Far-infrared nonlinear optics. II.χ(3)contributions from the dynamics of free carriers in semiconductors

We report the first bulk frequency tripling in the far-infrared. The experiments are carried out at 20 ${\mathrm{cm}}^{\mathrm{-}1}$ in the doped semiconductors Ge, Si, and GaAs. Good power conversion efficiency is obtained (${10}^{\mathrm{-}3}$). Our arrangement allows an absolute determination of the nonlinear susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$(3ω,ω,ω,ω). We show that in the far-infrared, ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ is dominated by free-carrier contributions. Hence, our measurement gives new insight into nonlinear transport properties such as the momentum dependence of the effective mass and of the relaxation time. Furthermore strong changes of ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ (as well as of the absorption) are found to occur at high laser intensity above 100 kW/${\mathrm{cm}}^2$, which we attribute to carrier heating and hot carrier transfer into higher energy-band minima.