DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Nonlinear dynamical effects in integrated optoelectronic structures (Teilprojekt D 8)

The focus of our research is on nonlinear dynamical effects in integrated optoelectronic structures characterized by systems of interacting laser devices, interaction of several modes in an optical cavity, and spatial inhomogeneities. This leads to essentially extended models and to mathematical problems like: nonlinear hyperbolic systems of partial differential equations with discontinuous coefficients; different time scales; mathematical model reduction (centre manifolds, attractors); efficient modelling on different levels of complexity of single components and their coupling in a laser structure; analytical and numerical investigation of local and global bifurcations in reduced models. The final goal of the project is to create design rules for new dynamical effects, to support the experimental development by mathematical simulations, and to optimize existing devices, especially with respect to the dynamical performance (speed, robustness, system conformity).