Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots

We have investigated the second-order nonlinear susceptibility in self-assembled quantum dots. The nonlinear susceptibility associated with intraband transitions in the conduction band and in the valence band is theoretically estimated for lens-shaped InAs/GaAs self-assembled quantum dots. The confined energy levels in the dots are calculated in the effective-mass approximation by solving the three-dimensional Schrödinger equation. Giant values of nonlinear susceptibility, about six orders of magnitude larger than the bull GaAs susceptibility, are predicted. We show that this enhancement results from three key features: (i) the achievement of the double resonance condition, (ii) the specific polarization selection rules of intraband transitions that allow both in-plane and z-polarized transitions with large dipole matrix elements to be optically active, and (iii) the small homogeneous linewidth of the intraband transitions. The conclusions of the calculations are supported by the measurement of the midinfrared nonlinear susceptibility in the valence band. The measurements have been performed using a picosecond free-electron laser. Both ${\chi }_{\mathrm{zzz}}^{\mathrm{}\left(2\right)\mathrm{}}$ and ${\chi }_{\mathrm{zxx}}^{\mathrm{}\left(2\right)\mathrm{}}$ components of the susceptibility tensor are observed. A satisfying agreement is found between theoretical and experimental values.