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 semiinfinite 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 an equation can then be solved by a series expansion, with the first term of the series corresponding 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 paper 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.

Reflection phase shift of one-dimensional plasmon polaritons in carbon nanotubes

“…[17] and ref. [22]. In the 2D case, the unbounded modes modify the phase shift from 0.3π to 0.25π [17], and similar improvement is expected in our 1D case by employing the unbounded modes.…”

Active control of micrometer plasmon propagation in suspended graphene

“…The minimum reflectance is 6.5% if the graphene bubble is nearly flat (d2=0, i.e., co-planar with the substrate surface). Since almost no free radiation is emitted in the scattering process under these conditions (green curve in Figure 4e), 36 the maximum energy crossing the air-dielectric interface can be considered to be 93.5%. By analogy to electronic devices, we can define the ratio between the maximum and minimum energies passing across the interface as the switch ratio of plasmonic devices; 37 the observed switch ratio reaches ＞14 by in situ changing the shape of suspended graphene.…”

Edge diffraction and plasmon launching in two-dimensional electron systems

“…Particularly, it is possible to study the scattering of surface waves by a step-like contrast of 2D conductivity or even by and edge of metal gate with uniform 2DES beneath it. Such studies are important for design of plasmonenhanced photodetectors 28,29 , and were addressed previously only with numerical 30,31 or approximate [32][33][34] techniques 35 .…”