volume | PIER Journals

Abstract

We present a three-dimensional finite element (FEM) field-flux eigenmode formulation, able to provide accurate modeling of the propagation characteristics of periodic structures featuring graphene. The proposed formulation leads to a linear eigenmode problem, where the effective refractive index is an unknown eigenvalue; the electric field intensity and magnetic flux density are the state variables; and graphene's contribution is efficiently incorporated via a finite conductivity boundary condition. The FEM formulation is spurious-mode free and capable of providing accurate dispersion diagrams and field distributions for arbitrary propagation directions, as opposed toother analytical or numerical approaches, while also efficiently dealing with graphene's dispersive nature. The novelty of the presented approximation is substantiated by computational results for structures incorporating graphene of random periodicity, both within passbands and bandgap frequencies.

1. Nikitin, A. Y., F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, "Edge and waveguide terahertz surface plasmon modes in graphene microribbons," Phys. Rev. B, Vol. 84, 161407, 2011.
doi:10.1103/PhysRevB.84.161407

2. Politano, A. and G. Chiarello, "Plasmon modes in graphene: Status and prospect," Nanoscale, Vol. 6, 10927-10940, 2014.
doi:10.1039/C4NR03143A

3. Vicarelli, L., M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, "Graphene field-effect transistors as room-temperature terahertz detectors," Nat. Mater., Vol. 11, 865-871, 2012.
doi:10.1038/nmat3417

4. Tomadin, A., A. Tredicucci, V. Pellegrini, M. S. Vitiello, and M. Polini, "Photocurrent-based detection of terahertz radiation in graphene," Appl. Phys. Lett., Vol. 103, 211120, 2013.
doi:10.1063/1.4831682

5. Spirito, D., D. Coquillat, S. L. De Bonis, A. Lombardo, M. Bruna, A. C. Ferrari, V. Pellegrini, A. Tredicucci, W. Knap, and M. S. Vitiello, "High performance bilayer-graphene terahertz detectors," Appl. Phys. Lett., Vol. 104, 061111, 2014.
doi:10.1063/1.4864082

6. Koppens, F. H. L., T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, "Photodetectors based on graphene, other two-dimensional materials and hybrid systems," Nat. Nanotechnol., Vol. 9, 780-793, 2014.
doi:10.1038/nnano.2014.215

7. Politano, A., H. K. Yu, D. Farías, and G. Chiarello, "Multiple acoustic surface plasmons in graphene/Cu(111) contacts," Phys. Rev. B, Vol. 97, 035414, 2018.
doi:10.1103/PhysRevB.97.035414

8. Politano, A., I. Radović, D. Borka, Z. L. Mišković, H. K. Yude, D. Farías, and G. Chiarello, "Dispersion and damping of the interband π plasmon in graphene grown on Cu(111) foils," Carbon, Vol. 114, 70-76, 2017.
doi:10.1016/j.carbon.2016.11.073

9. Politano, A., I. Radović, D. Borka, Z. L. Mišković, and G. Chiarello, "Interband plasmons in supported graphene on metal substrates: Theory and experiments," Carbon, Vol. 96, 91-97, 2016.
doi:10.1016/j.carbon.2015.09.053

10. Politano, A., A. R. Marino, V. Formoso, D. Farías, R. Miranda, and G. Chiarello, "Quadratic dispersion and damping processes of π plasmon in monolayer graphene on Pt(111)," Plasmonics, Vol. 7, 369-376, 2012.
doi:10.1007/s11468-011-9317-1

11. Politano, A., A. R. Marino, V. Formoso, D. Farías, R. Miranda, and G. Chiarello, "Evidence for acoustic-like plasmons on epitaxial graphene on Pt(111)," Phys. Rev. B, Vol. 84, 033401, 2011.
doi:10.1103/PhysRevB.84.033401

12. Cupolillo, A., A. Politano, N. Ligato, D. M. Cid Perez, G. Chiarello, and L. S. Caputi, "Substrate-dependent plasmonic properties of supported graphene," Surf. Sci., Vol. 634, 76, 2015.
doi:10.1016/j.susc.2014.11.002

13. Politano, A., G. Chiarello, and C. Spinella, "Plasmon spectroscopy of graphene and other two-dimensional materials with transmission electron microscopy," Mater. Sci. Semicond. Process., Vol. 65, 88-99, 2017.
doi:10.1016/j.mssp.2016.05.002

14. Ben Rhouma, M., M. Oueslati, and B. Guizal, "Surface plasmons on a doped graphene sheet with periodically modulated conductivity," Superlattices and Microstructures, Vol. 96, 212-219, 2016.
doi:10.1016/j.spmi.2016.05.021

15. Nikitin, A. Yu., F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, "Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons," Phys. Rev. B, Vol. 84, 161407, 2011.
doi:10.1103/PhysRevB.84.161407

16. Bludov, Y. V., N. M. R. Peres, and M. I. Vasilevskiy, "Graphene-based polaritonic crystal," Phys. Rev. B, Vol. 85, 081405, 2012.
doi:10.1103/PhysRevB.85.245409

17. Ferreira, A. and N. M. R. Peres, "Complete light absorption in graphene-metamaterial corrugated structures," Phys. Rev. B, Vol. 86, 205401, 2012.
doi:10.1103/PhysRevB.86.205401

18. Madani, A., S. Zhong, H. Tajalli, S. R. Entezar, A. Namdar, and Y. Ma, "Tunable metamaterials made of graphene-liquid crystal multilayers," Progress In Electromagnetics Research, Vol. 143, 545-558, 2013.
doi:10.2528/PIER13080302

19. Freitag, M., et al. "Photocurrent in graphene harnessed by tunable intrinsic plasmons," Nature Comm., Vol. 4, 1951, 2013.
doi:10.1038/ncomms2951

20. Gómez-Díaz, J. S., M. Esquius-Morote, and J. Perruisseau-Carrier, "Plane wave excitation-detection of non-resonant plasmons along finite-width graphene strips," Optics Express, Vol. 21, 24856-24872, 2013.
doi:10.1364/OE.21.024856

21. Malhat, H. A., S. H. Zainud-Deen, and S. M. Gaber, "Graphene based transmitarray for terahertz applications," Progress In Electromagnetics Research M, Vol. 36, 185-191, 2014.
doi:10.2528/PIERM14050705

22. Juneghani, F. A., A. Z. Nezhad, and R. Safian, "Analysis of diffraction graphene gratings using the C-method and design of a terahertz polarizer," Progress In Electromagnetics Research M, Vol. 65, 175-186, 2018.
doi:10.2528/PIERM17102901

23. Nitas, M., C. S. Antonopoulos, and T. V. Yioultsis, "EB eigenmode formulation for the analysis of lossy and evanescent modes in periodic structures and metamaterials," IEEE Trans. Magnetics, Vol. 53, 2017.
doi:10.1109/TMAG.2017.2683459

24. Monk, P., Finite Element Methods for Maxwell's Equations, Oxford University Press, 2003.
doi:10.1093/acprof:oso/9780198508885.001.0001

25. Boffi, D., F. Brezzi, and M. Fortin, Mixed Finite Element Methods and Applications, Springer, 2013.
doi:10.1007/978-3-642-36519-5

26. Zhu, Y. and A. C. Cangellaris (eds.), Multigrid Finite Element Methods for Electromagnetic Field Modeling, John Wiley & Sons, 2006.
doi:10.1002/0471786381

27. Salonikios, V., S. Amanatiadis, N. Kantartzis, and T. V. Yioultsis, "Modal analysis of graphene microtubes utilizing a two-dimensional vectorial finite element method," Applied Physics A, Vol. 122, 351, 2016.
doi:10.1007/s00339-016-9862-8

28. Hanson, G. W., "Dyadic Green's functions and guided surface waves for a surface conductivity model of graphene," J. Appl. Phys., Vol. 103, 064302, 2008.
doi:10.1063/1.2891452

29. Gonçalves, P. A. D., E. J. C. Dias, Y. V. Bludov, and N. M. R. Peres, "Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: An analytical approach," Phys. Rev. B, Vol. 94, 195421, 2016.
doi:10.1103/PhysRevB.94.195421

30. Politano, A. and G. Chiarello, "Emergence of a nonlinear plasmon in the electronic response of doped graphene," Carbon, Vol. 71, 176-80, 2014.
doi:10.1016/j.carbon.2014.01.026

Dr. Vasilis Salonikios

Dr. Michalis Nitas

Dr. Savvas Raptis

Prof. Traianos V. Yioultsis