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

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 ${\omega }_c\tau \gg 1$, 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 $m^{\ast }=e{B}_{\mathrm{res}}/\omega$. 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.