Nonlinear optical properties of GaAs/Ga1−xAlxAs superlattices

We calculate the third-order nonlinear optical susceptibility, ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$, of the GaAs/${\mathrm{Ga}}_{0.7}$ ${\mathrm{Al}}_{0.3}$As superlattice by determining the enhanced band nonparabolicity in the superlattice growth direction. A four-band k⋅p model is used for the band structure of the bulk semiconductors, and the superlattice conduction minibands are obtained using a transfer-matrix method developed earlier. Estimates for ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$, averaged over the Fermi distribution of energies, are made at T=0 K and at room temperature. The calculations are performed for a number of representative values for carrier concentrations in the conduction minibands and for various layer thicknesses. In-plane nonparabolicity is incorporated, and no approximations are made for the Fermi distribution of carriers over the lowest and the first excited minibands. For the GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As superlattice it is found that the in-plane nonparabolicity has a negligible effect on ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ both at T=0 and 300 K. For T=0 K, a superlinear behavior of ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ with carrier concentration is obtained for Fermi energies near the top of the lowest miniband. We find that significant contributions to ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ occur from the first excited miniband in the case of wide wells, and that the magnitude of ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ is enhanced for wider wells and/or barriers.