An Excitonic Approach to the Ultrafast Optical Response of Semiconductor Nano-Structures
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In this thesis, I present an excitonic approach to treating the coherent dynamics of optically generated charge carriers in semiconductor nanostructures. The main feature of this approach is that it includes exchange interactions and phase space filling effects, which have generally been omitted in previous excitonic treatments of coherent dynamics, so that it can go beyond the low excitation limit. In contrast to the well-known semiconductor Bloch equations, this approach treats intraband correlations without factorization. The excitonic formalism and the obtained excitonic equations are shown to be particularly advantageous in systems where bound excitons dominate the optical response and where intraband correlations play a central role. To demonstrate the application of the excitonic approach, we simulate the coherent carrier dynamics of an optically-excited, updoped AlGaAs superlattice in the presence of a terahertz pulse, where 1s excitonic states as well as higher in-plane excited states are included. We find that gain coefficients greater than 20/cm can be achieved over a tuning range of 3-11THz and that due to the coherent cascading of the carriers down the excitonic Wannier-Stark ladder, the gain coefficients have much higher gain saturation fields than comparable two-level systems. To investigate the effects of phase space filling and exchange interaction on exciton dynamics, we then apply the excitonic formalism to a simple model of a quantum ring as well as a realistic model of a quantum well. For the quantum ring, we have obtained numerical results regarding exciton population and interband polarization. We also compared our excitonic approach to the semiconductor Bloch equations in detail using this simple model. For the quantum well, in addition to the investigation of exciton dynamics, we propose and examine several approximations that can make our excitonic dynamic equations very efficient. The excitonic formalism presented in this thesis is an efficient approach that can be applied in a wide range of systems, which makes it a potential alternative to the standard miconductor Bloch equations for many systems where the intraband correlations are crucial.