Sign Up Submit Enquiry

THz graphene circulator with quadrupole mode resonator

Home THz graphene circulator with quadrupole mode resonator

Related Articles

Contact us

Article Content

Abstract

We present a compact and efficient three-port graphene-based circulator operating in the terahertz (THz) frequency range. Conventional designs are predicated on dipole resonances. In contrast, the present approach exploits the quadrupole mode of a circular graphene resonator, magnetized by a perpendicular direct current magnetic field. The structure is composed of a single-layer graphene resonator that is coupled to three graphene waveguides. These waveguides are supported by silica and silicon substrates. Through the optimization of resonator geometry and the tuning of graphene chemical potential, a substantial reduction in operational requirements was achieved, enabling functionality with a magnetic field of 0.2 T and a Fermi energy of 0.1 eV. Full-wave simulations performed in COMSOL Multiphysics demonstrate excellent nonreciprocal performance, with isolation better than –21 dB, insertion loss around –2.6 dB, and reflection of –18 dB at 5.38 THz. The frequency response is in good agreement with the predictions of temporal coupled-mode theory (TCMT), which confirms a fractional bandwidth of approximately 6.3% around the central frequency of 5.58 THz under the applied magnetic bias. A comparison of the proposed circulator with existing designs reveals a substantial reduction in both its physical dimensions and its weight. Furthermore, the circulator functions under conditions that demand less voltage and magnetic field strength than existing designs. In conclusion, the practical feasibility of device fabrication is discussed, with a focus on the compatibility of the proposed structure with current graphene-based photonic manufacturing technologies.

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

  • Graphene Oxide
  • Graphene
  • Microresonators
  • Metamaterials
  • Terahertz Optics
  • Free-Electron Lasers

Data availability

All data generated or analyzed during this study are included in this published article.

References

  1. Helszajn, J.: Waveguide Junction Circulators: Theory and Practice. Wiley, New York, NY, USA (1998)

    Google Scholar

  2. Xu, B., Zhang, D., Wang, Y., Hong, B., Shu, G., He, W.: Characterization of millimeter wave photonic crystal circulator with a ferrite sphere. Results Phys. 34, 105315 (2022). https://doi.org/10.1016/j.rinp.2022.105315

    Article Google Scholar

  3. Arunkumar, R., Robinson, S.: Investigation on ultra-compact 2d-pc based optical circulator for photonic integrated circuits. J. Optoelectron. Adv. Mater. 23, 112–118 (2021)

    Google Scholar

  4. Bonaccorso, F., Sun, Z., Hasan, T., Ferrari, A.: Graphene photonics and optoelectronics. Nat. Photon. 4(9), 611 (2010). https://doi.org/10.1038/nphoton.2010.186

    Article Google Scholar

  5. Ferrari, A.C., Bonaccorso, F., Fal’Ko, V., Novoselov, K.S., Roche, S., Bøggild, P., Borini, S., Koppens, F.H., Palermo, V., Pugno, N.: Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale 7(11), 4598–4810 (2015). https://doi.org/10.1039/C4NR01600A

    Article Google Scholar

  6. Avouris, P., Freitag, M.: Graphene photonics, plasmonics, and optoelectronics. IEEE J. Selected Top. Quant. Electron. 20(1), 72–83 (2013). https://doi.org/10.1109/JSTQE.2013.2272315

    Article Google Scholar

  7. Meng, Y., Ye, S., Shen, Y., Xiao, Q., Fu, X., Lu, R., Liu, Y., Gong, M.: Waveguide engineering of graphene optoelectronics-modulators and polarizers. IEEE Photon. J. 10(1), 1–17 (2018). https://doi.org/10.1109/JPHOT.2018.2789894

    Article Google Scholar

  8. Crassee, I., Levallois, J., Walter, A.L., Ostler, M., Bostwick, A., Rotenberg, E., Seyller, T., Van Der Marel, D., Kuzmenko, A.B.: Giant faraday rotation in single-and multilayer graphene. Nat. Phys. 7(1), 48 (2011). https://doi.org/10.1038/nphys1816

    Article Google Scholar

  9. Sounas, D., Skulason, H., Nguyen, H., Guermoune, A., Siaj, M., Szkopek, T., Caloz, C.: Faraday rotation in magnetically biased graphene at microwave frequencies. Appl. Phys. Lett. 102(19), 191901 (2013). https://doi.org/10.1063/1.4804437

    Article Google Scholar

  10. Dmitriev, V., Castro, W., Melo, G., Oliveira, C.: Graphene thz filter-switch dividers based on dipole-quadrupole and magneto-optical resonance effects. J. Optical Soc. America A 38(9), 1366–1371 (2021). https://doi.org/10.1364/JOSAA.431396

    Article Google Scholar

  11. Lin, X., Xu, Y., Zhang, B., Hao, R., Chen, H., Li, E.: Unidirectional surface plasmons in nonreciprocal graphene. New J. Phys. 15(11), 113003 (2013). https://doi.org/10.1088/1367-2630/15/11/113003

    Article Google Scholar

  12. Doust, S.K., Siahpoush, V., Asgari, A.: The tunability of surface plasmon polaritons in graphene waveguide structures. Plasmonics 12(5), 1633–1639 (2017). https://doi.org/10.1007/s11468-016-0428-6

    Article Google Scholar

  13. Xiao, S., Zhu, X., Li, B.-H., Mortensen, N.A.: Graphene-plasmon polaritons: From fundamental properties to potential applications. Front. Phys. 11(2), 117801 (2016). https://doi.org/10.1007/s11467-016-0551-z

    Article Google Scholar

  14. Liu, Y.-Q., Liu, P.-K.: Excitation of surface plasmon polaritons by electron beam with graphene ribbon arrays. J. ppl. Phys. 121(11), 113104 (2017). https://doi.org/10.1063/1.4978383

    Article Google Scholar

  15. Sheng, S., Li, K., Kong, F., Zhuang, H.: Analysis of a tunable band-pass plasmonic filter based on graphene nanodisk resonator. Optics Commun. 336, 189–196 (2015). https://doi.org/10.1016/j.optcom.2014.10.009

    Article Google Scholar

  16. Fallahi, A., Perruisseau-Carrier, J.: Manipulation of giant Faraday rotation in graphene metasurfaces. Appl. Phys. Lett. 101(23), 231605 (2012). https://doi.org/10.1063/1.4769095

    Article Google Scholar

  17. Tamagnone, M., Moldovan, C., Poumirol, J.-M., Kuzmenko, A.B., Ionescu, A.M., Mosig, J.R., Perruisseau-Carrier, J.: Near optimal graphene terahertz non-reciprocal isolator. Nat. Commun. 7(1), 11216 (2016). https://doi.org/10.1038/ncomms11216

    Article Google Scholar

  18. Xu, H., Xu, H., Yang, X., Li, M., Yu, H., Cheng, Y., Zhan, S., Chen, Z.: Polarization-sensitive asynchronous switch and notable slow-light based on tunable triple plasmon-induced transparency effect. Phys. Lett. A 504, 129401 (2024). https://doi.org/10.1016/j.physleta.2024.129401

    Article Google Scholar

  19. Li, M., Xu, H., Xu, H., Yang, X., Yu, H., Cheng, Y., Chen, Z.: Multi-frequency modulator of dual plasma-induced transparency in graphene-based metasurface. Optics Commun. 554, 130175 (2024). https://doi.org/10.1016/j.optcom.2023.130175

    Article Google Scholar

  20. Xu, H., Li, M., Yang, X., Xu, H., Chen, Z.: Dynamically tunable terahertz slow light device based on triple plasmonic induced transparency. SCIENTIA SINICA Physica, Mechanica & Astronomica 54(3), 234211 (2024). https://doi.org/10.1360/sspma-2023-0214

    Article Google Scholar

  21. Tavana, S., Bahadori-Haghighi, S., Ye, W.N.: Tunable and ultra-narrowband multifunctional terahertz devices using anisotropic graphene based hyperbolic metamaterials. Sci. Rep. 14(1), 31303 (2024). https://doi.org/10.1038/s41598-024-82763-3

    Article Google Scholar

  22. Nikkhah, V., Bakhtafrouz, A., Maddahali, M., Dezaki, S.K.: Three-port graphene-based electromagnetic circulator in the terahertz and infrared frequency ranges with a very low loss and wideband response. J. Opt. Soc. Am. B 35(8), 1754–1763 (2018). https://doi.org/10.1364/JOSAB.35.001754

    Article Google Scholar

  23. Hlali, A., Zairi, H.: Terahertz microstrip circulator based on graphene. J. Electromagn. Waves Appl. 34(17), 2339–2348 (2020). https://doi.org/10.1080/09205071.2020.1813639

    Article Google Scholar

  24. Dmitriev, V., Silva, S.L.M., Castro, W.: Ultrawideband graphene three-port circulator for thz region. Opt. Express 27(11), 15982–15995 (2019). https://doi.org/10.1364/OE.27.015982

    Article Google Scholar

  25. Dolatabady, A., Granpayeh, N.: Graphene based far-infrared junction circulator. IEEE Trans. Nanotechnol. 18, 200–207 (2019). https://doi.org/10.1109/TNANO.2018.2889522

    Article Google Scholar

  26. Dmitriev, V., Castro, W., Melo, G., Oliveira, C.: Controllable graphene w-shaped three-port thz circulator. Photon. Nanostruct.- Fundamentals Appl. 40, 100795 (2020). https://doi.org/10.1016/j.photonics.2020.100795

    Article Google Scholar

  27. Deng, L., Wu, Y., Zhang, C., Hong, W., Peng, B., Zhu, J., Li, S.: Manipulating of different-polarized reflected waves with graphene-based plasmonic metasurfaces in terahertz regime. Sci. Rep. 7(1), 10558 (2017). https://doi.org/10.1038/s41598-017-10726-y

    Article Google Scholar

  28. Ye, L., Sui, K., Liu, Y., Zhang, M., Liu, Q.H.: Graphene-based hybrid plasmonic waveguide for highly efficient broadband mid-infrared propagation and modulation. Optics Express 26(12), 15935–15947 (2018). https://doi.org/10.1364/OE.26.015935

    Article Google Scholar

  29. Gómez-Díaz, J., Esquius-Morote, M., Perruisseau-Carrier, J.: Plane wave excitation-detection of non-resonant plasmons along finite-width graphene strips. Optics Express 21(21), 24856–24872 (2013). https://doi.org/10.1364/OE.21.024856

    Article Google Scholar

  30. Helszajn, J.: The Stripline Circulator: Theory and Practice. John Wiley & Sons, Hoboken, NJ, USA (2008)

    Google Scholar

  31. Marzall, L., Psychogiou, D., Popović, Z.: Microstrip ferrite circulator design with control of magnetization distribution. IEEE Trans. Microw. Theory Techn. 69(2), 1217–1226 (2021). https://doi.org/10.1109/TMTT.2020.3045995

    Article Google Scholar

  32. Dmitriev, V., Martins, L., Portela, G., Assuncao, L.: Quadrupole resonator mode versus dipole one in photonic crystal ferrite circulators. Photon. Nanostruct.- Fundament. Appl. 46, 100954 (2021). https://doi.org/10.1016/j.photonics.2021.100954

    Article Google Scholar

  33. Davis, P.J.: Circulant Matrices, vol. 120. Wiley, New York, NY, USA (1979)

    Google Scholar

  34. Dmitriev, V., Castro, W.: Dynamically controllable terahertz graphene y-circulator. IEEE Trans. Magn. 55(2), 1–12 (2019). https://doi.org/10.1109/TMAG.2018.2883850

    Article Google Scholar

  35. Hanson, G.W.: Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene. J. Appl. Phys. 103(6), 064302 (2008). https://doi.org/10.1063/1.2891452

    Article Google Scholar

  36. Lin, H., Pantoja, M.F., Angulo, L.D., Alvarez, J., Martin, R.G., Garcia, S.G.: Fdtd modeling of graphene devices using complex conjugate dispersion material model. IEEE Microw. Wireless Comp. Lett. 22(12), 612–614 (2012). https://doi.org/10.1109/LMWC.2012.2227466

    Article Google Scholar

  37. Vakil, A., Engheta, N.: Transformation optics using graphene. Science 332(6035), 1291–1294 (2011). https://doi.org/10.1126/science.1202691

    Article Google Scholar

  38. Wang, B., Zhang, X., Yuan, X., Teng, J.: Optical coupling of surface plasmons between graphene sheets. Appl. Phys. Lett. 10(1063/1), 3698133 (2012)

    Google Scholar

  39. Gusynin, V., Sharapov, S., Carbotte, J.: Magneto-optical conductivity in graphene. J. Phys. Condensed Matter 19(2), 026222 (2006). https://doi.org/10.1088/0953-8984/19/2/026222

    Article Google Scholar

  40. Lovat, G., Hanson, G.W., Araneo, R., Burghignoli, P.: Semiclassical spatially dispersive intraband conductivity tensor and quantum capacitance of graphene. Phys. Rev. B-Condensed Matter Mater. Phys. 87(11), 115429 (2013). https://doi.org/10.1103/PhysRevB.87.115429

    Article Google Scholar

  41. Heydari, M.B., Samiei, M.H.V.: Three-port terahertz circulator with multi-layer triangular graphene-based post. Optik 231, 166457 (2021). https://doi.org/10.1016/j.ijleo.2021.166457

    Article Google Scholar

  42. Horng, J., Chen, C.-F., Geng, B., Girit, C., Zhang, Y., Hao, Z., Bechtel, H.A., Martin, M., Zettl, A., Crommie, M.F.: Drude conductivity of dirac fermions in graphene. Phys. Rev. B-Condensed Matter Mater. Phys. 83(16), 165113 (2011). https://doi.org/10.1103/PhysRevB.83.165113

    Article Google Scholar

  43. Bludov, Y.V., Ferreira, A., Peres, N.M., Vasilevskiy, M.I.: A primer on surface plasmon-polaritons in graphene. Int. J. Modern Phys. 27(10), 1341001 (2013). https://doi.org/10.1142/S0217979213410014

    Article MathSciNet Google Scholar

  44. Kazemi, A.H., Mokhtari, A., Zamani, M.: Graphene-based magneto-optical thz modulator with 100% depth of modulation for communication purposes. Optical Mater. 123, 111944 (2022). https://doi.org/10.1016/j.optmat.2021.111944

    Article Google Scholar

  45. Sounas, D.L., Caloz, C.: Gyrotropy and nonreciprocity of graphene for microwave applications. IEEE Trans. Microw. Theory Techn. 60(4), 901–914 (2012). https://doi.org/10.1109/TMTT.2011.2182205

    Article Google Scholar

  46. Principi, A., Vignale, G., Carrega, M., Polini, M.: Intrinsic lifetime of dirac plasmons in graphene. Phys. Rev. B-Condensed Matter Mater. Phys. 88(19), 195405 (2013). https://doi.org/10.1103/PhysRevB.88.195405

    Article Google Scholar

  47. Multiphysics, C.: Comsol multiphysics®, v. 5.5. Comsol AB, Stockholm, Sweden (2020)

  48. Gonçalves, P.A.D., Peres, N.M.R.: An Introduction to Graphene Plasmonics. World Scientific Publishing, Singapore, Singapore (2016). https://doi.org/10.1142/9948

  49. Wang, J., Lu, W.B., Li, X.B., Ni, Z.H., Qiu, T.: Graphene plasmon guided along a nanoribbon coupled with a nanoring. J. Phys. D: Appl. Phys. 47(13), 135106 (2014). https://doi.org/10.1088/0022-3727/47/13/135106

    Article Google Scholar

  50. Joannopoulos, J.D., Johnson, S.G., Winn, J.N., Meade, R.D.: Molding the flow of light. Princet. Univ. Press. Princeton, NJ [ua] 12 (2008)

  51. Wang, Z., Fan, S.: Magneto-optical defects in two-dimensional photonic crystals. Appl. Phys. B 81, 369–375 (2005). https://doi.org/10.1007/s00340-005-1846-x

    Article Google Scholar

  52. Yang, Y., Jiang, X., Xu, Z., Zhang, Y., Qiu, C., Guo, X., Su, Y.: Silicon-graphene hybrid slot waveguide with enhanced four-wave mixing efficiency. In: 2018 Optical Fiber Communications Conference and Exposition (OFC), pp. 1–3 (2018). https://doi.org/10.1364/OFC.2018.Tu2J.5 . IEEE

  53. Liu, M., Yin, X., Ulin-Avila, E., Geng, B., Zentgraf, T., Ju, L., Wang, F., Zhang, X.: A graphene-based broadband optical modulator. Nature 474(7349), 64–67 (2011). https://doi.org/10.1038/nature10067

    Article Google Scholar

  54. Liu, M., Yin, X., Zhang, X.: Double-layer graphene optical modulator. Nano Lett. 12(3), 1482–1485 (2012). https://doi.org/10.1021/nl204202k

    Article Google Scholar

  55. Zhao, Y., Berenschot, E., Jansen, H., Tas, N., Huskens, J., Elwenspoek, M.: Sub-10 nm silicon ridge nanofabrication by advanced edge lithography for nil applications. Microelectron. Eng. 86(4–6), 832–835 (2009). https://doi.org/10.1016/j.mee.2008.11.067

    Article Google Scholar

  56. Lee, Y., Bae, S., Jang, H., Jang, S., Zhu, S.-E., Sim, S.H., Song, Y.I., Hong, B.H., Ahn, J.-H.: Wafer-scale synthesis and transfer of graphene films. Nano Lett. 10(2), 490–493 (2010). https://doi.org/10.1021/nl903272n

    Article Google Scholar

  57. Zhuo, Q.-Q., Wang, Q., Zhang, Y.-P., Zhang, D., Li, Q.-L., Gao, C.-H., Sun, Y.-Q., Ding, L., Sun, Q.-J., Wang, S.-D.: Transfer-free synthesis of doped and patterned graphene films. ACS Nano 9(1), 594–601 (2015). https://doi.org/10.1021/nn505913v

    Article Google Scholar

  58. Zhang, Q., Li, X., Hossain, M.M., Xue, Y., Zhang, J., Song, J., Liu, J., Turner, M.D., Fan, S., Bao, Q.: Graphene surface plasmons at the near-infrared optical regime. Sci. Rep. 4(1), 6559 (2014). https://doi.org/10.1038/srep06559

    Article Google Scholar

  59. Xu, W., Zhu, Z., Liu, K., Zhang, J., Yuan, X., Lu, Q., Qin, S.: Toward integrated electrically controllable directional coupling based on dielectric loaded graphene plasmonic waveguide. Optics Lett. 40(7), 1603–1606 (2015). https://doi.org/10.1364/OL.40.001603

    Article Google Scholar

Download references

Funding

This work was supported by the Brazilian agencies National Council for Scientific and Technological Development (CNPq) and Coordination for the Improvement of Higher Education Personnel (CAPES).

Author information

Author notes

  1. Victor Dmitriev and Thiago Oliveira have contributed equally to this work.

Authors and Affiliations

  1. Electrical and Biomedical Engineering Department, Federal University of Pará, Av. Augusto Correa, 01, Belém, Pará, 66075-110, Brazil

    Victor Dmitriev & Thiago Oliveira

Contributions

V.D., and T.O. did conceptualization, writing—review and editing, formal analysis and investigation and gave methodology; T.O. done software and data curation and writing—original draft preparation; V.D. supervised and validated the study; all authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Thiago Oliveira.

Ethics declarations

Conflict of interest

The authors declare that they have no Conflict of interest.

Ethics approval and consent to participate

No human or animal participation in this work.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Cite this article

Dmitriev, V., Oliveira, T. THz graphene circulator with quadrupole mode resonator. J Comput Electron 24, 139 (2025). https://doi.org/10.1007/s10825-025-02379-2

Download citation

  • Received 
  • Accepted 
  • Published 
  • DOI  https://doi.org/10.1007/s10825-025-02379-2

Keywords

  • Circulator
  • Terahertz
  • Graphene
  • Surface plasmon polaritons
  • Quadrupole mode

Copyright © All rights reserved Designed and Developed by Digital Flavers

WhatsApp