Catastrophe optics of caustics in single and bilayer graphene: fine structure of caustics

Abstract

We theoretically study the scattering of a plane wave of a ballistic electron on a circular n-p junction 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 n-p junction 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.

arXiv comment4 pages, 5 figures This manuscript should be published in the proceedings volume of the conference IWEPNM 2010, in the Physica Status Solidi B

References in corpus (5)

• Chiral tunneling and the Klein paradox in graphene
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Caustics due to Negative Refractive Index in Circular Graphene p-n Junctions
• Focusing by Plano-Concave lens using Negative Refraction
• Electron Flow in Circular n-p Junctions of Bilayer Graphene

Cited by in corpus (4)

• Diffraction catastrophes and semiclassical quantum mechanics for Veselago lensing in graphene
• Symmetry breaking and (pseudo)spin polarization in Veselago lenses for massless Dirac fermions
• Electronic optics in graphene in the semiclassical approximation
• Intraband electron focusing in bilayer graphene