Second-order nonlinear optical susceptibility of asymmetric quantum wells

We give a detailed procedure for the calculation of the second-harmonic-generation susceptibility tensor in single and multiple asymmetric quantum wells (AQW’s). The effect of nonhomogeneity is explicitly included. Exciton states and continuum states are considered. The contributions due to the asymmetry of the confining potential and to the inversion asymmetry of the bulk material are separately assessed. Numerical calculations are carried out for two typical AQW’s of GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As. The results indicate larger values than in the bulk, in agreement with preliminary experimental data.