# Longitudinal plasmon oscillation

1. Jun 24, 2013

### scivet

Kittel solid state physics book ( chapter 14)says when dielectric permittivity is zero, then longitudinal polarization wave possibly exists. It is hard to imagine how this is possible. Can anybody explain this?
If the permittivity is zero, then there shouldn'n be any response, right? How come the longitudinal mode-are generated?

Last edited: Jun 24, 2013
2. Jun 25, 2013

### DrDu

Given that $D=\epsilon E$, $\epsilon=0$ means that you can have an electric field E without an associated displacement field. If you take the full Maxwell equations you can see that for slightly higher frequencies there exist free longitudinal solutions of these equations which are not bound to external sources.

3. Jun 25, 2013

### scivet

The epsilon is positive at the higher frequency than plasma, which means the transverse propagating wave. Right? So, epsilon is zero, then the electromagnetic wave equation says del^2 E is zero. How does this say the solution is longitudinal? It only says K, the wave vector must be also zero?

4. Jun 25, 2013

### DrDu

The longitudinal dielectric constant is a function of both omega and wavevector k.
If $D_L(\omega,k)=0$ due to $\epsilon_L(\omega,k)=0$then clearly $E_L(\omega, k)$ is a longitudinal solution of the free wave equation.