Abstract
The surface plasmon resonances of a monolayer graphene disk, excited by an impinging plane wave, are studied by means of an analytical-numerical technique based on the Helmholtz decomposition and the Galerkin method. An integral equation is obtained by imposing the impedance boundary condition on the disk surface, assuming the graphene surface conductivity provided by the Kubo formalism. The problem is equivalently formulated as a set of one-dimensional integral equations for the harmonics of the surface current density. The Helmholtz decomposition of each harmonic allows for scalar unknowns in the vector Hankel transform domain. A fast-converging Fredholm second-kind matrix operator equation is achieved by selecting the eigenfunctions of the most singular part of the integral operator, reconstructing the physical behavior of the unknowns, as expansion functions in a Galerkin scheme. The surface plasmon resonance frequencies are simply individuated by the peaks of the total scattering cross-section and the absorption cross-section, which are expressed in closed form. It is shown that the surface plasmon resonance frequencies can be tuned by operating on the chemical potential of the graphene and that, for orthogonal incidence, the corresponding near field behavior resembles a cylindrical standing wave with one variation along the disk azimuth.
Highlights
To the best of the author’s knowledge, the only alternative to the proposed approach is the guaranteed4 of 15 convergence method in [23]. It is based on Methods of Analytical Regularization (MAR) and the Nystrom-type discretization scheme and has been successfully applied to analyze the response of a graphene disk to a dipole-field excitation, whereas no results have been provided regarding the plane-wave scattering from a graphene disk
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The surface plasmon resonances (SPRs) were excited an planeplane wavewave and the resonance frequencies have been for the peaks byimpinging an impinging and the resonance frequencies havesearched been searched for the ofpeaks
Summary
A planar monolayer of carbon atoms which are arranged in a honeycomb lattice, has been receiving great interest from the scientific community as of late, due to its interesting mechanical, thermal, optical, and electronic properties [1,2,3,4,5,6,7,8], which make it a promising material for the development of a huge number of devices including transparent solar cells [9], amplifiers [10], plasmonic waveguides [11], ultra-high-speed transistors [12], giant Faraday rotation [13], cloaks [14], transformation optics [15], modulators [16], phaseshifters [17], switches [18], filters [19], novel antennas [20], and sensors [21], to name a few. By selecting the eigenfunctions of a suitable singular part of the integral operator, containing the most singular part of the operator itself, as expansion functions and adopting the Galerkin method, the obtained matrix operator turns out to be of the Fredholm second kind. To the best of the author’s knowledge, the only alternative to the proposed approach is the guaranteed of 15 convergence method in [23] It is based on MAR and the Nystrom-type discretization scheme and has been successfully applied to analyze the response of a graphene disk to a dipole-field excitation, whereas no results have been provided regarding the plane-wave scattering from a graphene disk.
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