# Why is a plasmon ocsilation considered a longitudinal wave?

1. Jul 9, 2007

### sinayu71

Hi guys:

Why people consider the plasmon ocsilation as a longitudinal wave?

Thank you for your answer.

sinayu

2. Jul 9, 2007

### olgranpappy

because it is a longitudinal wave

3. Jul 14, 2007

### fresnelspot

because when you have the dielectric constant zero in the solid you examine , that means the solid does not react with E field . Then the free electrons inside that solid start to move the same way as a sound wawe. Their force is in the same direction with their amplitude. They move back and forwards and they have their amplitude in that direction.

Another way of expressing this is that: When you let (epsilon) be zero , you ignite the longitudinal branches of that solid. Thatswhy they are told to be longitudinal.

4. Jul 14, 2007

### olgranpappy

to clarify, that means that there is a non-vanishing response even to vanishing external field. V_true = V_ext/eps. the electrons react to the "true" potential, or field, which can be non-zero even if V_ext is zero... if eps is also zero.

5. Jul 15, 2007

### marlon

Dielectric constant is zero in the solid you examine ? What solids respects that property ? Besides, what does this have to do with the OP's question ?

But isn't that always the case for free electrons in a metal or plasma or ... ?

Huh ?

I always though that plasmons arise because of the quantisation of plasma oscillations which are defined as periodic oscillations of charge density in conducting media such as plasmas or metals. Now, just think of how any charge density (by approximation free electrons) respond to the presence of an electrical field. Just think of Coulomb's law for that matter.

Isn't it much easier and clearer to answer the OP's question like that ?

marlon

Last edited: Jul 15, 2007
6. Jul 15, 2007

### fresnelspot

my fellow. I dont want to discuss it in the forum. Because it takes much time. If you send me your msn adress we can discuss more efficiently. Or i can clarify my thought

7. Jul 15, 2007

### olgranpappy

The dielectric function tells us about how the system responds to an external perturbations. If we characterize the external perturbation by a frequency
$$\omega$$ and a wavenumber $$q$$ then it is only for a small subset of q and omega that the dielectric function is zero.

For example, in the case of q=0 (very (infinitely) long wavelength probe) the dielectric function happens to be zero when omega equal the so-called "plasma frequency" $$\Omega_{p}^2=4\pi e^2/m\frac{N}{V}$$ where e is the electric charge, m is the electron mass, N is the number of electrons, and V is the volume of the system.

If the field is strong enough that the electrons can be treated as free then one can write down an expression for the long wavelength dielectric constant as
$$\epsilon(\omega)=1-\frac{\Omega_p^2}{\omega^2}$$

Well, yeah, roughly speaking. Actually, real metals and whatnot don't have really well defined "plasmons." Cheers.

Adam

8. Jul 15, 2007

### olgranpappy

I don't see why you would not discuss the point in the forum. It can't take any more time than discussing via msn. And in the forum, there is at least a tiny bit of "peer review."

9. Jul 16, 2007

### marlon

Please do, this is exactly what this forum is here for. I am very curious to read your answers to my questions because i did not understand anything of what you wrote as an asnwer to the OP.

Yes but how is this related to the definition of plasmons ? My point is, one does not need all the correct stuff you mention just to define plasmons.

regards
marlon

10. Jul 16, 2007

### fresnelspot

In fact you are right. The plasmons are the quanta of plasma oscillations. In an ionic solid , The electrons are mobile and the nuclei are not. So it was modelled as a plasma. I answered the question in this way because the thread was " solid state" I thought He wanted to know about the plasmons in an ionic solid. But if you are not satisfied by the things tha we wrote i can suggest you " introduction to solid state physics" by Kittel . In this book the 10 th chapter is about polarons, polaritons and plasmons.

Friends i dont want to discuss in here because i ve seen some people who tried to show off with their "narrow" knowledge of physics.And a second reason is that discussing in here does not seem efficent to me because i cant write the formulae here.

11. Jul 16, 2007

### olgranpappy

and why not?

12. Jul 16, 2007

### olgranpappy

The plasmon propagtor has a pole... where? You need to understand "all the correct stuff" to be able to interpret the meaning of the plasmon.

13. Jul 16, 2007

### marlon

I get your point and i agree with you. I just wanted to point out that we do not know the level of knowledge of the OP. In light of that, i guess we should keep things as easy as possible.

regards
marlon

14. Jul 16, 2007

### olgranpappy

the original post was about plasma oscillations in a metal and the simplest treatment is classical.

15. Jul 17, 2007

### marlon

Ok, well actually i have that book so that is really nice for both of us...

Anyways, i don't get the "because when you have the dielectric constant zero in the solid you examine , that means the solid does not react with E field "-part because the solid as a whole DOES react with the E-field. Actually, it is that interaction (free electrons vibrate simultaneously along with the E-field) that generates the plasma oscillations.

Yes you can, use the tex-format : $$\int f^2(x)dx$$

marlon

16. Jul 17, 2007

### fresnelspot

Thank you for the formula writing tip.

I mean that ,the solid (possibly an ionic one)Has a dielectric function that responds to the external electric field. When it comes to plasma oscillations , The dielectric function should be zero (i mean the function 10.1.17 in Kittel).
My question is can an EM wawe propogate if it has $$eps=0$$

17. Jul 17, 2007

### fresnelspot

Thank you for the formula writing tip.

I mean that ,the solid (possibly an ionic one)Has a dielectric function that responds to the external electric field. When it comes to plasma oscillations , The dielectric function should be zero (i mean the function 10.1.17 in Kittel).
My question is can an EM wawe propogate if it has dilelectric function whose value is zero. If you put 0 as the dielectric value it in The EM wawe equation it would be clear i think.
So it does not interact with the coming EM wawe whose angular frequency is equal to the plasma frequency of solid. As far as i know the data graphs for the plasma oscillationsare damped oscillations ( ofcourse under these circumstances) . again in kittel the 10.1.8 graph tells it i think. So it does not interact with the EM wawe whose Frequency is the plasma frequency .

Ofcourse i may be wrong and it will be my pleasure to amend my wrong ideas.
Note: Dude i hate solid state physics .When i started this my aim was to help a colleague . Now i ve found myself in a solid state discussion. But anyway it polished my knowledge

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