Scattering of graphene plasmons at abrupt interfaces: an analytic and numeric study

Abstract

We discuss the scattering of graphene surface plasmon-polaritons (SPPs) at an interface between two semi-infinite graphene sheets with different doping levels and/or different underlying dielectric substrates. We take into account retardation effects and the emission of free radiation in the scattering process. We derive approximate analytic expressions for the reflection and the transmission coefficients of the SPPs as well as the same quantities for the emitted free radiation. We show that the scattering problem can be recast as a Fredholm equation of the second kind. Such equation can then be solved by a series expansion, with the first term of the series correspond to our approximated analytical solution for the reflection and transmission amplitudes. We have found that almost no free radiation is emitted in the scattering process and that under typical experimental conditions the back-scattered SPP transports very little energy. This work provides a theoretical description of graphene plasmon scattering at an interface between distinct Fermi levels which could be relevant for the realization of plasmonic circuitry elements such as plasmonic lenses or reflectors, and for controlling plasmon propagation by modulating the potential landscape of graphene.

arXiv comment28 pages

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Cited by in corpus (7)

• Reflection Phase Shift of One-dimensional Plasmon Polaritons in Carbon Nanotubes
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• Study of volume and surface plasmons in small silicon-hydrogen nanoclusters by GW method
• Refraction laws for two-dimensional plasmons
• Excitation of SPP's in graphene by a waveguide mode
• Simulation of Scanning Near-Field Optical Microscopy Spectra of 1D Plasmonic Graphene Junctions
• Plasmonic band and defect mode of one dimensional graphene lattice