In this thesis, a new form of effective-mass theory is developed by introducing a mixing parameter of arbitrary strength into the Luttinger-Kohn(LK) representation for degenerate bands. It is proved that the choice of the particular mixing parameter has no physical significance, which is similar to the choice of gauge in electromagnetic theory. This permits some simplification of the analysis of degenerate valence states in an electric field. Through an approximate analytical model, this theory is applied here to calculate the complex dielectric tensor (i.e. Pockels linear electro-optic effect) of GaAs in an electric field. The results of the Pockels coefficient are in qualitative agreement with frequency-dependent experimental data. After analyzing the symmetry of the envelope function...[ Read more ]

In this thesis, a new form of effective-mass theory is developed by introducing a mixing parameter of arbitrary strength into the Luttinger-Kohn(LK) representation for degenerate bands. It is proved that the choice of the particular mixing parameter has no physical significance, which is similar to the choice of gauge in electromagnetic theory. This permits some simplification of the analysis of degenerate valence states in an electric field. Through an approximate analytical model, this theory is applied here to calculate the complex dielectric tensor (i.e. Pockels linear electro-optic effect) of GaAs in an electric field. The results of the Pockels coefficient are in qualitative agreement with frequency-dependent experimental data. After analyzing the symmetry of the envelope functions, the optical anisotropy and absorption coefficient have been studied with numerical calculations for the cases of zero and nonzero spin-orbit coupling. In both of these two cases, an oscillatory anisotropy for bulk crystals in an electric field is found. This anisotropy corresponds to the Pockels coefficient. It is found that piezo-electric effect terms, terms of order k³ in Hamiltonian and linear-k terms in momentum matrix have the most significant influence on the Pockels effect.