We present a simple but mathematically complete first-principles theory for the pump-probe differential reflectivity experiment at negative delay (probe preceding the pump) to show how it gives information about the perturbed-free-induction-decay of coherent polarization. The calculation, involving the optical Bloch equations to describe the induced polarization and the Ewald-Oseen idea to calculate the reflected signal as a consequence of the free oscillations of perturbed dipoles, also explicitly includes the process of lock-in detection of a double-chopped signal after it has passed through a monochromator. The theory giving a closed form expression for the measured signal in both time and spectal domains is compared with experiments on high quality GaAs quantum well sample. The dephasing time inferred experimentally at 4 K compares remarkably well with the inverse of the absorption linewidth of the continuous-wave photoluminescence excitation spectrum. Spectrally-resolved signal at negative delay calculated from our theoretical expression nicely reproduces the coherent spectral oscillations observed in our experiments, although exact fitting of the experimental spectra with the theoretical expression is difficult on account of multiple resonances.
We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small
+ve and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small
+ve $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both
+ve and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large
+ve $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small
+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.
Ultrafast phase dynamics of free-induction decay for carriers in bulk GaAs is studied with differential-phase spectroscopy. The instantaneous phase shifts of the free-induction decay with respect to the excitation pulses are extracted from simultaneously recorded laser pulse autocorrelation and free-induction decay in GaAs. Ultrafast phase dynamics during and immediately after the femtosecond pulse excitation are numerically evaluated with optical Bloch equations using pump pulse and semiconductor exciton parameters as input. Good agreement of the theory with experiment is obtained.
The nonlinear response of single GaAs quantum dots is studied in femtosecond near-field pump-probe experiments. At negative time delays, transient reflectivity spectra show pronounced oscillatory structure around the quantum dot exciton line, providing the first evidence for a perturbed free induction decay of the excitonic polarization. Phase-disturbing Coulomb interactions between the excitonic polarization and continuum excitations dominate the optical nonlinearity on ultrafast time scales. A theoretical analysis based on the semiconductor Bloch equations accounts for this behavior.
Optical nonlinearities of Al(x)Ga(1-x)As/GaAs asymmetric coupled quantum wells within a p-i-n structure have been observed by using time-resolved spectroscopy. Under photoexcitation, exciton absorption lines exhibit spectral shifts of as much as approximately 1 meV. The recovery times of these spectral shifts are of the order of hundreds of picoseconds when the excitation photon is above the lowest exciton state but become less than 10 psec when excitation is below the lowest exciton state, indicating a virtual process. The behavior of these spectral shifts is consistent with the presence of a polarization induced by optical pumping. The polarization is believed to be due to the excitons that have nonvanishing electric dipole moments along the axis of the asymmetric coupled quantum wells.
This dissertation presents investigations of fundamental optical nonlinearities in semi-conductor microstructures. Two distinct effects are studied. In the first part the excitonic optical Stark effect in InGaAs and GaAs multiple quantum-well structures is investigated by means of pump-probe spectroscopy. For nonresonant excitation below the excitonic transition the direction of the shift of the resonance depends on the polarization of the pump and probe pulses. In particular, for anti-circular polarization a surprising red-shift is observed. For resonant excitation, induced absorption energetically above and below the exciton transition and bleaching of the resonance is found. Experiments using both resonant and nonresonant excitation reveal the importance of bound and unbound two-exciton states in absorption changes of the 1s heavy-hole exciton resonance. It is found that higher-order Coulomb contributions determine the intensity as well as the time dependence of the differential excitonic absorption. In addition, the influence of light-hole excitons is analyzed. It is shown that the direction of the optical Stark shift for nonresonant excitation depends also sensitively on the heavy-hole to light-hole splitting and the detuning of the pump pulse. For very high pump intensities and nonresonant excitation the absorption is split when a circularly polarized pump and a linearly polarized probe beam are used. For co-circular excitation traces of hyper-Raman gain are observed. In the second part of this dissertation, the nonlinear optical response of semiconductor microcavities in the nonperturbative regime is studied in resonant single-beam transmission and pump-probe experiments. In both types of experiment, a pronounced third transmission peak lying spectrally between the two normal modes is observed. Its dependence on the probe intensity, pump intensity, pump-probe delay, exciton-cavity detuning and pump detuning is investigated. For single-beam transmission, the energy of the third peak parallels the position of the cavity resonance. It is more pronounced for circularly polarized excitation and lasts longer than the two normal modes. For pump-probe experiments, the third peak increases with decreasing probe intensity and increasing pump intensity. Its energy is close to the low-energy side of the pump spectrum and virtually unaffected by the cavity-exciton detuning. The appearance of the third peak requires temporal overlap of pump and probe pulses. The origin of this complex nonlinearity is the quantum nature of light, which induces intraband polarizations in the presence of a coherent driving field and a finite carrier density. It is found that the coupling of the intraband polarizations via guided modes to the polarization of the fundamental longitudinal mode is responsible for the third transmission peak. A fully quantized theory reproduces the experimental observations.