Optical properties of unbounded semiconducting crystals near the band gap

Stahl's constitutive equations for the band edge dynamics can be solved by using eigenfunctions of the Hamiltonian of the relative electron-hole motion. In this way linear interband susceptibility near the gap is calculated and its shape discussed for semiconductors with isotropic bands. Also expressions of the susceptibility for forbidden transitions at the Γ-point and for a quasi-two-dimensional model system are derived. By making use of standard perturbation methods the susceptibility for a crystal influenced by a uniform external electric field is calculated. Finally, within the range of validity of an iteration procedure, the third-order susceptibility χ(3) (ω, -ω, ω) is obtained as a series of terms which can be evaluated analytically