= 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 are
$$
\boxed{\omega_{H,L}=\sqrt{\omega_p^2/\epsilon_\infty+\omega_c^2/4}\ \pm\ \omega_c/2.}
$$
Between 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 $\epsilon\simeq\omega_p^2/(\omega\omega_c)>0$ 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.
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