Banachraum

It is planned to start from an applied motivation of the resonance optimization in optical cavities and to discuss connected numerical and analytical difficulties. Resonances are considered as eigenvalues of 2nd order ODEs or PDEs equipped with radiation or dissipative boundary conditions. The quality factor and the decay rate can be defined via imaginary and real parts of eigenvalues. A recently developed theory for the derivation of Euler-Lagrange equations for Pareto optimizers will be presented, as well as its application to the computation of optimal layered cavities. Connections with control theory, symmetry breaking, and multi-parameter perturbation theory will be also discussed.The talk is partially based on the joint works (Albeverio, Karabash `17), (Karabash, Logachova, Verbytskyi `17), (Karabash, Koch, Verbytskyi `18), and (Eller, Karabash `19).

Illia Karabash

Dortmund