Two-photon absorption in semiconductors: A multiband length gauge analysis

The simplest approach to deal with light excitations in direct-gap semiconductors is to model them as a two -band system: one conduction and one valence band. For such models, particularly simple analytical expressions are known to exist for the optical response such as multiphoton absorption coefficients. Here we show that generic multiband models do not require much more complicated expressions. Our length-gauge analysis is based on the semiconductors Bloch equations in the absence of all scattering processes. In the evaluation, we focus on two-photon excitation by a pump-probe scheme with possibly nondegenerate and arbitrarily polarized configurations. The theory is validated by application to graphene and its bilayer, described by a tight-binding model, as well as bulk zinc-blende semiconductors described by k center dot p theory.