Solution (source code)

= Solution

At zero magnetic field the two circular conductivities coincide, so an isotropic material has no magnetically induced <circular birefringence>. In the collisionless <Drude model> range the <dielectric function> is $\epsilon=\epsilon_\infty-\omega_p^2/\omega^2$. A high carrier density gives a large <plasma frequency>, often placing the screened plasma edge $\omega_p/\sqrt{\epsilon_\infty}$ in the infrared or visible range.

Below that edge the real <dielectric function> is negative and a transverse wave is evanescent in the bulk. The material is strongly reflecting, with penetration through a <skin depth> and losses set by finite $1/\tau$. Above the plasma edge propagation becomes possible, subject to absorption and interband transitions. Carrier density alone does not specify a complete optical spectrum: the statements assume the probe frequency relative to the plasma scale and the validity of the single-band <Drude model>.