Many-body theory of nonlinear optical absorption in coupled-band quantum wells

The operation of all-optical and optoelectronic semiconductor devices near the band gap relies on their highly nonlinear optical properties. Furthermore, quantum-well devices, especially those with strained layers, outperform their bulk-material counterparts in several operational characteristics and can have their properties custom designed for specific applications to a large extent. Realistic modeling of the nonlinear interaction of light with quantum wells is possible through generalized optical Bloch equations. The equations combine the influence of many-body, strain, and band-coupling effects. Figure 1(a) shows full numerical quasi-steady-state solutions of the equation for the interband polarization that gives rise to optical spectra for a 50-angstrom In_0.15 Ga_0.85As-GaAs quantum well at 300 K. The compressive strain within the InGaAs layers pushes the light-hole (lh) levels out of the confining potential, and they are unbound. We clearly see the exciton bleaching and the development of negative absorption (gain) for high carrier densities. Figure 1(b) displays results for an unstrained 50-angstrom GaAs-Al_0.23 Ga_0.77As well. In this case both the heavy-hole (hh) and lh components of the transition dipole contribute to the (TE) spectra and the valence subbands are significantly coupled. Note the larger broadening of the lh peak. This is a consequence of the added contributions from the lh band near k ≈ 0 with the non-zero k contributions of the hh, which are due to valence-band coupling. In both Figs. 1(a) and 1(b), and for low densities, the reduction of the exciton binding energy due to phase-space filling and plasma screening compensates the red-shifting effect of the exchange and Coulomb-hole self-energy corrections. For high densities, the bandgap shrinkage overcompensates for the excitonic bleaching and the absorption peaks are red shifted. The excess red shift for GaAs is a consequence of the simple quasi-static model used. The computed refractive-index changes of the first four nonlinear spectra with respect to the linear curves of Figs. 1(a) and 1(b) are shown, respectively, in Figs. 1(c) and 1(d). The computed saturation densities for the peak of TE absorption of the hh1 exciton are N_s ≈ 0.31 for the strained case are N_s = 0.57 for the unstrained case. We have used a fit to the simple law α(N) = α₀/(1 + N/N_s).