Past exam of the condensed matter physics major option course of the University of Oxford / 2015 / 5 / c / iii / Solution

At high density the plasma scale remains large, but a strong magnetic field separates the two circular dielectric responses. Ignoring damping, the positive plasma cutoffs areBetween suitable cutoffs one circular wave can propagate while the other is excluded; reflection and transmission are strongly polarization dependent. Around the cyclotron frequency the active response is resonant, while at optical frequencies far above ${\omega }_c$ the splitting can be a relatively small correction to a large plasma edge.

There is also a low-frequency window: for the active component, $0<\omega \ll {\omega }_c$ gives $ϵ\simeq {\omega }_p^2/(\omega {\omega }_c)>0$ when losses are small. This supports a helicon-like mode even when $\omega \ll {\omega }_p$. That does not make an ordinary metal broadly transparent; the large index, boundary coupling, collisions and skin geometry still matter. In the common regime ${\omega }_c\ll {\omega }_p$, bulk cyclotron absorption remains hidden from straightforward transmission, motivating a surface-sensitive experiment. Thus the relevant comparisons are among $\omega$, ${\omega }_c$, ${\omega }_p$ and $1/\tau$, not carrier density and field in isolation.