# Negative dielectric constant

• TheDestroyer

#### TheDestroyer

Hi Guys,

I was reading about plasmons on wikipedia and I found that there are some materials with negative dielectric constant, what I know is that there are complex dielectric and reflection coefficient constants due to reflection in metals, can we relate the the complex dielectric constants to negative dielectric constants?

and what is the physical explanation and results for having negative dielectric constant?

Usually negative refractive index materials are called "metamaterials" because of the way they are constructed. I don't know the details, but the components (split-ring resonators, etc) are used in a region where the dispersion is very high and very negative, near an absorption peak. A consequence of this is that the absorption is usually high for these devices.

Thanks Andy Resnick,

Anybody else can explain more?

Hi,

I don't speak with any authority and can't give you a definate answer, but I seem to remember that you can obtain a negative refractive index when the frequency of the incident EM wave is greater then the plasma frequency of the electrons in that material. I think they use this to focus X-rays and other high energy waves. Might be worth having a quick look into, although its been a while since I've done this so could be miles off.

Regards

Thanks Barny,

Also I'm waiting for more explanations

First of all, for any normal material the imaginary part of the dielectric function is always positive for positive frequencies of radiaiton (the zeros of the dielectric function are actually in the lower half complex plane).

There are many cases (for regular everyday materials) when the real part of the dielectric function is negative. For example, the real part of the dielectric function of boron nitride is negative for incoming frequencies near 2 (eV/hbar). This is pretty typical.

Also, it is interesting to consider when the real part of the dielectric function is less than one. This occurs for all types of materials when the incoming frequency is much greater than the plasma frequency. In this regime the dielectric function is roughly given by
$$1-\frac{\omega_{\rm plasma}^2}{\omega^2}$$

Well olgranpappy, Do you mean that the dielectric constant is a function of frequency, and if the frequency of a metal is greater than plasma frequency then the real part will become negative?

i.e. We care only about the real part, Is this true? and if the preceeding discussion was true, can you explain me to the way that change occurs? i mean is this change continuous? or got a breakoff point like the properties of super-conductivity before reaching it?

Thanks

I mean the dielectric constant is a function of the frequency of the incident radiation. You shine light of some frequency on a material and the material responds. The response is determined by the dielectric function and the dielectric function's value is different for difference incident frequencies.

No, we don't only care about real part. the imaginary part is important because it determines, for example, absorption.

Well olgranpappy, Do you mean that the dielectric constant is a function of frequency, and if the frequency of a metal is greater than plasma frequency then the real part will become negative?

I said that if the frequency of the incident radiation is much higher than the plasma frequency of the metal then the dielectric function is less than one, not negative tho. I said that the dielectric function *can* be negative but only over certain specific regions of frequency.

Thanks again

thankyou...the information seems very useful