 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 $ϵ={ϵ}_{\infty }-{\omega }_p^2/{\omega }^2$. A high carrier density gives a large plasma frequency, often placing the screened plasma edge ${\omega }_p/\sqrt{{ϵ}_{\infty }}$ 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.