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An Analytical Study of Magneto-Plasmons in Anisotropic Multi-layer Structures Containing Magnetically Biased Graphene Sheets

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Abstract

This article proposes a novel analytical model for the anisotropic multi-layer structures containing magnetically biased graphene sheets. The multi-layer structure is composed of various magnetic materials, each one has the permittivity and permeability tensors of \( \overline{\overline{\upvarepsilon}} \) and \( \overline{\overline{\mu}} \), respectively. An external magnetic field is applied, normal to the structure surface. Each graphene sheet, with anisotropic conductivity tensor (\( \overline{\overline{\sigma}} \)), has been sandwiched between two adjacent magnetic materials. Our model is used to find the dispersion relation of the structure. Now, obtaining plasmonic features of the structure, such as the effective index and propagation loss is straightforward. Four exemplary structural variants have been investigated to show the richness of the proposed general structure regarding the related specific plasmonic wave phenomena and effects. These aspects are essential to form our structural design platform to propose novel plasmonic devices such as biosensors, modulators, absorbers, transparent electrodes, and tunable metamaterials in THz frequencies. A very good agreement between the analytical and full-wave simulation results is seen.

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References

  1. Shinohara H, Tiwari A (2015) Graphene: an introduction to the fundamentals and industrial applications. John Wiley & Sons

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

    CAS  Google Scholar 

  3. Hanson GW (2008) Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene. J Appl Phys 103(6):064302

    Google Scholar 

  4. Hanson GW (2008) Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide. J Appl Phys 104(8):084314

    Google Scholar 

  5. Hanson GW (2008) Dyadic Green’s functions for an anisotropic, non-local model of biased graphene. IEEE Trans Antennas Propag 56(3):747–757

    Google Scholar 

  6. Heydari MB, Samiei MHV (2018) Plasmonic graphene waveguides: a literature review. arXiv preprint arXiv:180909937

  7. Fuscaldo W, Burghignoli P, Baccarelli P, Galli A (2015) Complex mode spectra of graphene-based planar structures for THz applications. J Infrared Milli Terahz Waves 36(8):720–733

    CAS  Google Scholar 

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

  9. Ahn KJ (2015) Graphene plasmon modes on slab waveguides at telecom wavelengths. J Korean Phys Soc 67(12):2096–2100

    CAS  Google Scholar 

  10. Correas-Serrano D, Gomez-Diaz JS, Perruisseau-Carrier J, Álvarez-Melcón A (2013) Spatially dispersive graphene single and parallel plate waveguides: analysis and circuit model. IEEE Trans Microwave Theory Tech 61(12):4333–4344

    Google Scholar 

  11. Zhu J, Xu Z, Xu W, Fu D, Wei D (2018) Surface plasmon polariton waveguide by bottom and top of graphene. Plasmonics 13(5):1513–1522

    CAS  Google Scholar 

  12. Doust SK, Siahpoush V, Asgari A (2017) The tunability of surface plasmon polaritons in graphene waveguide structures. Plasmonics 12(5):1633–1639

    Google Scholar 

  13. Joshi N, Pathak NP (2017) Modeling of graphene coplanar waveguide and its discontinuities for THz integrated circuits applications. Plasmonics 12(5):1545–1554

    CAS  Google Scholar 

  14. Zheng P, Yang H, Fan M, Hu G, Zhang R, Yun B, Cui Y (2018) A hybrid plasmonic modulator based on graphene on channel plasmonic polariton waveguide. Plasmonics 13(6):2029–2035

    CAS  Google Scholar 

  15. Koufogiannis ID, Mattes M, Mosig JR (2015) On the development and evaluation of spatial-domain Green’s functions for multilayered structures with conductive sheets. IEEE Trans Microwave Theory Tech 63(1):20–29

    Google Scholar 

  16. Smirnova D, Iorsh I, Shadrivov I, Kivshar YS (2014) Multilayer graphene waveguides. JETP Lett 99(8):456–460

    CAS  Google Scholar 

  17. Qin C, Wang B, Lu P (2015) Surface plasmon supermodes in graphene multilayers. In: 2015 11th Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR). IEEE, pp 1–2

  18. Kuzmin DA, Bychkov IV, Shavrov VG (2014) Electromagnetic waves reflectance of graphene—magnetic semiconductor superlattice in magnetic field. IEEE Trans Magn 50(11):1–4

    Google Scholar 

  19. Kuzmin D, Bychkov I, Shavrov V (2015) Electromagnetic waves absorption by graphene magnetic semiconductor multilayered nanostructure in external magnetic field: Voight geometry. Acta Phys Polon A 127:528

    Google Scholar 

  20. Ardakani AG, Ghasemi Z, Golshan MM (2017) A new transfer matrix for investigation of surface plasmon modes in multilayer structures containing anisotropic graphene layers. Eur Phys J Plus 132(5):206

    Google Scholar 

  21. Madani A, Zhong S, Tajalli H, Roshan Entezar S, Namdar A, Ma Y (2013) Tunable metamaterials made of graphene-liquid crystal multilayers. Prog Electromagn Res 143:545–558

    Google Scholar 

  22. Iorsh IV, Mukhin IS, Shadrivov IV, Belov PA, Kivshar YS (2013) Hyperbolic metamaterials based on multilayer graphene structures. Phys Rev B 87(7):075416

    Google Scholar 

  23. Othman MA, Guclu C, Capolino F (2013) Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption. Opt Express 21(6):7614–7632

    CAS  PubMed  Google Scholar 

  24. Zhu W, Xiao F, Kang M, Sikdar D, Premaratne M (2014) Tunable terahertz left-handed metamaterial based on multi-layer graphene-dielectric composite. Appl Phys Lett 104(5):051902

    Google Scholar 

  25. Batrakov K, Kuzhir P, Maksimenko S, Paddubskaya A, Voronovich S, Lambin P, Kaplas T, Svirko Y (2014) Flexible transparent graphene/polymer multilayers for efficient electromagnetic field absorption. Sci Rep 4:7191

    CAS  PubMed  PubMed Central  Google Scholar 

  26. Nefedov IS, Valagiannopoulos CA, Melnikov LA (2013) Perfect absorption in graphene multilayers. J Opt 15(11):114003

    Google Scholar 

  27. Maharana PK, Jha R, Palei S (2014) Sensitivity enhancement by air mediated graphene multilayer based surface plasmon resonance biosensor for near infrared. Sensors Actuators B Chem 190:494–501

    CAS  Google Scholar 

  28. Khromova I, Andryieuski A, Lavrinenko A (2014) Ultrasensitive terahertz/infrared waveguide modulators based on multilayer graphene metamaterials. Laser Photonics Rev 8(6):916–923

    CAS  Google Scholar 

  29. Patel K, Tyagi PK (2017) P-type multilayer graphene as a highly efficient transparent conducting electrode in silicon heterojunction solar cells. Carbon 116:744–752

    CAS  Google Scholar 

  30. Jo G, Choe M, Cho C-Y, Kim JH, Park W, Lee S, Hong W-K, Kim T-W, Park S-J, Hong BH (2010) Large-scale patterned multi-layer graphene films as transparent conducting electrodes for GaN light-emitting diodes. Nanotechnology 21(17):175201

    PubMed  Google Scholar 

  31. Ardakani AG (2014) Strong enhancement of Faraday rotation using one-dimensional conjugated photonic crystals containing graphene layers. Appl Opt 53(36):8374–8380

    PubMed  Google Scholar 

  32. Ghasempour Ardakani A, Firoozi FB (2017) Highly tunable bistability using an external magnetic field in photonic crystals containing graphene and magnetooptical layers. J Appl Phys 121(2):023105

    Google Scholar 

  33. An YQ, Nelson F, Lee JU, Diebold AC (2013) Enhanced optical second-harmonic generation from the current-biased graphene/SiO2/Si (001) structure. Nano Lett 13(5):2104–2109

    CAS  PubMed  Google Scholar 

  34. Gurevich A, Jakovlev JM, Karpovich V, Ageev A, Rubalskaja E (1972) Ferromagnetic resonance anisotropy in CdCr2Se4. Phys Lett A 40(1):69–70

    CAS  Google Scholar 

  35. Lehmann H, Harbeke G (1967) Semiconducting and optical properties of ferromagnetic CdCr2S4 and CdCr2Se4. J Appl Phys 38(3):946–946

    Google Scholar 

  36. Medvedkin GA, Ishibashi T, Nishi T, Hayata K, Hasegawa Y, Sato K (2000) Room temperature ferromagnetism in novel diluted magnetic semiconductor Cd1-xMnxGeP2. Jpn J Appl Phys 39(10A):L949

    CAS  Google Scholar 

  37. Matsumoto Y, Murakami M, Shono T, Hasegawa T, Fukumura T, Kawasaki M, Ahmet P, Chikyow T, S-y K, Koinuma H (2001) Room-temperature ferromagnetism in transparent transition metal-doped titanium dioxide. Science 291(5505):854–856

    CAS  PubMed  Google Scholar 

  38. Sharma P, Gupta A, Rao K, Owens FJ, Sharma R, Ahuja R, Guillen JO, Johansson B, Gehring G (2003) Ferromagnetism above room temperature in bulk and transparent thin films of Mn-doped ZnO. Nat Mater 2(10):673–677

    CAS  PubMed  Google Scholar 

  39. Fan F, Guo Z, Bai J-J, Wang X-H, Chang S-J (2011) Magnetic photonic crystals for terahertz tunable filter and multifunctional polarization controller. JOSA B 28(4):697–702

    CAS  Google Scholar 

  40. Umamaheswari C, Raja AS (2017) Exploration of photonic crystal circulator based on gyromagnetic properties and scaling of ferrite materials. Opt Commun 382:186–195

    CAS  Google Scholar 

  41. Komandin G, Torgashev V, Volkov A, Porodinkov O, Spektor I, Bush A (2010) Optical properties of BiFeO 3 ceramics in the frequency range 0.3–30.0 THz. Phys Solid State 52(4):734–743

    CAS  Google Scholar 

  42. Qing-Hui Y, Huai-Wu Z, Ying-Li L, Qi-Ye W, Jie Z (2008) An artificially garnet crystal materials using in terahertz waveguide. Chin Phys Lett 25(11):3957

    Google Scholar 

  43. Nakajima M, Namai A, Ohkoshi S, Suemoto T (2010) Ultrafast time domain demonstration of bulk magnetization precession at zero magnetic field ferromagnetic resonance induced by terahertz magnetic field. Opt Express 18(17):18260–18268

    CAS  PubMed  Google Scholar 

  44. Langner M, Kantner C, Chu Y, Martin L, Yu P, Seidel J, Ramesh R, Orenstein J (2009) Observation of ferromagnetic resonance in SrRuO 3 by the time-resolved magneto-optical Kerr effect. Phys Rev Lett 102(17):177601

    CAS  PubMed  Google Scholar 

  45. Van Slageren J, Vongtragool S, Mukhin A, Gorshunov B, Dressel M (2005) Terahertz Faraday effect in single molecule magnets. Phys Rev B 72(2):020401

    Google Scholar 

  46. Gurevich AG, Melkov GA (1996) Magnetization oscillations and waves. CRC press

  47. Bass FG, Bulgakov AA (1997) Kinetic and electrodynamic phenomena in classical and quantum semiconductor superlattices. Nova Publishers

  48. Mathur P, Kataria N, Jain S, Sharma V (1975) Electron mobility in n-InSb from 77 to 300K. J Phys C Solid State Phys 9(4):L89

    Google Scholar 

  49. Alfaramawi K, Alzamil M (2009) Temperature-dependent scattering processes of n-type indium antimonide. Optoelectron Adv Mater 3:569–573

    CAS  Google Scholar 

  50. Cunningham R, Gruber J (1970) Intrinsic concentration and heavy-hole mass in InSb. J Appl Phys 41(4):1804–1809

    CAS  Google Scholar 

  51. Oszwałldowski M, Zimpel M (1988) Temperature dependence of intrinsic carrier concentration and density of states effective mass of heavy holes in InSb. J Phys Chem Solids 49(10):1179–1185

    Google Scholar 

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

    Google Scholar 

  53. Berini P (2006) Figures of merit for surface plasmon waveguides. Opt Express 14(26):13030–13042

    PubMed  Google Scholar 

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  1. School of Electrical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran

    Mohammad Bagher Heydari & Mohammad Hashem Vadjed Samiei

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  1. Mohammad Bagher Heydari
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  2. Mohammad Hashem Vadjed Samiei
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Correspondence to Mohammad Hashem Vadjed Samiei.

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Heydari, M.B., Vadjed Samiei, M.H. An Analytical Study of Magneto-Plasmons in Anisotropic Multi-layer Structures Containing Magnetically Biased Graphene Sheets. Plasmonics 15, 1183–1198 (2020). https://doi.org/10.1007/s11468-020-01136-4

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