Comparative study of the intra- and intervalley contributions to the free-carrier induced optical nonlinearity in n-GaAs

We performed a theoretical study about the optical nonlinearity connected with the redistribution of free electrons between the Γ and L valley of highly doped n-GaAs. An extended comparison was made between the intravalley (or nonparabolicity) and the intervalley contribution. In the energy relaxation process, intravalley transitions in the Γ and L valley by means of the emission of optical phonons and equivalent intervalley transitions in the L valley by means of intervalley phonons were considered as the main mechanism of energy transfer to the lattice. It is demonstrated that when the frequency of light matches with the plasma frequency of the n-doped GaAs the nonlinearity is quite big. At a doping concentration of 7×1018 cm−3 we calculated a nonlinear refractive index n2=1.74×10−8 cm2/W at 10.6 μm. The doping and intensity dependent energy relaxation times of electrons are calculated: for Γ-valley electrons τenΓ∼(3–5) ps and for L-valley electrons τenΓ∼(0.3–0.5) ps. It is believed that the response time of the free-carrier induced nonlinearity is determined by the decay time of longitudinal optical phonons (6–7 ps).