Lecture -- Special Cases of Drude Model

This video discusses in more detail the physical meaning of the plasma frequency and illustrates the origin of a plasmon. The Drude model at very low and very high frequencies is also discussed.

[@Ckngummand]

I love how you explain this so clearly. Thank you.

[@hamidk4772]

Outstanding.

[@sambhavi2599]

wow ..

[@billy-cg1qq]

So if I understand correctly. Let's say there is a rectangular piece of metal standing upward and facing an incoming electromagnetic wave. Because of the presence of the electric field in the EM wave, the electrons start oscillating up and down the metal piece. There is a resonance frequency for these oscillating electrons called plasma frequency. If you hit the plasma frequency, the propagation of the electromagnetic wave stops. No further penetration of the EM wave through that metal, but can propagate at different frequencies. When you said, "long came something, like electric field." from where did the electric field come from, like what direction?

[@empossible1577]

The utility of the plasma frequency (other than calculations) is that below the plasma frequency the metal behaves like a good metal and above the plasma frequency the metal behaves more like a lossy dielectric. This is why x-rays can penetrate metal to see through them. Electric fields can come from applied light beams, electromagnetic waves from antennas, or just about any source.

[@billy-cg1qq]

@@empossible1577 I read from a website that at plasma frequency the propagation vector vanishes. In transverse waves we have atomic motion normal to the propagation, and longitudinal waves atomic motion is along the propagation. It's this that I find unclear, not the low and high frequencies. Like what happens? Why propagation vector vanishes? How does the atoms move at different frequencies including the high and low and plasma frequencies?

[@empossible1577]

@@billy-cg1qq An electric field puts a force on charged particles that literally push them around. A transverse wave has the electric field polarized in the transverse direction so the force and the displacement of the charges is in the transverse direction. The plasma frequency is a resonance and things always get crazy at resonance. Resonance is the reason we have parameters such as permittivity and permeability. In fact, those are not real things. Those are "macroscopic" properties that help is simplify the interaction of charges and fields. On the plasma frequency, the permittivity goes exactly to zero. This means refractive index is exactly zero, which also means the propagation vector (I call it wave vector) is exactly zero. Physically, this means the electron oscillation is exactly in phase and synchronized perfectly with the oscillation of the electric field. This means the second waves radiated by the oscillating charges perfectly cancels the applied electric field and the electric field also vanishes. In a sense waves at the plasma frequency are prohibited from propagating through the medium. Hope this helps!!

[@ayoutubechannelname]

So basically it is misleading or n00b to say that metals have infinite permittivity.

[@empossible1577]

It is definitely incorrect to say this. However, at low frequencies it is a very simplifying approximation to make and gives reasonably accurate results. At higher frequencies, metals start to look more like very lossy dielectrics and the perfect electric conductor (PEC) approximation does not give accurate results at all. This is definitely true at optical frequencies.