Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of unidirectional backscattering-immune topological electromagnetic states


One of the most striking phenomena in condensed-matter physics is the quantum Hall effect, which arises in two-dimensional electron systems1,2,3,4 subject to a large magnetic field applied perpendicular to the plane in which the electrons reside. In such circumstances, current is carried by electrons along the edges of the system, in so-called chiral edge states (CESs). These are states that, as a consequence of nontrivial topological properties of the bulk electronic band structure, have a unique directionality and are robust against scattering from disorder. Recently, it was theoretically predicted5,6,7 that electromagnetic analogues of such electronic edge states could be observed in photonic crystals, which are materials having refractive-index variations with a periodicity comparable to the wavelength of the light passing through them. Here we report the experimental realization and observation of such electromagnetic CESs in a magneto-optical photonic crystal7 fabricated in the microwave regime. We demonstrate that, like their electronic counterparts8,9,10,11,12,13, electromagnetic CESs can travel in only one direction and are very robust against scattering from disorder; we find that even large metallic scatterers placed in the path of the propagating edge modes do not induce reflections. These modes may enable the production of new classes of electromagnetic device and experiments that would be impossible using conventional reciprocal photonic states alone. Furthermore, our experimental demonstration and study of photonic CESs provides strong support for the generalization and application of topological band theories to classical and bosonic systems, and may lead to the realization and observation of topological phenomena in a generally much more controlled and customizable fashion than is typically possible with electronic systems.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Figure 1: Microwave waveguide supporting CESs.
Figure 2: Photonic CESs and effects of a large scatterer.
Figure 3: CES-facilitated waveguiding in a photonic crystal.
Figure 4: CES transmission spectra in the presence of a large scatterer.


  1. von Klitzing, K., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980)

    Article  ADS  CAS  Google Scholar 

  2. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982)

    Article  ADS  CAS  Google Scholar 

  3. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005)

    Article  ADS  CAS  Google Scholar 

  4. Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005)

    Article  ADS  CAS  Google Scholar 

  5. Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008)

    Article  ADS  CAS  Google Scholar 

  6. Raghu, S. & Haldane, F. D. M. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834 (2008)

    Article  ADS  Google Scholar 

  7. Wang, Z., Chong, Y. D., Joannopoulos, J. D. & Soljacic, M. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett. 100, 013905 (2008)

    Article  ADS  Google Scholar 

  8. Prange, R. E. & Girvin, S. M. The Quantum Hall effect (Springer, 1987)

    Book  Google Scholar 

  9. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & Dennijs, M. Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982)

    Article  ADS  CAS  Google Scholar 

  10. Simon, B. Holonomy, the quantum adiabatic theorem, and Berry phase. Phys. Rev. Lett. 51, 2167–2170 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  11. Kohmoto, M. Topological invariant and the quantization of the Hall conductance. Ann. Phys. 160, 343–354 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  12. Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1988)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  13. Hatsugai, Y. Chern number and edge states in the integer quantum Hall effect. Phys. Rev. Lett. 71, 3697–3700 (1993)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  14. Yablonovitch, E. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58, 2059–2062 (1987)

    Article  ADS  CAS  Google Scholar 

  15. John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987)

    Article  ADS  CAS  Google Scholar 

  16. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008)

    MATH  Google Scholar 

  17. Chong, Y. D., Wen, X. G. & Soljacic, M. Effective theory of quadratic degeneracies. Phys. Rev. B 77, 235125 (2008)

    Article  ADS  Google Scholar 

  18. Pozar, D. M. Microwave Engineering 2nd edn (Wiley, 1998)

    Google Scholar 

  19. Murakami, S., Nagaosa, N. & Zhang, S.-C. Dissipationless quantum spin current at room temperature. Science 301, 1348–1351 (2003)

    Article  ADS  CAS  Google Scholar 

  20. Kane, C. L., Mele, E. J. & Z (2) topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005)

    Article  ADS  CAS  Google Scholar 

  21. Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006)

    Article  ADS  CAS  Google Scholar 

  22. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–975 (2008)

    Article  ADS  CAS  Google Scholar 

  23. Moore, J. E., Ran, Y. & Wen, X.-G. Topological surface states in three-dimensional magnetic insulators. Phys. Rev. Lett. 101, 186805 (2008)

    Article  ADS  Google Scholar 

  24. Yu, Z. F. & Fan, S. H. Complete optical isolation created by indirect interband photonic transitions. Nature Photon. 3, 91–94 (2009)

    Article  ADS  CAS  Google Scholar 

  25. Baba, T. Slow light in photonic crystals. Nature Photon. 2, 465–473 (2008)

    Article  ADS  CAS  Google Scholar 

  26. Thevenaz, L. Slow and fast light in optical fibres. Nature Photon. 2, 474–481 (2008)

    Article  ADS  CAS  Google Scholar 

  27. Povinelli, M. L. et al. Effect of a photonic band gap on scattering from waveguide disorder. Appl. Phys. Lett. 84, 3639–3641 (2004)

    Article  ADS  CAS  Google Scholar 

  28. Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999)

    Article  ADS  Google Scholar 

  29. Yen, T. J. et al. Terahertz magnetic response from artificial materials. Science 303, 1494–1496 (2004)

    Article  ADS  CAS  Google Scholar 

  30. Linden, S. et al. Magnetic response of metamaterials at 100 terahertz. Science 306, 1351–1353 (2004)

    Article  ADS  CAS  Google Scholar 

Download references


We are very grateful to P. Fisher and U. J. Becker for generously providing access to the synchrotron magnet at Massachusetts Institute of Technology. We should like to thank I. Chuang, P. Bermel, J. Bravo-Abad, S. Johnson and P. Rakich for comments. This work was supported in part by the Materials Research Science and Engineering Program of the US National Science Foundation under award number DMR-0819762, and also in part by the US Army Research Office through the Institute for Soldier Nanotechnologies under contract no. W911NF-07-D-0004.

Author Contributions Z.W., Y.C, J.D.J and M.S. designed the photonic-crystal system, analysed the data and wrote the manuscript. Z.W. and Y.C. fabricated the structure and performed all the experimental measurements.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Zheng Wang.

Supplementary information

Supplementary Information

This file contains Supplementary Notes, Supplementary Figures S-1-S-2 with Legends, Notes and Legends for Supplementary Movies S1-S5 and a Supplementary Reference. (PDF 1584 kb)

Supplementary Movie 1

This file shows a one-way CES mode being excited by a dipole antenna - see file s1. (MOV 294 kb)

Supplementary Movie 2

This movie file shows a one-way CES mode circumventing a metallic scatterer see file s1. (MOV 527 kb)

Supplementary Movie 3

This movie file shows a conventional waveguide excited by a dipole antenna see file s1. (MOV 322 kb)

Supplementary Movie 4

This movie file shows a conventional waveguide with a small metallic scatterer see file s1. (MOV 235 kb)

Supplementary Movie 5

This movie file shows a conventional waveguide with a metallic scatterer identical to the one in Movie S2. (MOV 181 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wang, Z., Chong, Y., Joannopoulos, J. et al. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing