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Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances

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  • Mario Lucido

    (Department of Electrical and Information Engineering “Maurizio Scarano” (DIEI), University of Cassino and Southern Lazio, 03043 Cassino, Italy)

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.

Suggested Citation

  • Mario Lucido, 2021. "Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1429-:d:577893
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    References listed on IDEAS

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    1. Berardi Sensale-Rodriguez & Rusen Yan & Michelle M. Kelly & Tian Fang & Kristof Tahy & Wan Sik Hwang & Debdeep Jena & Lei Liu & Huili Grace Xing, 2012. "Broadband graphene terahertz modulators enabled by intraband transitions," Nature Communications, Nature, vol. 3(1), pages 1-7, January.
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    Cited by:

    1. Ammar Armghan & Meshari Alsharari & Khaled Aliqab & Osamah Alsalman & Juveriya Parmar & Shobhit K. Patel, 2023. "Graphene Twistronics: Tuning the Absorption Spectrum and Achieving Metamaterial Properties," Mathematics, MDPI, vol. 11(7), pages 1-17, March.
    2. Nikolaos L. Tsitsas, 2023. "Analytical Methods in Wave Scattering and Diffraction Volume I," Mathematics, MDPI, vol. 11(4), pages 1-5, February.

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