Marginally Unstable Periodic Orbits in Semiclassical Mushroom Billiards

Optical mushroom shaped billiards offer a unique opportunity to isolate and study non-dispersive, marginally unstable periodic orbits. Here we show that the openness of the cavity to external fields presents unanticipated consequences for the far-field distribution, including directional emission. This is mediated by interactions of marginally unstable periodic orbits with chaotic modes and is potentially relevant for the design of microcavity lasers. We also show that such orbits are robust against perturbations to the shape of the cavity, despite the non-generic character of the classical counterpart and the lack of structural stability of the corresponding classical orbits.