# What exactly does negative permittivity mean?

1. Apr 20, 2013

### 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 :)

2. Apr 24, 2013

### zrek

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

3. Apr 22, 2014

### 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?

4. Apr 22, 2014

### 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.

Last edited: Apr 22, 2014
5. Apr 22, 2014

### UltrafastPED

6. Apr 22, 2014

### zixue

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.

Last edited: Apr 22, 2014
7. Apr 22, 2014

### zixue

8. Apr 22, 2014

9. Jun 9, 2014

### zixue

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?