k.p-based multiband simulations of non-degenerate two-photon absorption in bulk GaAs

We use k•p perturbation theory as an input for simulations of nonlinear optical properties. A numerical solution of a 30-band k•p-model for bulk gallium arsenide yields both the band structure and complex dipole matrix elements. However, the matrix elements have undesirable features which make them not directly suitable for describing the nonlinear response for far-below resonance excitation frequencies. Besides a random phase originating from numerical diagonalizations, we trace this back to a numerical mixing of near-degenerate bands. As an attempt to resolve this problem we introduce a basis transformation which leads to smooth matrix elements. The material input is used in the semiconductor Bloch equations including the inter- and intraband parts of the light-matter interaction. As an example we evaluate non-degenerate two-photon absorption and compare our results with simpler models.