Nonlinear optics and light localization in quantum dot samples

I propose to study the light propagation in so-called quantum dot semiconductor structures with the ultimate aim of realizing light bullets. These are propagating 'balls' of light with an extension of a few micrometers to the ten micrometer range in the direction(s) orthogonal as well as parallel to the propagation axis. The latter corresponds also to a time axis. For any fixed position along the axis, there will be light only for a short time (in the picosecond or tens of picosecond range). As a consequence, light bullets are spatio-temporally localized 'patches' or wavepackets of light.These objects will be self-localized, i.e. they will form spontaneously from a broad-area input beam filling the whole aperture of the device and being constant ('continuous-wave') in time by self-organization after some suitable perturbation. This is in strong contrast to the natural tendency of light (and other waves) to broaden: Usually, light does not stay confined to small regions in space or time. We will utilize that this broadening can be balanced by nonlinearities. These nonlinearities arise from the fact that the optical properties of a medium -- notably its refractive index -- become dependent on the light field itself, if it is sufficiently intense, as is the case for laser light. The resulting self-localized and shape-stable state is often referred to as a solitary wave or, more simply, as a soliton.Interest in these intriguing objects stems from two sides. On the one hand, self-localization is an important aspect of self-organization, i.e. the problem addressed in the interdisciplinary field of Nonlinear Science, why non-trivial structures in space and time are ubiquitous. Optical solitons have counterparts in hydrodynamics, plasma physics, chemistry and possibly biology and nature. The demonstration of simultaneous space-time self-localization in an optical system would constitute an important advance in our knowledge on self-localization phenomena. On the other hand, the realization of these light bullets opens interesting opportunities in all-optical photonics where one aim is to confine light (or photons) to the smallest possible dimensions, e.g. for optical communications. In addition, due to the optical nonlinearities, it is possible to control the emission of a photonic device using other light beams, similar to electronics where the flow of electrons is controlled by other electrons. Specifically, the envisaged solitons will be bistable, i.e. they can be present or absent under the same conditions, and this status can be manipulated by external light beams, which opens obvious possibilities for all-optical buffering or processing devices. Since we will place these structures in an optical cavity, we refer to the resulting localized wavepackets as cavity solitons and cavity light bullets.A major thrust of modern photonics is the use of meta-materials which do not exists in nature in order to tailor optical properties for specific demands. We will use quantum dots, a kind of artificial atom, in order to realize a so-called self-focusing nonlinearity in a semiconductor and to reach the wavelength region around 1.3 micrometers relevant for telecommunications using the beneficial GaAs material system. The project will proceed over a sequence of characterizing measurements on the nonlinear optical properties of absorbing and amplifying quantum dot samples over their theoretical analysis and the extraction of device parameters relevant to future modelling to experiments in cavities including the characterization of bistability and the accompanying spatial structures. This will yield the interesting parameter regimes to look for cavity solitons and finally cavity light bullets. The results obtained on the way will be also helpful in impoving the understanding of the operation characteristics and performance limiting instabilities of the emerging novel lasers and amplifier structures based on quantum dots.