Tailored Noise Correlations and Generalized Levy Wave Dynamics in Multimode Systems*

Multi-mode systems, like cavities, fibers etc, often suffer from the presence of environmental noise which causes mode mixing and subsequent interferences between various modes. In many occasions the study of the exact wave dynamic is a formidable task due to the many degrees of freedom that have to be taken into account in the equations of motion that describe such systems. Instead, a statistical theory of wave propagation might be a best way to describe the transport in such framework. We have utilized a Random Matrix Theory modeling which allow us to study the spreading of an initial mode excitation in the mode-space due to the environmental noise. Using this method we have developed a systematic approach that enforces a generalized Levy-type wave dynamics with a power law that it is imposed from the noise correlations. Our theoretical predictions have been tested in realistic circumstances like in paraxial light propagation in multimode fibers with tailored quenched disorder or in quantum dots with time-modulated boundaries.