Plasma Oscillation¶

If you had a neutral plasma (which can be the free charges in a metal) and you pulled the negative and positive charges apart and let them go, they would oscillate due to the electrostatic potential. This is an excitation known as a plasma oscillation.

Plasma is a gas of charge particles. In metals, it is a neutral plasma, i.e., equal number of positive and negative charges are equal.

Basic Calculation¶

Drude Model EM responses of metal are mostly governed by "free electrons ". Equation of motion:

\(m\frac{d^2X}{dt^2} = -qE \rightarrow -m\omega^2X = -qE\)

Average dipole moment:

\(P = -nqX = -\frac{nq^2}{mw^2} E\)

where, n is the free electron number density.

\(\boxed{\epsilon = \left(1 -\frac{\omega_p^2}{\omega^2}\right)}, \text{where } \omega_p^2 = \frac{nq^2}{m\epsilon_0}\)

\(\omega_p :\) Plasma frequency.

This tells us that the plasma frequency goes up with the free particle density. This is plasma oscillation. A plasmon is a single quantum of a plasma oscillation. This is similar to a photon, which is a quantum of electromagnetic oscillation, where the exchange in energy is between electric and magnetic stored energies.

At lower frequencies, the damping is severe enough so that the electron kinetic energy no longer will play a role, so the response will be purely magnetic (caused by charge motion) and electric (caused by charge separation). At low enough frequencies, the mass of the charge carrier should play a role, as a heavier mass would result in reduced magnetic and electric response, due to reduced amplitude and speed of motion.

Polaritons are also a quasiparticle that is produced when plasmons and em wave (photon) interacts/couples each other, usually strong interaction between them.