What exactly does negative permittivity mean?

In summary, metamaterials have negative permittivity and negative permeability. This occurs in some region above a resonance. Metals naturally have negative permittivity, though it is unclear whether this is always the case. What this means is that the electric displacement vector D and electric field are 180 degrees out of phase, which can lead to negative pemittivity and negative permeability.
  • #1
spikethecake
1
0
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 :)
 
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  • #2
Good question, may I join to you, I wonder too what is the answer :smile:
 
  • #3
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
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.
 
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  • #6
DrDu said:
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.
 
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  • #9
DrDu said:
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?
 

1. What is permittivity and how is it related to negative permittivity?

Permittivity is a measure of a material's ability to store an electric field. Negative permittivity occurs when a material has a negative value for its permittivity. It is related to permittivity because it indicates that the material has a different response to electric fields compared to a material with positive permittivity.

2. How is negative permittivity observed in materials?

Negative permittivity is observed in materials that exhibit a negative dielectric constant, meaning they have a negative response to an applied electric field. This can occur in materials such as metals, semiconductors, and certain types of composites.

3. What are the practical applications of materials with negative permittivity?

Materials with negative permittivity have a variety of practical applications, including in the design of high-frequency antennas, microwave circuits, and optical devices. They can also be used in metamaterials, which have unique properties such as negative refraction and superlensing.

4. Can negative permittivity be manipulated or controlled?

Yes, negative permittivity can be manipulated and controlled through various techniques such as changing the material composition, applying external fields, or using metamaterial structures. This allows for the design and development of novel devices with specific properties and functionalities.

5. Are there any potential drawbacks to using materials with negative permittivity?

One potential drawback is that materials with negative permittivity often have high loss factors, meaning they absorb and dissipate energy. This can limit their usefulness in certain applications. Additionally, the fabrication and integration of materials with negative permittivity can be complex and expensive.

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