  We consider waveguides formed by single or multiple two-dimensional chaotic
cavities connected to leads. The cavities are chaotic in the sense that the ray
(or equivalently, classical particle) dynamics within them is chaotic.
Geometrical parameters are chosen to produce a mixed phase space (chaotic
regions surrounding islands of stability where motion is regular). Incoming
rays (or particles) cannot penetrate into these islands but incoming plane
waves dynamically tunnel into them at a certain discrete set of frequencies
(energies). The support of the corresponding quasi-bound states is along the
trajectories of periodic orbits trapped within the cavity. We take advantage of
this difference in the ray/wave behavior to demonstrate how chaotic waveguides
can be used to design beam splitters and microlasers. We also present some
preliminary experimental results in a microwave realization of such chaotic
waveguide.
