Catastrophe optics of caustics in single and bilayer graphene: Fine structure of caustics
Absztrakt:
We theoretically study the scattering of a plane wave of a
ballistic electron on a circular n-p junction (NPJ) in single
and bilayer graphene. We compare the exact wave function inside
the junction to that obtained from a semiclassical formula
developed in catastrophe optics. In the semiclassical picture
short wavelength electrons are treated as rays of particles that
can get reflected and refracted at the NPJ according to Snell's
law with negative refraction index. We show that for short
wavelength and close to caustics this semiclassical
approximation gives good agreement with the exact results in the
case of single-layer graphene. We also verify the universal
scaling laws that govern the shrinking rate and intensity
divergence of caustics in the semiclassical limit. It is
straightforward to generalize our semiclassical method to more
complex geometries, offering a way to efficiently design and
model graphene-based electron-optical systems. (C) 2010 WILEY-
VCH Verlag GmbH & Co. KGaA, Weinheim