Two-photon transitions to excitons in quantum wells.

Abstract

We calculate two-photon transition rates of exciton states in GaAs quantum wells for varying well widths. The exciton states are described in the effective-mass approximation and are obtained variationally assuming wave functions that are separable in the r coordinates. The two-photon transition rate is calculated taking explicitly into account the sum over all the intermediate states, using a variational procedure. We calculate transition rates of excitons of s symmetry as well as of p symmetry, which are allowed for polarization of the radiation beam along the growth axis and in the layer planes, respectively. From our calculations we find that transitions to s-type excitons have sufficiently large rates to be observable, whereas transitions to p-type excitons seem to have rates too small to be observable; these results are in agreement with experiment. The transition rate of s excitons increases significantly for decreasing well width, whereas the transition rate of p excitons is found to be almost independent of the well width. Moreover, our model allows us to calculate transition rates for photons of different energy. We have shown the resonant enhancement of the transition rate of s-type excitons when one of the photon energies approaches the energy of an intermediate state.