SECOND-HARMONIC GENERATION BY DAMPED ALFVEN WAVES AND HELICONS IN PURE AND DOPED BISMUTH

The results of a study of second-harmonic generation by damped Alfvén waves and helicons propagating parallel to the static magnetic field along the three principal axes of pure and tellurium-doped bismuth are reported. The observed anisotropy and polarization dependences are shown to be consistent with the occurrence of a magnetic dipole nonlinearity caused by the influence of the magnetic field of the wave on the conductivity of the medium. A theory of harmonic generation by plane waves propagating in a semi-infinite anisotropic conducting medium and in a slab is developed and applied to this case. It is shown that the concept of magnetic point groups can be applied to the determination of the form of the thirdrank tensors governing the effect, which leads to the conclusion that the forms of these tensors are, in fact, known for all crystal classes. A method of calculating these tensors after their reduction by symmetry from standard transport theory for bismuth is developed and results for some of the coefficients relevant to the experiments are given. © 1969 The American Physical Society.