  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 multi-photon absorption
coefficients. Here we show that generic multi-band 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 non-degenerate 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 Zincblende semiconductors described by k.p
theory.
