Skip to main content
SpringerLink
Log in

Goos–Hänchen shift observed from stratified medium

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

Abstract

In this paper, we have theoretically examined Goos–Hänchen shift (GHS) obtained from a stratified epsilon-near-zero (ENZ) medium placed in air. Transfer matrix method is used to calculate GHS for a sandwich structure composed of odd number of slabs. The impact of changing the material permittivity, thickness and number of slabs on GHS is discussed in detail for TE and TM polarized light. Significant increase in GHS is observed as the number of ENZ slabs in stratified structure is increased. When all the slabs have equal permittivity, published results for a single ENZ slab are recovered. The presented work will help in designing stratified ENZ medium with required GHS and reflectivity for optical sensors.

Graphic abstract

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

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 is no experimental data available].

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  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 ptse 2 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. 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 

  15. 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, 596278 (2013)

    Article  Google Scholar 

  16. L.-G. Wang, S.-Y. Zhu, Large positive and negative goos-hänchen shifts from a weakly absorbing left-handed slab. J. Appl. Phys. 98(4), 043522 (2005)

    Article  ADS  Google Scholar 

  17. J. Wen, J. Zhang, L.-G. Wang, S.-Y. Zhu, Goos-hänchen shifts in an epsilon-near-zero slab. JOSA B 34(11), 2310–2316 (2017)

    Article  ADS  Google Scholar 

  18. I.V. Shadrivov, A.A. Zharov, Y.S. Kivshar, Giant goos-hänchen effect at the reflection from left-handed metamaterials. Appl. Phys. Lett. 83(13), 2713–2715 (2003)

    Article  ADS  Google Scholar 

  19. W. Ding, L. Chen, C.-H. Liang, Numerical study of goos-h änchen shift on the surface of anisotropic left-handed materials. Prog. Electromagn. Res. B 2, 151–164 (2008)

    Article  Google Scholar 

  20. W. Zhen, D. Deng, J. Guo, Goos-hänchen shifts of gaussian beams reflected from surfaces coated with cross-anisotropic metasurfaces. Opt. Laser Technol. 135, 106679 (2021)

    Article  Google Scholar 

  21. L.-G. Wang, H. Chen, N.-H. Liu, S.-Y. Zhu, Negative and positive lateral shift of a light beam reflected from a grounded slab. Opt. Lett. 31(8), 1124–1126 (2006)

    Article  ADS  Google Scholar 

  22. L. Han, J. Pan, C. Wu, K. Li, H. Ding, Q. Ji, M. Yang, J. Wang, H. Zhang, T. Huang, Giant goos-hänchen shifts in au-ito-tmdcs-graphene heterostructure and its potential for high performance sensor. Sensors 20(4), 1028 (2020)

    Article  ADS  Google Scholar 

  23. 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 

  24. W. Zhen, D. Deng, Goos-hänchen shifts for airy beams impinging on graphene-substrate surfaces. Opt. Express 28(16), 24104–24114 (2020)

    Article  ADS  Google Scholar 

  25. Ziauddin, S. Qamar, Gain-assisted control of the goos-hänchen shift. Phys. Rev. A 84(5), 053844 (2011)

    Article  ADS  Google Scholar 

  26. J. Wu, Z.T. Xie, Y. Sha, H. Fu, Q. Li, Epsilon-near-zero photonics: infinite potentials. Photon. Res. 9(8), 1616–1644 (2021)

    Article  Google Scholar 

  27. P.B. Johnson, R.-W. Christy, Optical constants of the noble metals. Phys. Rev. B 6(12), 4370 (1972)

    Article  ADS  Google Scholar 

  28. R. Maas, J. Parsons, N. Engheta, A. Polman, Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths. Nat. Photon. 7(11), 907–912 (2013)

    Article  ADS  Google Scholar 

  29. Y.U. Lee, E. Garoni, H. Kita, K. Kamada, B.H. Woo, Y.C. Jun, S.M. Chae, H.J. Kim, K.J. Lee, S. Yoon et al., Strong nonlinear optical response in the visible spectral range with epsilon-near-zero organic thin films. Adv. Opt. Mater. 6(14), 1701400 (2018)

    Article  Google Scholar 

  30. A. Alu, M.G. Silveirinha, A. Salandrino, N. Engheta, Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern. Phys. Rev. B 75(15), 155410 (2007)

    Article  ADS  Google Scholar 

  31. Y. Xu, C.T. Chan, H. Chen, Goos-hänchen effect in epsilon-near-zero metamaterials. Sci. Rep. 5(1), 1–5 (2015)

    Google Scholar 

  32. C. Ziauddin, R.-K. Lee et al., Negative and positive goos-hänchen shifts of partially coherent light fields. Phys. Rev. A 91(1), 013803 (2015)

    Article  ADS  Google Scholar 

  33. 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 

  34. C. Zhai, S. Zhang, Goos-hänchen shift of an airy beam reflected in an epsilon-near-zero metamaterial. Optik 184, 234–240 (2019)

    Article  ADS  Google Scholar 

  35. N. Ali, W.I. Waseer, Q. Naqvi et al., Analysis of goos-hanchen shift for an epsilon-near-zero slab sandwiched between two non-integer dimensional media. Opt. Commun. 501, 127348 (2021)

    Article  Google Scholar 

  36. 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 

  37. 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, 8822273 (2020)

    Article  Google Scholar 

  38. L. Salasnich, Enhancement of four reflection shifts by a three-layer surface-plasmon resonance. Phys. Rev. A 86(5), 055801 (2012)

    Article  ADS  Google Scholar 

  39. Y.S. Dadoenkova, N. Dadoenkova, I. Lyubchanskii, Y. Lee, Goos-hänchen shift at the reflection of light from the complex structures composed of superconducting and dielectric layers. J. Appl. Phys. 118(21), 213101 (2015)

    Article  ADS  Google Scholar 

  40. M. Abbas, L.G. Wang, Magnitude of the goos-hänchen shift depends on the beam propagation in a medium. J. Opt. Soc. Am. B 36(1), 119–124 (2019)

    Article  ADS  Google Scholar 

  41. S. Bassiri, C. Papas, N. Engheta, Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab. JOSA A 5(9), 1450–1459 (1988)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, COMSATS University, Islamabad, 45550, Pakistan

    Khawer Javaid Manzoor, Waleed Iqbal Waseer & Muhammad Junaid Mughal

  2. Department of Electronics, Quaid-i-Azam University, Islamabad, 45320, Pakistan

    Waleed Iqbal Waseer & Qaisar Abbas Naqvi

Authors
  1. Khawer Javaid Manzoor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Waleed Iqbal Waseer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qaisar Abbas Naqvi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Junaid Mughal
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manzoor, K.J., Waseer, W.I., Naqvi, Q.A. et al. Goos–Hänchen shift observed from stratified medium. Eur. Phys. J. D 76, 82 (2022). https://doi.org/10.1140/epjd/s10053-022-00409-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-022-00409-3

Keywords

Search

Navigation