EFFECTS OF TRAPPED STATES ON SPECTRA OF 4-WAVE-MIXING AND DIFFERENTIAL TRANSMISSION

Excitons are sometimes trapped at impurities in crystals and at defects on interfaces in the confined systems, such as quantum wells and microcrystallites embedded in a host matrix. We discuss these trapping effects on the third-order optical polarization under nearly resonant pumping of the exciton. First we predict an enhancement of chi(3)(OMEGA;OMEGA, - OMEGA,OMEGA) by a factor-GAMMA(n-->T/GAMMA(T-->g) multiplicatively on that enhanced by the large excitonic dipole moments. Here GAMMA(n-->T and GAMMA(T-->g) are, respectively, the rate at which the exciton is trapped and the decay rate of the trapped electron into the ground state. In many Cases, GAMMA(n-->T) is much larger than GAMMA(T-->g) so that a large enhancement of chi(3) is expected. Second, the four-wave mixing spectrum \chi(3))(2-OMEGA-1 - OMEGA-2;OMEGA-1, - OMEGA-2, OMEGA-1)\ under two beams OMEGA-1 and OMEGA-2 is shown to consist of three hierarchical structures as a function of OMEGA-1 - OMEGA-2, i.e., the sharpest spike around OMEGA-1 - OMEGA-2 = 0 with the linewidth \OMEGA-1 - OMEGA-2\ = GAMMA(T-->g), the steep shoulder with the center also at OMEGA-1 - OMEGA-2 = 0 and the width GAMMA(n) (the exciton decay rate), and the wide structure with the width GAMMA(ng) around OMEGA-1 = omega-1s and OMEGA-2 = omega-1s. Here GAMMA(ng) is the relaxation rate of the exciton polarization and H-omega-1sBAR the lowest exciton energy. Third, the differential transmission spectrum is found to show the strong absorption saturation peak or the sharp induced absorption dip as a function of pump-probe detuning OMEGA-2 -OMEGA-1, depending upon the pump frequency OMEGA-1 relative to the exciton peak omega-1s.