2005_ramakrishna_physics_nim.pdf

Thanks ultrafastped! looking at it right now.

 

[DrDu]

You may find this article of interest: "Physics of negative refractive index materials" (2005)

http://muri.lci.kent.edu/References/NIM_Papers/nim_overview/2005_ramakrishna_physics_nim.pdf

The article shows the "electrical engineering" point of view of negative refraction. Interesting is also the article by Agranovich and Gartstein, which discusses the phenomenon as an effect of spatial dispersion:
http://iopscience.iop.org/1063-7869/49/10/R03

 

[zixue]

The article shows the "electrical engineering" point of view of negative refraction. Interesting is also the article by Agranovich and Gartstein, which discusses the phenomenon as an effect of spatial dispersion:
http://iopscience.iop.org/1063-7869/49/10/R03

Thank you DrDu.

I was wondering where can we find reported data with negative capacitance as a function of frequency for conductors. It is quite hard to get a data comparison for common metals.
Does anyone got any idea?