Skip to main content
Log in

Electrically tunable Goos–Hänchen shift from epsilon-near-zero (ENZ) structure with graphene

  • Regular Article – Optical Phenomena and Photonics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

In this paper, we have studied electrically tunable Goos–Hänchen shift (GHS) for TM/p polarized light wave incident on a multilayered epsilon-near-zero (ENZ) structure containing graphene. Transfer matrix method has been used to obtain GHS for the multilayered structure composed of three slabs. We have studied the impact of changing Fermi energy, incident angle and graphene layer position on the obtained GHS. We observed that by adjusting the Fermi energy, the direction of GHS in the multilayered structure can be changed. Moreover, the imaginary part of graphene conductivity affects the magnitude and sign of GHS while real part of conductivity is closely linked with Brewster angle position. Besides, we have discussed the effect of changing permittivity of slabs and number of graphene layers on the obtained GHS. Published results for single epsilon-near-zero (ENZ) slab were recovered by using equal slab permittivity and zero conductivity for graphene. The results presented in this work will help in designing optical sensors using multilayered ENZ medium.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Author’s comment: This is a theoretical study and there are no experimental data available].

References

  1. F. Goos, H. Hänchen, A new and fundamental experiment on total reflection. Ann. Phys. (Leipz.) 1(7–8), 333–346 (1947)

    Article  ADS  Google Scholar 

  2. K. Artmann, Berechnung der seitenversetzung des totalreflektierten strahles. Ann. Phys. 437(1–2), 87–102 (1948)

    Article  MATH  Google Scholar 

  3. W.I. Waseer, Q.A. Naqvi, M.J. Mughal, Goos–hänchen shift at the planar interface of NID dielectric and topological insulator. Optik 227, 166023 (2021)

    Article  ADS  Google Scholar 

  4. K. Ali, A.A. Syed, W.I. Waseer, Q.A. Naqvi, Goos–Hanchen-effect for near-zero-index metamaterials excited by fractional dual fields. Optik 243, 167501 (2021)

    Article  ADS  Google Scholar 

  5. W.I. Waseer, R. Parveen, Q.A. Naqvi, M.J. Mughal, Observing the Goos–Hänchen shift for a planar interface of dielectric and orthorhombic anisotropic medium. JOSA B 37(8), 2366–2371 (2020)

    Article  ADS  Google Scholar 

  6. W.I. Waseer, Q.A. Naqvi, M.J. Mughal, Analysis of the Goos Hanchen shift for a planar interface of NID dielectric and general medium. Optik 218, 165140 (2020)

    Article  ADS  Google Scholar 

  7. A. Othman, The general treatment of giant Goos–Hänchen shift in a slab cavity. J. Taibah Univ. Sci. 14(1), 1147–1155 (2020)

    Article  Google Scholar 

  8. A. Razaque, Q. Minhas, Q.A. Naqvi, W.I. Waseer, Analysis of the Goos–Hänchen shift for a planar dielectric-chiral interface excited by fractional dual fields. Optik 216, 164659 (2020)

    Article  ADS  Google Scholar 

  9. I.Z.U. Haq, A.A. Syed, Q.A. Naqvi, Observing the Goos–Hänchen shift in non-integer dimensional medium. Optik 206, 164071 (2020)

    Article  ADS  Google Scholar 

  10. Y. Guo, N.M. Singh, C.M. Das, Q. Ouyang, L. Kang, K. Li, P. Coquet, K.-T. Yong, Two-dimensional PtSe2 theoretically enhanced Goos–Hänchen shift sensitive plasmonic biosensors. Plasmonics 15, 1815–1826 (2020)

    Article  Google Scholar 

  11. M. Gao, D. Deng, Spatial Goos–Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy airy beams. Opt. Express 28(7), 10531–10541 (2020)

    Article  ADS  Google Scholar 

  12. D. Xu, S. He, J. Zhou, S. Chen, S. Wen, H. Luo, Goos–Hänchen effect enabled optical differential operation and image edge detection. Appl. Phys. Lett. 116(21), 211103 (2020)

    Article  ADS  Google Scholar 

  13. Y. Ding, D. Deng, X. Zhou, W. Zhen, M. Gao, Y. Zhang, Barcode encryption based on negative and positive Goos–Hänchen shifts in a graphene-ITO/TIO2/ITO sandwich structure. Opt. Express 29(25), 41164–41175 (2021)

    Article  ADS  Google Scholar 

  14. J. Wang, H. Huang, C. Chen, H. He, Y. Dong, H. Qi, Goos–Hänchen lateral displacements at the interface between isotropic and gyroelectric media. Int. J. Antennas Propag. 2013 (2013)

  15. Y.-L. Chuang, S. Qamar, R.-K. Lee et al., Goos–Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials. Sci. Rep. 6(1), 1–6 (2016)

    Google Scholar 

  16. A.K. Geim, Graphene: status and prospects. Science 324(5934), 1530–1534 (2009)

    Article  ADS  Google Scholar 

  17. Y. Zhang, Y.-W. Tan, H.L. Stormer, P. Kim, Experimental observation of the quantum hall effect and berry’s phase in graphene. Nature 438(7065), 201–204 (2005)

    Article  ADS  Google Scholar 

  18. Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, C.M. Soukoulis, Graphene plasmonics: a platform for 2D optics. Adv. Opt. Mater. 7(3), 1800537 (2019)

    Article  Google Scholar 

  19. F.H. Koppens, D.E. Chang, F.J. García de Abajo, Graphene plasmonics: a platform for strong light-matter interactions. Nano Lett. 11(8), 3370–3377 (2011)

    Article  ADS  Google Scholar 

  20. A.C. Neto, F. Guinea, N.M. Peres, K.S. Novoselov, A.K. Geim, The electronic properties of graphene. Rev. Mod. Phys. 81(1), 109 (2009)

    Article  ADS  Google Scholar 

  21. V. Ginis, P. Tassin, T. Koschny, C.M. Soukoulis, Tunable terahertz frequency comb generation using time-dependent graphene sheets. Phys. Rev. B 91(16), 161403 (2015)

    Article  ADS  Google Scholar 

  22. D. Abergel, V.I. Fal’ko, Optical and magneto-optical far-infrared properties of bilayer graphene. Phys. Rev. B 75(15), 155430 (2007)

    Article  ADS  Google Scholar 

  23. L. Jiang, Q. Wang, Y. Xiang, X. Dai, S. Wen, Electrically tunable Goos–Hänchen shift of light beam reflected from a graphene-on-dielectric surface. IEEE Photonics J. 5(3), 6500108–6500108 (2013)

    Article  ADS  Google Scholar 

  24. X. Li, P. Wang, F. Xing, X.-D. Chen, Z.-B. Liu, J.-G. Tian, Experimental observation of a giant Goos–Hänchen shift in graphene using a beam splitter scanning method. Opt. Lett. 39(19), 5574–5577 (2014)

    Article  ADS  Google Scholar 

  25. S. Grosche, M. Ornigotti, A. Szameit, Goos–Hänchen and Imbert-Fedorov shifts for gaussian beams impinging on graphene-coated surfaces. Opt. Express 23(23), 30195–30203 (2015)

    Article  ADS  Google Scholar 

  26. G. Xu, M. Cao, C. Liu, J. Sun, T. Pan, Tunable lateral and angular shifts of a reflected beam from a graphene-based structure. Optik 127(5), 2521–2524 (2016)

    Article  ADS  Google Scholar 

  27. Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, C.M. Soukoulis, Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime. Adv. Opt. Mater. 4(11), 1824–1828 (2016)

    Article  Google Scholar 

  28. C. Wang, F. Wang, R. Liang, Z. Wei, H. Meng, H. Dong, H. Cen, N. Lin, Electrically tunable Goos–Hänchen shifts in weakly absorbing epsilon-near-zero slab. Opt. Mater. Express 8(4), 718–726 (2018)

    Article  ADS  Google Scholar 

  29. R. Peng, Z. Xiao, Q. Zhao, F. Zhang, Y. Meng, B. Li, J. Zhou, Y. Fan, P. Zhang, N.-H. Shen et al., Temperature-controlled chameleonlike cloak. Phys. Rev. X 7(1), 011033 (2017)

    Google Scholar 

  30. K.J. Manzoor, W.I. Waseer, Q.A. Naqvi, M.J. Mughal, Goos–Hänchen shift observed from stratified medium. Eur. Phys. J. D 76(5), 1–11 (2022)

  31. N.A.F. Zambale, J.L.B. Sagisi, N.P. Hermosa, Goos-h\(\backslash \)” anchen shifts due to 2D materials with complex conductivity. arXiv preprint arXiv:1803.08223 (2018)

  32. Q. Yue, W. Zhen, Y. Ding, X. Zhou, D. Deng, Giant Goos–Hänchen shifts controlled by exceptional points in a pt-symmetric periodic multilayered structure coated with graphene. Opt. Mater. Express 11(12), 3954–3965 (2021)

    Article  ADS  Google Scholar 

  33. W. Lin, Z. Xiao, W. Zhou, M. Ren, Z. Zheng, Graphene-assisted Goos–Hänchen shift in a planar multilayer configuration in the visible light range. Adv. Condens. Matter Phys. 2020 (2020)

  34. X. Zhou, S. Liu, Y. Ding, L. Min, Z. Luo, Precise control of positive and negative Goos–Hänchen shifts in graphene. Carbon 149, 604–608 (2019)

    Article  Google Scholar 

  35. C. How Gan, Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection. Appl. Phys. Lett. 101(11), 111609 (2012)

    Article  ADS  Google Scholar 

  36. H. Tian, Y. Yang, J. Tang, L. Jiang, Y. Xiang, Graphene Tamm plasmon-induced enhanced and tunable photonic spin hall effect of reflected light in terahertz band. Results Phys. 25, 104300 (2021)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed substantially and equally to this work.

Corresponding author

Correspondence to Khawer Javaid Manzoor.

Ethics declarations

Conflict of interest

The authors have declared that no competing interests exist.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manzoor, K.J., Naqvi, Q.A. & Mughal, M.J. Electrically tunable Goos–Hänchen shift from epsilon-near-zero (ENZ) structure with graphene. Eur. Phys. J. D 76, 239 (2022). https://doi.org/10.1140/epjd/s10053-022-00570-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-022-00570-9

Navigation