We present second-harmonic generation experiments in $p$-doped asymmetrically stepped quantum wells using the emission of a free-electron laser in the wavelength interval between 13 and 18 μm. The wells are designed such that the three lowest valence-subbands are about equally spaced. We measured the angular and frequency dependence of the second-harmonic signal excited by intense laser irradiation chosen to be nearly resonant with the transitions between the three lowest valence subbands. We see evidence of the optical second-order susceptibility components ${\chi }_{\mathrm{xxz}}^{\mathrm{}\left(2\right)\mathrm{}},$ ${\chi }_{\mathrm{zxx}}^{\mathrm{}\left(2\right)\mathrm{}}$ and ${\chi }_{\mathrm{zxy}}^{\mathrm{}\left(2\right)\mathrm{}},$ ${\chi }_{\mathrm{xyz}}^{\mathrm{}\left(2\right)\mathrm{}}$ in the quantum wells and determine their enhancement with respect to ${\chi }_{\mathrm{xyz}}^{\mathrm{}\left(2\right)\mathrm{}}$ of bulk GaAs.

• Received 17 March 1997

DOI:https://doi.org/10.1103/PhysRevB.56.10428