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What exactly does negative permittivity mean?

  1. Apr 20, 2013 #1
    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. jcsd
  3. Apr 24, 2013 #2
    Good question, may I join to you, I wonder too what is the answer :smile:
  4. Apr 22, 2014 #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?
  5. Apr 22, 2014 #4


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    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
  6. Apr 22, 2014 #5


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  7. Apr 22, 2014 #6
    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
  8. Apr 22, 2014 #7
  9. Apr 22, 2014 #8


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  10. Jun 9, 2014 #9
    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?
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