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New analytical investigation of anisotropic graphene nano-waveguides with bi-gyrotropic cover and substrate backed by a PEMC layer

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Abstract

This paper aims to study the magneto-plasmons in an anisotropic graphene nano-waveguide with bi-gyrotropic cover and substrate. The substrate is backed by a perfect electromagnetic conductor (PEMC) layer, a general and ideal boundary, which can be transformed easily into the perfect electric conductor (PEC) or the perfect magnetic conductor (PMC) boundaries. The upper and bottom layers of the graphene sheet are made of different magnetic materials, each one has the permittivity and permeability tensors of \(\bar{\bar{\varepsilon }}\) and, \(\bar{\bar{\mu }}\) respectively. The external magnetic field is applied perpendicularly to the structure surface, which can be provided by a permanent magnet placed underneath the ground plane. Hence, the graphene sheet has anisotropic conductivity tensor (\(\bar{\bar{\sigma }}\)). A novel analytical model has been proposed for the general nano-waveguide to find its propagation properties. As special cases of the proposed general structure, two important new waveguides have been introduced and studied to show, first the richness of the proposed general nano-waveguide regarding the related specific plasmonic wave phenomena and effects, and second the validity and the high accuracy of the proposed model. The analytical and the simulation results are in an excellent agreement. It is shown that the modal properties of the proposed structure can be tuned effectively via the external magnetic field and the chemical potential of the graphene. Harnessing the non-reciprocity effect of anisotropic materials and the graphene sheet, the presented analytical model can be exploited to design tunable innovative devices in THz frequencies.

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References

  1. Bass, F.G., Bulgakov, A.A.: Kinetic and electrodynamic phenomena in classical and quantum semiconductor superlattices. Nova Publishers, New york (1997)

  2. Cheng, Z., Qin, C., Wang, F., He, H., Goda, K.: Progress on mid-IR graphene photonics and biochemical applications. Frontiers of Optoelectronics 9(2), 259–269 (2016)

  3. Couture, S., Sounas, D., Caloz, C.: Surface and leaky-wave modes in a grounded dielectric slab covered with graphene. In: IEEE International Symposium on Antennas and Propagation.(ISAP) 2011

  4. Diest, K., Dionne, J.A., Spain, M., Atwater, H.A.: Tunable color filters based on metal − insulator − metal resonators. Nano Lett. 9(7), 2579–2583 (2009)

  5. Feurer, T., Stoyanov, N.S., Ward, D.W., Vaughan, J.C., Statz, E.R., Nelson, K.A.: Terahertz polaritonics. Annu. Rev. Mater. Res. 37, 317–350 (2007)

  6. Fuscaldo, W., Burghignoli, P., Baccarelli, P., Galli, A.: Complex mode spectra of graphene-based planar structures for THz applications. Journal of Infrared, Millimeter, and Terahertz Waves 36(8), 720–733 (2015)

  7. Gao, Y., Ren, G., Zhu, B., Huang, L., Li, H., Yin, B., Jian, S.: Tunable plasmonic filter based on graphene split-ring. Plasmonics 11(1), 291–296 (2016)

  8. Goerbig, M.: Electronic properties of graphene in a strong magnetic field. Rev. Mod. Phys. 83(4), 1193–1243 (2011)

  9. Gomez-Diaz, J.S., Alù, A.: Graphene plasmonics: Theory and experiments. In: Antennas and Propagation & USNC/URSI National Radio Science Meeting, 2015 IEEE International Symposium on 2015, pp. 800–801. IEEE

  10. Gric, T.: Tunable terahertz structure based on graphene hyperbolic metamaterials. Opt. Quant. Electron. 51(6), 202 (2019)

  11. Gric, T., Cada, M.: Analytic solution to field distribution in one-dimensional inhomogeneous media. Optics Communications 322, 183–187 (2014)

  12. Gric, T., Hess, O.: Controlling hybrid-polarization surface plasmon polaritons in dielectric-transparent conducting oxides metamaterials via their effective properties. J. Appl. Phys. 122(19), 193105 (2017)

  13. Gu, X.-Q., Yin, W.-Y., Zheng, T.: Attenuation characteristics of the guided THz wave in parallel-plate ferroelectric-graphene waveguides. Optics Communications 330, 19–23 (2014)

  14. Gu, X., Lin, I.-T., Liu, J.-M.: Gu, X., Lin, I.-T., Liu, J.-M.: Extremely confined terahertz surface plasmon-polaritons in graphene-metal structures. Applied Physics Letters 103(7), 071103 (2013). Appl. Phys. Lett. 103(7), 071103 (2013)

  15. Gurevich, A.G., Melkov, G.A.: Magnetization oscillations and waves. CRC Press, Boca Raton (1996)

  16. Gusynin, V., Sharapov, S., Carbotte, J.: Magneto-optical conductivity in graphene. J. Phys.: Condens. Matter 19(2), 026222 (2006)

  17. He, M.-D., Wang, K.-J., Wang, L., Li, J.-B., Liu, J.-Q., Huang, Z.-R., Wang, L., Wang, L., Hu, W.-D., Chen, X.: Graphene-based terahertz tunable plasmonic directional coupler. Appl. Phys. Lett. 105(8), 081903 (2014)

  18. Heydari, M.B., Samiei, M.H.V.: Plasmonic Graphene Waveguides: A Literature Review. arXiv preprint arXiv:1809.09937 (2018)

  19. Jablan, M., Buljan, H., Soljačić, M.: Plasmonics in graphene at infrared frequencies. Physical review B 80(24), 245435 (2009)

  20. Li, H.-J., Wang, L.-L., Liu, J.-Q., Huang, Z.-R., Sun, B., Zhai, X.: Investigation of the graphene based planar plasmonic filters. Appl. Phys. Lett. 103(21), 211104 (2013)

  21. Lindell, I.V., Sihvola, A.: Electromagnetic boundary and its realization with anisotropic metamaterial. Phys. Rev. E 79(2), 026604 (2009)

  22. Lindell, I.V., Sihvola, A.H.: Perfect electromagnetic conductor. J Electromagnetic Waves Appl 19(7), 861–869 (2005a)

  23. Lindell, I.V., Sihvola, A.H.: Realization of the PEMC boundary. IEEE Trans. Antennas Propag. 53(9), 3012–3018 (2005b)

  24. Lindell, I.V., Sihvola, A.H.: Losses in the PEMC boundary. IEEE Trans. Antennas Propag. 54(9), 2553–2558 (2006)

  25. Locatelli, A., Capobianco, A.-D., Nalesso, G., Boscolo, S., Midrio, M., De Angelis, C.: Graphene-based electro-optical control of the beat length of dielectric couplers. Optics Communications 318, 175–179 (2014)

  26. Lovat, G.: Transverse-resonance analysis of dominant-mode propagation in graphene nano-waveguides. In: International Symposium on Electromagnetic Compatibility-EMC EUROPE 2012, pp. 1–5. IEEE

  27. Malekabadi, A., Charlebois, S.A., Deslandes, D.: Parallel plate waveguide with anisotropic graphene plates: effect of electric and magnetic biases. J. Appl. Phys. 113(11), 113708 (2013)

  28. Mostaan, S.M.A., Saghai, H.R.: Plasmonic split disk resonator based on graphene. Opt. Quant. Electron. 50(5), 211 (2018)

  29. Pitilakis, A., Chatzidimitriou, D., Kriezis, E.E.: Theoretical and numerical modeling of linear and nonlinear propagation in graphene waveguides. Opt. Quant. Electron. 48(4), 243 (2016)

  30. Poole, D.: Linear algebra: A modern introduction. Cengage Learning, Boston (2014)

  31. Qu, S., Ma, C., Wang, S., Liu, H., Dong, L.: Modulation speed limits of a graphene-based modulator. Opt. Quant. Electron. 50(2), 105 (2018)

  32. Sadaghiani, V.K., Zavvari, M., Tavakkoli, M.B., Horri, A.: Design of graphene-based hybrid waveguides for nonlinear applications. Opt. Quant. Electron. 51(2), 49 (2019)

  33. Sepioni, M.: Magnetic properties of graphene pp. 1–136. (Doctoral dissertation, University of Manchester) (2013)

  34. Shahvarpour, A., Kodera, T., Parsa, A., Caloz, C.: Realization of the PEMC boundary. IEEE Trans. on Antennas Propag 58(11), 2781–2792 (2010)

  35. Shinohara, H., Tiwari, A.: Graphene: An Introduction to the Fundamentals and Industrial Applications. Wiley, London (2015)

  36. Singh, V., Joung, D., Zhai, L., Das, S., Khondaker, S.I., Seal, S.: Graphene based materials: past, present and future. Prog. Mater Sci. 56(8), 1178–1271 (2011)

  37. Süli, E., Mayers, D.F.: An Introduction to Numerical Analysis. Cambridge University Press, Cambridge (2003)

  38. Wallbank, J.R.: Electronic Properties Of Graphene Heterostructures With Hexagonal Crystals. Springer, Berlin (2014)

  39. Wang, M., Li, D., Wang, R., Zhu, J., Ren, Z.: PDMS-assisted graphene microfiber ring resonator for temperature sensor. Opt. Quant. Electron. 50(3), 132 (2018)

  40. Ye-xin, S., Jiu-sheng, L., Le, Z.: Graphene-integrated split-ring resonator terahertz modulator. Opt. Quant. Electron. 49(11), 350 (2017)

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Correspondence to Mohammad Hashem Vadjed Samiei.

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Heydari, M.B., Vadjed Samiei, M.H. New analytical investigation of anisotropic graphene nano-waveguides with bi-gyrotropic cover and substrate backed by a PEMC layer. Opt Quant Electron 52, 108 (2020). https://doi.org/10.1007/s11082-020-2222-0

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Keywords

  • Anisotropic graphene sheet
  • Permeability tensor
  • Analytical model
  • PEMC
  • Bi-gyrotropic media
  • Permittivity tensor
  • Effective index
  • Propagation loss