Far-infrared second-harmonic generation in GaAs/AlxGa1-xAs heterostructures: Perturbative and nonperturbative response.

We report measurements of far-infrared (FIR) harmonic generation from GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heter- ostructures. The samples studied were a modulation-doped ${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As/GaAs heterojunction and a sample with ten modulation-doped half-parabolic quantum wells. The samples were driven with intense far-infrared radiation from a molecular gas laser at 29.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and the University of California\char21{}Santa Barbara free-electron laser at 51.3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The FIR radiation was polarized parallel to the growth direction. Second harmonics of the FIR were detected from both the semi-insulating GaAs substrate and from the confined electrons. For the heterojunction sample, the second-harmonic power generated by the electrons depended quadratically on fundamental power at low power, as expected from time-dependent perturbation theory. However, this dependence became subquadratic at higher powers, indicating a nonperturbative response. At high FIR powers, electrons were also ionized from the heterojunction and half-parabolic wells. For the heterojunction at f=29.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in the perturbative regime, the surface second-order susceptibility was computed to be ${\mathrm{\ensuremath{\chi}}}_{\mathit{S}}^{(2)}$=1.0\ifmmode\pm\else\textpm\fi{}0.75\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{esu}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{cm}}^{3}$. This value agrees, within experimental error, with a simple model of the heterojunction as a triangular quantum well. The second-order polarizability of a conduction electron in the heterojunction is nine orders of magnitude larger than that of a valence electron in pure GaAs.