DYNAMICS OF MULTI-PHOTON PROCESSES IN SEMICONDUCTOR HETEROSTRUCTURES

Abstract

The present work is devoted to the study of the dynamics of multi-photon processes in semiconductor heterostructures. A time-dependent description is important for understanding in detail the transient response of semiconductors excited by ultrashort optical pulses. In the first part of this thesis, we set up a phenomenological model based on rate equations, in order to investigate the possibility of measuring degenerate two-photon gain in a semiconductor microcavity. The amplification predicted by the model is fairly low ( 2%) and mainly limited by the intra-band relaxation of the carriers, which leads to rapid saturation. In the second part, we develop a general theory for the dynamics of multi-photon processes in semiconductors. It will give insight into complex effects related to the coherence between the bands, which are not included in usual absorption coefficients or susceptibilities. For this purpose, we derive effective multi-band Bloch equations that include resonant multi-photon processes induced by two linearly polarized electromagnetic pulses of frequency close to the band gap and close to the half of the band gap respectively. The benefit of the proposed approach is two-fold. First, the description of the dynamics is restricted to a reduced number of bands. However, the discarded bands are not neglected, but consistently taken into account in the higher order processes. Second, all quantities appearing in the effective multi-band Bloch equations vary on the same time scale, which makes the numerical integration much more efficient. The time-dependent polarization current, as well as some susceptibilities, are derived on a consistent level of approximation, and are discussed in detail. The propagation of the electromagnetic fields is neglected. Such a model is appropriate for the description of low-dimensional quantum confined systems (e.g. quantum wells or quantum wires) excited by two colinearly propagating pulses. It accounts for various linear and nonlinear optical processes, such as one- and two-photon absorption, second-harmonic generation, difference-frequency mixing, or coherent control of photocurrent. In this thesis, the general theory is applied to the study of three specific physical situations. First, we investigate the charge and spin current in a symmetric AlGaAs/GaAs quantum well, injected by interference between one- and two-photon inter-band transitions. We identify new coherent terms in the expression of the current, which contribute significantly to the terahertz emission. The effects of the Stark shifts and the inter-valence band two-photon transitions are also calculated and discussed. Second, we calculate the anisotropic two-photon absorption spectra of an AlGaAs/GaAs V-shaped quantum wire with realistic band structure. The Coulomb interaction is taken into account within the Hartree-Fock approximation. The various excitonic peaks are identified with respect to the involved subbands and to the symmetry properties. We also show that excitons that are dark for one-photon excitation may become bright for two-photon spectroscopy, when the light is polarized perpendicularly to the growth direction, but not along a symmetry axis of the wire. Finally, the last application focuses on the optical injection of current in the presence of excitonic effects. Concentrating on the same AlGaAs/GaAs V-shaped quantum wire, we show that the Coulomb interaction within the Hartree-Fock approximation induces terahertz oscillations in the injected charge current. The oscillation frequency corresponds to the energy spacing between the two lowest excitonic resonances, slightly below the band gap, excited respectively by the laser pulse with frequency close to the band gap, and the one with frequency close to the half of the band gap.