Abstract
The phase of graphene plasmon upon edge-reflection plays a crucial role on determining the spectral properties of graphene structures. In this article, by using the full-wave simulation, we demonstrate that the mid-infrared graphene plasmons are nearly totally reflected at the boundary together with a phase jump of approximately 0.27π, regardless of the environments surrounding it. Appling this phase pickup, a Fabry-Perot model is formulated that can predict accurately the resonant wavelengths of graphene nano-ribbons. Furthermore, we find that the magnitude of the phase jump will either increase or reduce when two neighboring coplanar graphene sheets couple with each other. This could be used to explain the red-shift of resonant wavelength of periodic ribbon arrays with respect to an isolated ribbon. We provide a straightforward way to uncover the phase jump of graphene plasmons that would be helpful for designing and engineering graphene resonators and waveguides as well as their associated applications.
Highlights
When a light illuminates on to a smooth conductor surface or nano-structures, the collective oscillation of free electrons with incident radiation is possible under certain conditions, generating the so-called surface plasmons (SPs) [1]
These unique properties associated with SPs host a variety of applications ranging from bio-sensing [3, 4], imaging [5, 6], and Raman spectroscopy [7,8,9] to the miniaturization of nanophotonics circuits [10]
We study for the first time the phase of SPs upon reflection at the boundary of graphene, which is extracted from the interference fringes between the forward and reflected SPs
Summary
When a light illuminates on to a smooth conductor surface or nano-structures, the collective oscillation of free electrons with incident radiation is possible under certain conditions, generating the so-called surface plasmons (SPs) [1]. It was predicted that a highly-doped graphene is able to support SPs at mid-infrared frequencies with much higher degree of spatial confinement and relatively lower losses with respect to the noble metal plasmons, and more notably, with tunability either by chemical or electrical doping [16]. Assuming that the boundary of graphene locates at x = 0, the electric field can mathematically be expressed as: Ez. By fitting the electric field from FDTD [Fig. 1(c)] with Eq (3), the phase pickup of graphene plasmon together with the reflection magnitude and wave-vector can be obtained. It is noted that the magnitude of phase pickup calculated from Eq (5) deviates from the ones from FDTD modeling This may result from the neglect of the local modes confined at the graphene edge except for the propagating graphene plasmons [42]. We conclude that such neglect will not give a significant change on the spectral trend of the reflection coefficient
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