Quantum optical and nonlinear optical properties of semiconductors and semiconductor heterostructures in photonic crystals

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Tayloring the photonic dispersion relation in "photonic crystals", a periodic arrangement of dielectric materials on the length scale of the optical wavelength, influences the lightmatter interaction fundamentally. The radiative life time of an excited state, for instance, can be varied over several orders of magnitude by reducing the photonic density of states in the corresponding spectral region. Also the effective coupling strength between light and matter can be tuned by altering the photonic density of states. Direct-gap semiconductor heterostructures provide particularly interesting material systems to study the possibilities of manipulating the light-matter interaction for both fundamental and practical reasons. They exhibit strong excitonic resonances even at room temperature, the quantum efficiency of well-designed opto-electronic devices is limited by spontaneous emission and they can be grown with almost molecular precision. Within this project, we want to theoretically study the interaction between semiconductors and semiconductor heterostructures and photonic crystals. The basis of our approach are the semiconductor luminescence equations, which are an extension of the semiconductor Bloch equations for a fully quantized light field. The quantization of the light field is crucial to understand the strong light-matter coupling, since the spontaneous emission rate, in particular, is modified in photonic crystals. We are especially interested in light emission properties, lasing and pulse propagation effects, as well as quantum optical effects like the radiative life of excitons and the excitonic and light field statistics.