  High-mobility graphene hosting massless charge carriers with linear
dispersion provides a promising platform for electron optics phenomena.
Inspired by the physics of dielectric optical micro-cavities where the photon
emission characteristics can be efficiently tuned via the cavity shape, we
study corresponding mechanisms for trapped Dirac fermionic resonant states in
deformed micro-disk graphene billiards and directed emission from those. In
such graphene devices a back-gate voltage provides an additional tunable
parameter to mimic different effective refractive indices and thereby the
corresponding Fresnel laws at the boundaries. Moreover, cavities based on
single-layer and double-layer graphene exhibit Klein- and anti-Klein tunneling,
respectively, leading to distinct differences with respect to dwell times and
resulting emission profiles of the cavity states. Moreover, we find a variety
of different emission characteristics depending on the position of the source
where charge carriers are fed into the cavites. Combining quantum mechanical
simulations with optical ray tracing and a corresponding phase-space analysis,
we demonstrate strong confinement of the emitted charge carriers in the mid
field of single-layer graphene systems and can relate this to a lensing effect.
For bilayer graphene, trapping of the resonant states is more efficient and the
emission characteristics do less depend on the source position.
