This book includes chapters that discuss applications and updates in fractal analysis across the full spectrum of sciences, including mathematical concepts, cities, material physics, medicine, climate, and image processing.

This thesis sheds light on the unique dynamics of optoelectronic devices based on semiconductor quantum-dots. The complex scattering processes involved in filling the optically active quantum-dot states and the presence of charge-carrier nonequilibrium conditions are identified as sources for the distinct dynamical behavior of quantum-dot based devices. Comprehensive theoretical models, which allow for an accurate description of such devices, are presented and applied to recent experimental observations. The low sensitivity of quantum-dot lasers to optical perturbations is directly attributed to their unique charge-carrier dynamics and amplitude-phase-coupling, which is found not to be accurately described by conventional approaches. The potential of quantum-dot semiconductor optical amplifiers for novel applications such as simultaneous multi-state amplification, ultra-wide wavelength conversion, and coherent pulse shaping is investigated. The scattering mechanisms and the unique electronic structure of semiconductor quantum-dots are found to make such devices prime candidates for the implementation of next-generation optoelectronic applications, which could significantly simplify optical telecommunication networks and open up novel high-speed data transmission schemes.