Microwave Chaotic Open Cavities. Applications of Dynamical Trapping

We consider 2D microwave open cavities whose ray dynamics is chaotic. In particular, we estudy theoretically and experimentally, cavities which yield mixed (chaotic ad regular) phase space. Such cavities are connected to leads to form electromagnetic waveguides with single or multiple cavities. The principal feature of mixed chaos is the existence of islands of stability (resonance islands) in phase space. In this paper we focus on cavities yielding a single large resonance island. Ray trajectories within this island are trapped within the cavity and hence are not accessible to rays incoming from the leads. However the wave behavior is drastically different: at resonant frequencies, the incoming waves penetrate into these regions. We call this dynamical trapping and use it for the design of various multicavity resonators. We show some experimental evidence of dynamical trapping in a microwave experiment. We also discuss possible applications of dynamical trapping in multicavities for microlasers, electro-optical beam splitters, and switches. For these 2D systems there is a complete analogy between the field equation governing the microwave propagation, the Helmholtz equation and that of the quantum problem, the Schroedinger equation. Hence our results are directly pertinent to microscopic electron wave guides in the ballistic regime.