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 w ith the redistribution of free electrons between the Gamma and L valley of highly doped n-GaAs. An extended comparison was made between the intravalle y (or nonparabolicity) and the intervalley contribution. In the energy rela xation process, intravalley transitions in the Gamma and L valley by means of the emission of optical phonons and equivalent intervalley transitions i n 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 t he frequency of light matches with the plasma frequency of the n-doped GaAs the nonlinearity is quite big. At a doping concentration of 7 X 10(18) cm( -3) we calculated a nonlinear refractive index n(2) = 1.74 X 10(-8) cm(2)/W at 10.6 mm. The doping and intensity dependent energy relaxation times of electrons are calculated: for Gamma-valley electrons tau(en)(Gamma) similar to ( 3-5) ps and for L-valley electrons tau(en)(Gamma) similar to (0.3-0.5 ) ps. It is believed that the response time of the free-carrier induced non linearity is determined by the decay time of longitudinal optical phonons ( 6-7 ps). (C) 1999 American Institute of Physics. [S0021-8979(99)07707-5].