Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Analysis of a conformal invisible device

  • 83 Accesses

  • 4 Citations


We perform a semi-analytical calculation of the field distributions of a conformal invisible device via mode expansions. For a discrete set of frequencies in the regime of wave optics, the conformal invisible device is perfectly transparent, which stems from the special conformal mapping and the refractiveindex profile of the Mikaelian lens.

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


  1. 1.

    U. Leonhardt, Optical conformal mapping, Science 312(5781), 1777 (2006)

  2. 2.

    J. B. Pendry, D. Schurig, and D. R. Smith, Controlling electromagnetic fields, Science 312(5781), 1780 (2006)

  3. 3.

    H. Y. Chen, C. T. Chan, and P. Sheng, Transformation optics and metamaterials, Nat. Mater. 9(5), 387 (2010)

  4. 4.

    A. V. Kildishev and V. M. Shalaev, Transformation optics and metamaterials, Phys. Usp. 54(1), 53 (2011)

  5. 5.

    Y. Liu and X. Zhang, Recent advances in transformation optics, Nanoscale 4(17), 5277 (2012)

  6. 6.

    P. Kinsler and M. W. McCall, The futures of transformations and metamaterials, Photonics and Nanostructures–Fundamentals and Applications 15, 10 (2015)

  7. 7.

    D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Metamaterial electromagnetic cloak at microwave frequencies, Science 314(5801), 977 (2006)

  8. 8.

    J. Li and J. B. Pendry, Hiding under the carpet: A new strategy for cloaking, Phys. Rev. Lett. 101(20), 203901 (2008)

  9. 9.

    R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Broadband ground-plane cloak, Science 323(5912), 366 (2009)

  10. 10.

    J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, An optical cloak made of dielectrics, Nat. Mater. 8(7), 568 (2009)

  11. 11.

    L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, Silicon nanostructure cloak operating at optical frequencies, Nat. Photonics 3(8), 461 (2009)

  12. 12.

    T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Three-dimensional invisibility cloak at optical wavelengths, Science 328(5976), 337 (2010)

  13. 13.

    H. F. Ma and T. J. Cui, Three-dimensional broadband ground-plane cloak made of metamaterials, Nat. Commun. 1(3), 1 (2010)

  14. 14.

    H. Y. Chen and C. T. Chan, Transformation media that rotate electromagnetic fields, Appl. Phys. Lett. 90(24), 241105 (2007)

  15. 15.

    H. Y. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, Design and experimental realization of a broadband transformation media field rotator at microwave frequencies, Phys. Rev. Lett. 102(18), 183903 (2009)

  16. 16.

    M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations, Photonics and Nanostructures–Fundamentals and Applications 6(1), 87 (2008)

  17. 17.

    M. M. Sadeghi, S. Li, L. Xu, B. Hou, and H. Y. Chen, Transformation optics with Fabry–Perot resonances, Sci. Rep. 5(1), 8680 (2015)

  18. 18.

    U. Leonhardt and T. G. Philbin, General relativity in electrical engineering, New J. Phys. 8(10), 247 (2006)

  19. 19.

    U. Leonhardt and T. Philbin, Geometry and Light: The Science of Invisibility, New York: Dover, Mineola, 2010

  20. 20.

    L. Xu and H. Y. Chen, Conformal transformation optics, Nat. Photonics 9(1), 15 (2014)

  21. 21.

    J. P. Turpin, A. T. Massoud, Z. H. Jiang, P. L. Werner, and D. H. Werner, Conformal mappings to achieve simple material parameters for transformation optics devices, Opt. Express 18(1), 244 (2010)

  22. 22.

    H. Y. Chen, U. Leonhardt, and T. Tyc, Conformal cloak for waves, Phys. Rev. A 83(5), 055801 (2011)

  23. 23.

    L. Xu, H. Y. Chen, T. Tyc, Y. Xie and S. A. Cummer, Perfect conformal invisible device with feasible refractive indexes, Phys. Rev. B 93, 041406(R) (2016)

  24. 24.

    Z. Nehari, Conformal Mapping, New York: McGraw-Hill, 1952

  25. 25.

    L. Xu and H. Y. Chen, Logarithm conformal mapping brings the cloaking effect, Sci. Rep. 4(1), 6862 (2015)

  26. 26.

    A. L. Mikaelian, The use of medium properties to focus waves, Dokl. USSR Acad. Sci. Issue 81, 569 (1951)

  27. 27.

    A. L. Mikaelian and A. M. Prokhorov, Self-focusing media with variable index of refraction, Prog. Opt. 17, 279 (1980)

  28. 28.

    T. Tyc, H. L. Dao, and A. J. Danner, Absolute optical instruments without spherical symmetry, Phys. Rev. A 92(5), 053827 (2015)

  29. 29.

    T. G. Philbin, Making geometrical optics exact, J. Mod. Opt. 61(7), 552 (2014)

  30. 30.

    H. Kan, L. Xu, Y. Xu, and H. Chen, Conformal cloaks from a function composition, Europhys. Lett. 117(3), 34002 (2017)

Download references


This work was supported by the National Natural Science Foundation of China for Excellent Young Scientists (Grant No. 61322504), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201217), and Fundamental Research Funds for the Central Universities (Grant No. 20720170015).

Author information

Correspondence to Huan-Yang Chen.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, L., Xiong, Z. & Chen, H. Analysis of a conformal invisible device. Front. Phys. 13, 134203 (2018). https://doi.org/10.1007/s11467-017-0733-3

Download citation


  • conformal transformation optics
  • conformal invisible device
  • refractive-index profile

PACS numbers

  • 42.25.Bs
  • 42.30.Va
  • 42.79.-e