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Finite-element Method Analysis of Sodium Based Elliptical Hybrid Plasmonic Waveguides with Ultra-low Loss

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Abstract

Surface plasmons possess the capability to overcome the diffraction limit, making them highly promising for a wide range of applications in the field of nanophotonics. Here we design a sodium-based hybrid plasmonic waveguide consisting of an elliptical Si nanowire separated from the Na film by a low-index SiO2 layer. The modal properties of the proposed waveguide are thoroughly investigated by using the finite element method with a focus on parameters such as effective mode index, propagation length, normalized mode area, and figure of merit. The results show that the hybrid modes exhibit ultra-low loss with propagation length in the millimeter range as well as high figure of merit over 103. Besides, the hybrid plasmonic waveguide with a vertical elliptical nanowire provides a stronger energy constrain ability compared with that with a horizontal elliptical nanowire. The proposed waveguide may contribute to the development of nanoscale devices in photonic integration circuits, such as lasers, sensors, and modulators.

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Data Availability

The numerical analysis is done with Comsol Multiphysics and also data will be available on reasonable request.

References

  1. Ozbay E (2006) Plasmonics: merging photonics and electronics at nanoscale dimensions. Science 311(5758):189–193

    Article  CAS  PubMed  Google Scholar 

  2. Wang Y, Zhao B, Min C, Zhang Y, Yang J, Guo C, Yuan X (2020) Research progress of femtosecond surface plasmon polariton. Chin Phys B 29(2):027302

    Article  CAS  Google Scholar 

  3. Han Z, Bozhevolnyi SI (2012) Radiation guiding with surface plasmon polaritons. Rep Prog Phys 76(1):016402

    Article  PubMed  Google Scholar 

  4. Xia Y, Halas NJ (2005) Shape-controlled synthesis and surface plasmonic properties of metallic nanostructures. MRS Bull 30(05):338–348

    Article  CAS  Google Scholar 

  5. Yang W, Chou Chau YF, Jheng SC (2013) Analysis of transmittance properties of surface plasmon modes on periodic solid/outline bowtie nanoantenna arrays. Phys Plasmas 20(6):064503

    Article  Google Scholar 

  6. Chou Chau YF, Yeh HH, Tsai DP (2010) A new type of optical antenna: plasmonics nanoshell bowtie antenna with dielectric hole. J Electromagn Waves Appl 24(11–12):1621–1632

    Article  Google Scholar 

  7. Chou Chau TC, Chou Chau YF, Mahadi AH, Jumat SZBH, Kooh MRR, Kumara NTRN, Chiang HP (2021) Plasmonic refractive index sensor based on the combination of rectangular and circular resonators including baffles. Chin J Phys 71:286–299

    Article  Google Scholar 

  8. Kim Y, Park BJ, Kim M, Jin YH, Park NR, Kim MK (2020) Light engineering in nanometer space. Adv Mater 32(51):2003051

    Article  CAS  Google Scholar 

  9. Kim S, Yan R (2018) Recent developments in photonic, plasmonic and hybrid nanowire waveguides. J Mater Chem C 6(44):11795–11816

    Article  CAS  Google Scholar 

  10. Fang Y, Sun M (2015) Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits. Light: Science & Applications 4(6):e294

  11. Chou Chau CT, Chou Chau YF, Chiang HP (2021) Highly sensitive metal-insulator-metal plasmonic refractive index sensor with a centrally coupled nanoring containing defects. J Phys D 54(11):115301

    Article  Google Scholar 

  12. Chou Chau YF, Ming TY, Chou Chao CT, Thotagamuge R, Kooh MRR, Huang HJ, Lim CM, Chiang HP (2021) Significantly enhanced coupling effect and gap plasmon resonance in a MIM-cavity based sensing structure. Sci Rep 11(1):18515

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Calafell IA, Rozema LA, Iranzo DA, Trenti A, Jenke PK, Cox JD, Kumar A, Bieliaiev H, Nanot S, Peng C, Efetov DK, Hong JY, Kong J, Englund DR, Abajo F, Koppens FHL, Walther P (2021) Giant enhancement of third-harmonic generation in graphene–metal heterostructures. Nat Nanotechnol 16(3):318–324

    Article  Google Scholar 

  14. Huang TJ, Yin LZ, Zhao J, Du CH, Liu PK (2020) Amplifying evanescent waves by dispersion-induced plasmons: defying the materials limitation of the superlens. ACS Photonics 7(8):2173–2181

    Article  CAS  Google Scholar 

  15. Oulton RF, Sorger VJ, Genov DA, Pile DFP, Zhang X (2008) A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation. Nat Photonics 2(8):496–500

    Article  CAS  Google Scholar 

  16. Alam MZ, Meier J, Aitchison JS, Mojahedi M (2007) Super mode propagation in low index medium. Quantum Electronics and Laser Science Conference JThD112

  17. Xu J, Shi N, Chen Y, Lu X, Wei H, Lu Y, Liu N, Zhang B, Wang J (2018) TM01 mode in a cylindrical hybrid plasmonic waveguide with large propagation length. Appl Opt 57(15):4043–4047

    Article  CAS  PubMed  Google Scholar 

  18. Zhang M, Wu G, Chen D, Liu B (2019) Mode and sensing properties of a silicon-based hybrid plasmonic microring resonator. J Opt 48:308–313

    Article  Google Scholar 

  19. Bian Y, Ren Q, Kang L, Yue T, Werner PL, Werner DH (2018) Deep-subwavelength light transmission in hybrid nanowire-loaded silicon nano-rib waveguides. Photonics Res 6(1):37–45

    Article  CAS  Google Scholar 

  20. Teng D, Guo J, Yang Y, Ma W, Wang K (2020) Study of modal properties in graphene-coated nanowires integrated with substrates. Appl Phys B 126:173

    Article  CAS  Google Scholar 

  21. Zhang L, Xiong Q, Li X, Ma J (2015) Elliptic cylindrical silicon nanowire hybrid surface plasmon polariton waveguide. Appl Opt 54(23):7037–7044

    Article  CAS  PubMed  Google Scholar 

  22. Zhang B, Bian Y, Ren L, Guo F, Tang SY, Mao Z, Liu X, Sun J, Gong J, Guo X, Huang TJ (2017) Hybrid dielectric-loaded nanoridge plasmonic waveguide for low-loss light transmission at the subwavelength scale. Sci Rep 71(7):40479

    Article  Google Scholar 

  23. Kumar S, Kumar P, Ranjan R (2022) A metal-cap wedge shape hybrid plasmonic waveguide for nano-scale light confinement and long propagation range. Plasmonics 17(1):95–105

    Article  CAS  Google Scholar 

  24. Jafari MR, Asadi A, Shahmansouri M (2023) Ultra-deep subwavelength confinement palladium-based elliptical cylinder plasmonic waveguide in the near-infrared range. Plasmonics 18:1037–1045

    Article  CAS  Google Scholar 

  25. Teng D, Cao Q, Wang K (2017) An extension of the generalized nonlocal theory for the mode analysis of plasmonic waveguides at telecommunication frequency. J Opt 19(5):055003

    Article  Google Scholar 

  26. Huang CC, Chang RJ, Huang CC (2021) Nanostructured hybrid plasmonic waveguide in a slot structure for high-performance light transmission. Opt Express 29(18):29341–29356

    Article  CAS  PubMed  Google Scholar 

  27. Teng D, Wang K, Li Z, Zhao Y (2019) Graphene-coated nanowire dimers for deep subwavelength waveguiding in mid-infrared range. Opt Express 27(9):12458–12469

    Article  CAS  PubMed  Google Scholar 

  28. Teng D, Wang K, Huan Q, Chen W, Li Z (2020) High-performance light transmission based on graphene plasmonic waveguides. J Mater Chem C 8(20):6832–6838

    Article  CAS  Google Scholar 

  29. Teng D, Yang Y, Guo J, Ma W, Tang Y, Wang K (2020) Efficient guiding mid-infrared waves with graphene-coated nanowire based Plasmon waveguides. Results in Physics 17:103169

    Article  Google Scholar 

  30. Asadi A, Jafari MR, Shahmansouri M (2022) Characteristics of a symmetric mid-infrared graphene dielectric hybrid plasmonic waveguide with ultra-deep subwavelength confinement. Plasmonics 17(4):1819–1829

    Article  CAS  Google Scholar 

  31. Qin Y, Ma C, Huang L, Yuan Y, Sha M, Ye X, Zheng K (2023) Highly confined low-loss light transmission in linear array-enabled hybrid plasmonic waveguides. J Opt 25(6):065802

    Article  Google Scholar 

  32. Tu PY, Huang CC (2022) Analysis of hybrid plasmon-phonon-polariton modes in hBN/graphene/hBN stacks for mid-infrared waveguiding. Opt Express 30(2):2863–2876

    Article  CAS  PubMed  Google Scholar 

  33. Zhang J, Guan Z, Ma K, Teng D (2023) Perovskite nanowires-based graphene plasmonic waveguides with low loss and low gain threshold. Diam Relat Mater 140:110540

    Article  CAS  Google Scholar 

  34. Teng D, Wang K, Li Z (2020) Graphene-coated nanowire waveguides and their applications. Nanomaterials 10(2):229

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Saeed M, Ghaffar A, Rehman SU, Naz MY, Shukrullah S, Naqvi QA (2022) Graphene-based plasmonic waveguides: a mini review. Plasmonics 17(3):901–911

    Article  Google Scholar 

  36. Hassan HMI, Areed NFF, EL-Mikati HA, Hameed MFO, Obayya SSA (2023) Low loss hybrid plasmonic waveguide with graphene multilayers. Mansoura Eng J 48(5):4

    Article  Google Scholar 

  37. Hou B, Li Z, He L, Yi Z, Song Q, Yang H, Yi Y, Li H (2023) Enhanced quasi-BIC refractive index sensing based on controlling the Fermi energy of Dirac semimetal metasurface. Opt Laser Technol 164:109537

    Article  CAS  Google Scholar 

  38. He X, Liu F, Lin F, Shi W (2021) Tunable 3D Dirac-semimetals supported mid-IR hybrid plasmonic waveguides. Opt Lett 46(3):472–475

    Article  PubMed  Google Scholar 

  39. Zheng K, Song J, Qu J (2018) Hybrid low-permittivity slot-rib plasmonic waveguide based on monolayer two dimensional transition metal dichalcogenide with ultra-high energy confinement. Opt Express 26(12):15819–15824

    Article  CAS  PubMed  Google Scholar 

  40. Zheng K, Yuan Y, He J, Gu J, Zhang F, Chen Y, Song J, Qu J (2019) Ultra-high light confinement and ultra-long propagation distance design for integratable optical chips based on plasmonic technology. Nanoscale 11(10):4601–4613

    Article  CAS  PubMed  Google Scholar 

  41. Xu L, Li F, Wei L, Zhou J, Liu S (2018) Design of surface plasmon nanolaser based on MoS2. Appl Sci 8(11):2110

    Article  CAS  Google Scholar 

  42. Naik GV, Shalaev VM, Boltasseva A (2013) Alternative plasmonic materials: beyond gold and silver. Adv Mater 25(24):3264–3294

    Article  CAS  PubMed  Google Scholar 

  43. Wang Y, Yu J, Mao Y, Chen J, Wang S, Chen H, Zhang Y, Wang S, Chen X, Li T, Zhou L, Ma R, Zhu S, Cai W, Zhu J (2020) Stable, high-performance sodium-based plasmonic devices in the near infrared. Nature 581(7809):401–405

    Article  CAS  PubMed  Google Scholar 

  44. Teng D, Tian Y, Hu X, Guan Z, Gao W, Li P, Fang H, Yan J, Wang Z, Wang K (2022) Sodium-based cylindrical plasmonic waveguides in the near-infrared. Nanomaterials 12(12):1950

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Gao J, Hou C, Wang F, Liu H, Ma T (2021) A directional coupler based on graphene-enhanced Na-loaded plasmonic rib waveguide. Opt Commun 499:127316

    Article  CAS  Google Scholar 

  46. Ma T, Ma J, Liu H, Tian Y, Liu S, Wang F (2022) Electro-optic tunable directional coupler based on a LiNbO3/Na surface plasmonic waveguide. Acta Phys Sinica 71(5):054205

    Article  Google Scholar 

  47. Rawashdeh A, Lupa S, Welch W, Yang A (2021) Sodium surface lattice plasmons. J Phys Chem C 125(45):25148–25154

    Article  CAS  Google Scholar 

  48. Rawashdeh A, Wildenborg A, Liu E, Gao Z, Czaplewski DA, Qu H, Suh JY, Yang A (2023) High-quality surface plasmon polaritons in large-area sodium nanostructures. Nano Lett 23(2):469–475

    Article  CAS  PubMed  Google Scholar 

  49. Ye H, Chen C, Zhou J, Meng Z (2021) Sodium-based surface plasmon resonances for high-performance optical sensing in the near infrared. IEEE J Sel Top Quantum Electron 27(5):4601308

    Article  CAS  Google Scholar 

  50. Ye H, Huang X, Wen K, Xue J, Zhou J, Meng Z (2022) Near-infrared narrow plasmonic resonances for high-performance optical sensing in a sodium-based nanograting. Results in Physics 38:105566

    Article  Google Scholar 

  51. Akbar J, Bin X, Hou L, Marsh JH, Liu X (2022) Surface plasmon polaritons excitation at the interface of graphene and sodium media. Eur Phys J Plus 137(3):291

    Article  CAS  Google Scholar 

  52. Schinke C, Christian-Peest P, Schmidt J, Brendel R, Bothe K, Vogt MR, Kröger I, Winter S, Schirmacher A, Lim S, Nguyen HT, MacDonald D (2015) Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon. AIP Adv 5:067168

    Article  Google Scholar 

  53. Khurgin JB (2022) Expanding the photonic palette: exploring high index materials. ACS Photon 9(3):743–751

    Article  CAS  Google Scholar 

  54. Teng D, Wang Y, Xu T, Wang H, Shao Q, Tang Y (2021) Symmetric graphene dielectric nanowaveguides as ultra-compact photonic structures. Nanomaterials 11(5):1281

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Hajati M, Hajati Y (2016) High-performance and low-loss plasmon waveguiding in graphene-coated nanowire with substrate. J Opt Soc Am B 33(12):2560–2565

    Article  CAS  Google Scholar 

  56. Teng D, Wang K, Huan Q, Zhao Y, Tang Y (2019) High-performance transmission of surface plasmons in graphene-covered nanowire pairs with substrate. Nanomaterials 9(11):1594

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  57. Said A, Atia K, Obayya SSA (2020) On modeling of plasmonic devices: overview. J Opt Soc Am B 37(11):A163–A174

    Article  CAS  Google Scholar 

  58. Ono M, Hata M, Tsunekawa M, Nozaki K, Sumikura H, Chiba H, Notomi M (2020) Ultrafast and energy-efficient all-optical switching with graphene-loaded deep-subwavelength plasmonic waveguides. Nat Photonics 14(1):37–43

    Article  CAS  Google Scholar 

  59. Duan J, Álvarez-Pérez G, Tresguerres-Mata AIF, Taboada-Gutierrez J, Voronin KV, Bylinkin A, Chang B, Xiao S, Liu S, Edgar JH, Martin JI, Volkov VS, Hillenbrand R, Martin-Sanchez J, Nikitin AY, Alonso-Gonzalez R (2021) Planar refraction and lensing of highly confined polaritons in anisotropic media. Nat Commun 12(1):4325

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Qin T, Ma W, Wang T (2023) Phonon polaritons in Van Der Waals polar heterostructures for broadband strong light-matter interactions. Nanoscale 15:12000–12007

    Article  CAS  PubMed  Google Scholar 

  61. Chou Chau YF, Chou Chau CT, Huang HJ, Wang YC, Chiang HP, Idris MNSM, Masri Z, Lim CM (2019) Strong and tunable plasmonic field coupling and enhancement generating from the protruded metal nanorods and dielectric cores. Results in Physics 13:102290

    Article  Google Scholar 

  62. Chou Chau YF, Jheng CY, Joe SF, Wang SF, Yang W, Jheng SC, Sun YS, Chu Y, Wei JH (2013) Structurally and materially sensitive hybrid surface plasmon modes in periodic silver-shell nanopearl and its dimer arrays. J Nanopart Res 15(3):1424

    Article  Google Scholar 

  63. Chou Chau YF, Lim CM, Lee C, Huang HJ, Lin CT, Kumara NTRN, Yoong VN, Chiang HP (2016) Tailoring surface plasmon resonance and dipole cavity plasmon modes of scattering cross section spectra on the single solid-gold/gold-shell nanorod. J Appl Phys 120(9):093110

    Article  Google Scholar 

  64. Chau Y, Jiang Z, Li H, Lin G, Wu F, Lin W (2011) Localized resonance of composite core-shell nanospheres, nanobars and nanospherical chains. Progress in Electromagnetics Research B 28:183–199

    Article  Google Scholar 

  65. Zhang Q, Li G, Liu X, Qian F, Li Y, Sum TC, Lieber CM, Xiong Q (2014) A room temperature low-threshold ultraviolet plasmonic nanolaser. Nat Commun 5(1):4953

    Article  CAS  PubMed  Google Scholar 

  66. Oulton RF, Sorger VJ, Zentgraf T, Ma RM, Gladden C, Dai L, Bartal G, Zhang X (2009) Plasmon lasers at deep subwavelength scale. Nature 461(7264):629–632

    Article  CAS  PubMed  Google Scholar 

  67. Chou YH, Chou BT, Chiang CK, Lai YY, Yang CT, Li H, Lin TR, Lin CC, Kuo HC, Wang SC, Lu TC (2015) Ultrastrong mode confinement in ZnO surface plasmon nanolasers. ACS Nano 9(4):3978–3983

    Article  CAS  PubMed  Google Scholar 

  68. Ma Z, Kikunaga K, Wang H, Sun S, Amin R, Maiti R, Tahersima MH, Dalir, Miscuglio M, Sorger VJ (2020) Compact graphene plasmonic slot photodetector on Silicon-on-insulator with high responsivity. ACS Photonics 7(4):932–940

    Article  CAS  Google Scholar 

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Funding

Key Scientific Research Project of Colleges and Universities in Henan Province (24B140014), Special Fund for the Construction of Innovative Experimental Plan for College Students of Zhengzhou Normal University (DCY2022006), Henan Student’s Project for Innovation and Entrepreneurship Training Program (202312949013).

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Da Teng proposed the concept and supervised the research. Lingjie Bu developed methodology in the given study. Lingjie Bu, Yuying Liu and Rumeng Zhang performed the calculations and analyzed numerical data. All the authors have discussed the results thoroughly and contributed to the writing and review of the manuscript.

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Correspondence to Da Teng.

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Bu, L., Liu, Y., Zhang, R. et al. Finite-element Method Analysis of Sodium Based Elliptical Hybrid Plasmonic Waveguides with Ultra-low Loss. Plasmonics (2023). https://doi.org/10.1007/s11468-023-02114-2

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