Analytical approach for the Floquet theory of delay differential equations.

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincaré-Lindstedt and the Shohat expansions, which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows us to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions.

Stabilization of chaotic spatiotemporal filamentation in large broad area lasers by spatially structured optical feedback.

In large high-power broad-area lasers the spatiotemporal filamentation processes and instabilities occur macroscopic as well as on microscopic scales. Numerical simulations on the basis of Maxwell- Bloch equations for large longitudinally and transversely extended semiconductor lasers reveal the internal spatial and temporal processes, providing the relevant scales on which control for stabilization consequently has to occur. It is demonstrated that the combined longitudinal instabilities, filamentation, and propagation effects may be controlled by suitable spatially structured delayed optical feedback allowing, in particular, the control of coherent regimes in originally temporally and spatially chaotic states.