Solution (source code)

= Solution

At low density, the <plasma frequency> and free-carrier <dielectric screening> are smaller, so radiation can penetrate a suitable semiconductor sample. In a high field with $\omega_c\tau\gg1$, the active circular component has a resolved cyclotron absorption line near $\omega=\omega_c$, with width of order $1/\tau$. The opposite circular component lacks that positive-frequency resonance.

Different complex refractive indices for the two components produce <Faraday rotation> and <circular dichroism>. Transmission with controlled <circular polarization> therefore isolates the <cyclotron resonance> and measures $m^*=eB_{\rm res}/\omega$. The low-density/high-field labels do not by themselves imply complete transparency at every frequency; one must still avoid the plasma stop bands, strong interband absorption and excessive sample thickness.