Second-order optical susceptibility of biased quantum wells in the interband regime

We develop a theory within the effective-mass approximation of the second-order susceptibility of a quantum well subject to an applied electric field. We show that close to the midgap of the structure it is possible within that approximation to reduce the normally derived triple sums over subbands to a simple sum over all the optically allowed transitions. We have demonstrated that in realistic structures, higher-energy transitions play a strong role for quantitative results. This strong influence of the higher-energy transitions on the second-order susceptibility has the consequence that it is not generally possible to define a quantum-well susceptibility independent of the structure in which the well is inserted. Numerical results indicate that the quantum wells should not lead to spectacular enhancements of the second-harmonic-generation susceptibility.