Dispersion of Ordinary and Extraordinary High-Frequency Waves in Metals

This paper is an extended discussion of the dispersion curves of the high-frequency waves (HFW) occurring in simple metals near the Azbel-Kaner cyclotron resonances. The conductivity $\mathbf{\sigma }(\mathbf{k},\omega ,{\omega }_c)$ for the case of a general ellipsoidal Fermi surface is derived, and the spherical and cylindrical Fermi surfaces are then treated as limiting cases. Numerical calculations of the dispersion curves of both ordinary and extraordinary HFW, for the case of a spherical Fermi surface, are evaluated over a range of wavelengths that bridges the long-wavelength limit, which has been observed experimentally, and the short-wavelength limit, which was predicted by Kaner and Skobov. The dispersion curves show oscillatory characteristics at intermediate wavelengths. The oscillatory character manifests itself most strongly for the case of a cylindrical Fermi surface, where its physical origin becomes apparent.