Skip to main content

Thank you for visiting nature.com. 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.

Two-dimensional topological photonics

Nature Photonics volume 11, pages 763–773 (2017)Cite this article

Subjects

Abstract

Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.

Topology is a branch of mathematics that deals with highly robust conserved quantities that do not change when physical objects are continuously deformed, no matter how much. For example, the number of holes (or handles) of a complex connected surface can be characterized by its genus. This topological index does not change as the surface is deformed without introducing any cuts. Therefore, it can be thought of as being topologically robust. It is not surprising that topology finds a welcoming home in physics, which has a rich tradition (going back to Emmy Noether’s theorem) of appealing to conserved quantities such as energy, momentum, angular momentum and many others. It is easy to see, however, how topological indices are more robust than, for example, angular momentum: the class of deformations that preserve topological indices is much broader than that preserving angular momentum. For example, the stringent condition for the conservation of the angular momentum is that the system remains rotationally invariant.

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

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Fig. 1: Classification scheme of topological orders in 2D photonic systems.
Fig. 2: Topologically protected photonic transport with broken time-reversal symmetry.
Fig. 3: Topological photonics in meta-waveguides with bianisotropy-induced spin–orbit interactions.
Fig. 4: Photonic topological insulator protected by lattice symmetry.
Fig. 5: Floquet topological insulators with spatial modulation.

References

  1. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405 (1982).

    Article  ADS  Google Scholar 

  2. 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  Google Scholar 

  3. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. Ser. A 392, 45 (1984).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698 (1979).

    Article  ADS  Google Scholar 

  5. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    Article  ADS  Google Scholar 

  6. 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  Google Scholar 

  7. Rycerz, A., Tworzydło, J. & Beenakker, C. Valley filter and valley valve in graphene. Nat. Phys. 3, 172–175 (2007).

    Article  Google Scholar 

  8. Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).

    Article  ADS  Google Scholar 

  9. Yao, W., Xiao, D. & Niu, Q. Valley-dependent optoelectronics from inversion symmetry breaking. Phys. Rev. B 77, 235406 (2008).

    Article  ADS  Google Scholar 

  10. Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).

    Article  ADS  Google Scholar 

  11. Kim, Y., Choi, K., Ihm, J. & Jin, H. Topological domain walls and quantum valley Hall effects in silicene. Phys. Rev. B 89, 085429 (2014).

    Article  ADS  Google Scholar 

  12. Moore, J. E. The birth of topological insulators. Nature 464, 194–198 (2010).

    Article  ADS  Google Scholar 

  13. Yablonovitch, E. Photonic crystals: semiconductors of light. Sci. Am. 12, 47 (2001).

    Google Scholar 

  14. Lu, L., Joannopoulos, J. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Wang, Z., Chong, Y., Joannopoulos, J. & Soljačić, M. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett. 100, 13905 (2008).

    Article  ADS  Google Scholar 

  17. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

    Article  ADS  Google Scholar 

  18. Poo, Y., Wu, R., Lin, Z., Yang, Y. & Chan, C. T. Experimental realization of self-guiding unidirectional electromagnetic edge states. Phys. Rev. Lett. 106, 093903 (2011).

    Article  ADS  Google Scholar 

  19. Skirlo, S. A., Lu, L. & Soljačić, M. Multimode one-way waveguides of large Chern numbers. Phys. Rev. Lett. 113, 113904 (2014).

    Article  ADS  Google Scholar 

  20. Skirlo, S. A. et al. Experimental observation of large Chern numbers in photonic crystals. Phys. Rev. Lett. 115, 253901 (2015).

    Article  ADS  Google Scholar 

  21. Lu, L. et al. Symmetry-protected topological photonic crystal in three dimensions. Nat. Phys. 12, 337 (2016).

    Article  Google Scholar 

  22. Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Ma, T. & Shvets, G. All-Si valley-Hall photonic topological insulator. New J. Phys. 18, 025012 (2016).

    Article  ADS  Google Scholar 

  24. Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  Google Scholar 

  25. Mong, R. S. & Shivamoggi, V. Edge states and the bulk-boundary correspondence in Dirac Hamiltonians. Phys. Rev. B 83, 125109 (2011).

    Article  ADS  Google Scholar 

  26. Ezawa, M. Topological Kirchhoff law and bulk-edge correspondence for valley Chern and spin-valley Chern numbers. Phys. Rev. B 88, 161406 (2013).

    Article  ADS  Google Scholar 

  27. Umucalılar, R. O. & Carusotto, I. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).

    Article  ADS  Google Scholar 

  28. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).

    Article  Google Scholar 

  29. Schine, N., Ryou, A., Gromov, A., Sommer, A. & Simon, J. Synthetic Landau levels for photons. Nature 534, 671–675 (2016).

    Article  ADS  Google Scholar 

  30. Sala, V. et al. Spin-orbit coupling for photons and polaritons in microstructures. Phys. Rev. X 5, 011034 (2015).

    Google Scholar 

  31. Qi, X.-L. & Zhang, S.-C. The quantum spin Hall effect and topological insulators. Phys. Today 63, 33 (2010).

    Article  Google Scholar 

  32. Fu, L. Topological crystalline insulators. Phys. Rev. Lett. 106, 106802 (2011).

    Article  ADS  Google Scholar 

  33. Linder, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nat. Phys. 7, 490–495 (2011).

    Article  Google Scholar 

  34. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

    Article  ADS  Google Scholar 

  35. Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater. 12, 233–239 (2013).

    Article  ADS  Google Scholar 

  36. Gao, F. et al. Probing topological protection using a designer surface plasmon structure. Nat. Commun. 7, 11619 (2016).

    Article  ADS  Google Scholar 

  37. Chen, W.-J. et al. Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide. Nat. Commun 5, 5782 (2014).

    Article  Google Scholar 

  38. Cheng, X. et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nat. Mater. 15, 542–548 (2016).

    Article  ADS  Google Scholar 

  39. Lai, K., Ma, T., Bo, X., Anlage, S. & Shvets, G. Experimental realization of a reflections-free compact delay line based on a photonic topological insulator. Sci. Rep. 6, 28453 (2016).

    Article  ADS  Google Scholar 

  40. Slobozhanyuk, A. P. Experimental demonstration of topological effects in bianisotropic metamaterials. Sci. Rep. 6, 22270 (2016).

    Article  ADS  Google Scholar 

  41. Xiao, B. et al. Exciting reflectionless unidirectional edge modes in a reciprocal photonic topological insulator medium. Phys. Rev. B 94, 195427 (2016).

    Article  ADS  Google Scholar 

  42. Ma, T., Khanikaev, A. B., Mousavi, S. H. & Shvets, G. Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides. Phys. Rev. Lett. 114, 127401 (2015).

    Article  ADS  Google Scholar 

  43. Wu, L.-H. & Hu, X. Scheme for achieving a topological photonic crystal by using dielectric material. Phys. Rev. Lett. 114, 223901 (2015).

    Article  ADS  Google Scholar 

  44. Jung, J., Zhang, F., Qiao, Z. & MacDonald, A. Valley-Hall kink and edge states in multilayer graphene. Phys. Rev. B 84, 075418 (2011).

    Article  ADS  Google Scholar 

  45. Mittal, S. et al. Topologically robust transport of photons in a synthetic gauge field. Phys. Rev. Lett. 113, 087403 (2014).

    Article  ADS  Google Scholar 

  46. Ma, T. & Shvets, G. Scattering-free edge states between heterogeneous photonic topological insulators. Phys. Rev. B 95, 165102 (2017).

    Article  ADS  Google Scholar 

  47. Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009).

    Article  ADS  Google Scholar 

  48. Ezawa, M. Monolayer topological insulators: silicene, germanene, and stanene. J. Phys. Soc. Jpn 84, 121003 (2015).

    Article  ADS  Google Scholar 

  49. Gorbachev, R. V. et al. Detecting topological currents in graphene superlattices. Science 346, 448–451 (2014).

    Article  ADS  Google Scholar 

  50. Chen, X.-D. & Dong, J.-W. Valley-protected backscattering suppression in silicon photonic graphene. Preprint at https://arxiv.org/abs/1602.03352 (2016).

  51. Chen, X.-D., Zhao, F.-L., Chen, M. & Dong, J.-W. Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation. Phys. Rev. B 96, 020202(R) (2017).

  52. Noh, J., Huang, S., Chen, K. & Rechtsman, M. C. Observation of photonic topological valley-Hall edge states. Preprint at https://arxiv.org/abs/1706.00059 (2017).

  53. Qiao, Z., Jiang, H., Li, X., Yao, Y. & Niu, Q. Microscopic theory of quantum anomalous Hall effect in graphene. Phys. Rev. B 85, 115439 (2012).

    Article  ADS  Google Scholar 

  54. Ezawa, M. Topological phase transition and electrically tunable diamagnetism in silicene. Eur. Phys. J. B 85, 363 (2012).

    Article  ADS  Google Scholar 

  55. Yao, W., Yang, S. A. & Niu, Q. Edge states in graphene: from gapped flat-band to gapless chiral modes. Phys. Rev. Lett. 102, 096801 (2009).

    Article  ADS  Google Scholar 

  56. Zhang, F., MacDonald, A. H. & Mele, E. J. Valley Chern numbers and boundary modes in gapped bilayer graphene. Proc. Natl Acad. Sci. USA 110, 10546–10551 (2013).

    Article  ADS  Google Scholar 

  57. Qiao, Z., Jung, J., Niu, Q. & MacDonald, A. H. Electronic highways in bilayer graphene. Nano Lett. 11, 3453–3459 (2011).

    Article  ADS  Google Scholar 

  58. Gao, F. et al. Topologically-protected refraction of robust kink states in valley photonic crystals. Preprint at https://arxiv.org/abs/1706.04731 (2017).

  59. Yang, Y. et al. Visualization of unidirectional optical waveguide using topological photonic crystals made of dielectric material. Preprint at https://arxiv.org/abs/1610.07780 (2016).

  60. Yves, S. et al. Crystalline metamaterials for topological properties at subwavelength scales. Nat. Commun. 8, 16023 (2017).

    Article  ADS  Google Scholar 

  61. Gorlach, M. A. et al. Controlling scattering of light through topological transitions in all-dielectric metasurfaces. Preprint at https://arxiv.org/abs/1705.04236 (2017).

  62. Kitagawa, T., Berg, E., Rudner, M. & Demler, E. Topological characterization of periodically driven quantum systems. Phys. Rev. B 82, 235114 (2010).

    Article  ADS  Google Scholar 

  63. Fang, K., Yu, Z. & Fan, S. Photonic Aharonov–Bohm effect based on dynamic modulation. Phys. Rev. Lett. 108, 153901 (2012).

    Article  ADS  Google Scholar 

  64. Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photon. 6, 782–787 (2012).

    Article  ADS  Google Scholar 

  65. Fang, K., Yu, Z. & Fan, S. Experimental demonstration of a photonic Aharonov–Bohm effect at radio frequencies. Phys. Rev. B 87, 060301(R) (2013).

    Article  ADS  Google Scholar 

  66. Lira, H., Yu, Z., Fan, S. & Lipson, M. Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip. Phys. Rev. Lett. 109, 033901 (2012).

    Article  ADS  Google Scholar 

  67. Tzuang, L. D., Fang, K., Nussenzveig, P., Fan, S. & Lipson, M. Non-reciprocal phase shift induced by an effective magnetic flux for light. Nat. Photon. 8, 701–705 (2014).

    Article  ADS  Google Scholar 

  68. Sounas, D. L., Caloz, C. & Alù, A. Giant non-reciprocity at the subwavelength scale using angular momentum-biased metamaterials. Nat. Commun. 4, 2407 (2014).

    Google Scholar 

  69. Estep, N. A., Sounas, D. L., Soric, J. & Alù, A. Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops. Nat. Phys. 10, 923–927 (2014).

    Article  Google Scholar 

  70. Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

    Article  ADS  Google Scholar 

  71. Maczewsky, L. J., Zeuner, J. M., Nolte, S. & Szameit, A. Observation of photonic anomalous floquet topological insulators. Nat. Commun. 8, 13756 (2017).

    Article  ADS  Google Scholar 

  72. Mukherjee, S. et al. Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice. Nat. Commun. 8, 13918 (2017).

    Article  ADS  Google Scholar 

  73. Rudner, M. S., Lindner, N. H., Berg, E. & Levin, M. Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems. Phys. Rev. X 3, 031005 (2013).

    Google Scholar 

  74. Pasek, M. & Chong, Y. Network models of photonic Floquet topological insulators. Phys. Rev. B 89, 075113 (2014).

    Article  ADS  Google Scholar 

  75. Hu, W. et al. Measurement of a topological edge invariant in a microwave network. Phys. Rev. X 5, 011012 (2015).

    Google Scholar 

  76. Atala, M. et al. Direct measurement of the Zak phase in topological Bloch bands. Nat. Phys. 9, 795–800 (2013).

    Article  Google Scholar 

  77. Mittal, S., Ganeshan, S., Fan, J., Vaezi, A. & Hafezi, M. Measurement of topological invariants in a 2D photonic system. Nat. Photon. 10, 180–183 (2016).

    Article  ADS  Google Scholar 

  78. Xiao, M., Zhang, Z. & Chan, C. Surface impedance and bulk band geometric phases in one-dimensional systems. Phys. Rev. X 4, 021017 (2014).

    Google Scholar 

  79. Lu, L., Fu, L., Joannopoulos, J. D. & Soljačić, M. Weyl points and line nodes in gyroid photonic crystals. Nat. Photon. 7, 294–299 (2013).

    Article  ADS  Google Scholar 

  80. Chen, W.-J., Xiao, M. & Chan, C. T. Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states. Nat. Commun. 7, 13038 (2016).

    Article  ADS  Google Scholar 

  81. Slobozhanyuk, A. et al. Three-dimensional all-dielectric photonic topological insulator. Nat. Photon. 11, 130–136 (2017).

    Article  ADS  Google Scholar 

  82. Ozawa, T., Price, H. M., Goldman, N., Zilberberg, O. & Carusotto, I. Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics. Phys. Rev. A 93, 043827 (2016).

    Article  ADS  Google Scholar 

  83. Zilberberg, O. et al. Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system. Preprint at https://arxiv.org/abs/1705.08361 (2017).

  84. Verbin, M., Zilberberg, O., Kraus, Y. E., Lahini, Y. & Silberberg, Y. Observation of topological phase transitions in photonic quasicrystals. Phys. Rev. Lett. 110, 076403 (2013).

    Article  ADS  Google Scholar 

  85. Bandres, M. A., Rechtsman, M. C. & Segev, M. Topological photonic quasicrystals: fractal topological spectrum and protected transport. Phys. Rev. X 6, 011016 (2016).

    Google Scholar 

  86. Lin, Q., Xiao, M., Yuan, L. & Fan, S. Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension. Nat. Commun. 7, 13731 (2016).

    Article  ADS  Google Scholar 

  87. Dong, J. W., Chen, X. D., Zhu, H., Wang, Y. & Zhang, X. Valley photonic crystals for control of spin and topology. Nat. Mater. 16, 298–302 (2016).

    Article  ADS  Google Scholar 

  88. St-Jean, P. et al. Lasing in topological edge states of a 1D lattice. Preprint at https://arxiv.org/abs/1704.07310 (2017).

  89. Peano, V., Houde, M., Marquardt, F. & Clerk, A. A. Topological quantum fluctuations and traveling wave amplifiers. Phys. Rev. X 6, 041026 (2016).

    Google Scholar 

  90. Peano, V., Brendel, C., Schmidt, M. & Marquardt, F. Topological phases of sound and light. Phys. Rev. X 5, 031011 (2015).

    Google Scholar 

  91. Karzig, T., Bardyn, C.-E., Lindner, N. H. & Refael, G. Topological polaritons. Phys. Rev. X 5, 031001 (2015).

    Google Scholar 

  92. Nalitov, A.  V., Solnyshkov, D. D. & Malpuech, G. Polariton Z topological insulator. Phys. Rev. Lett. 114, 116401 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  93. Milićević, M. et al. Orbital edge states in a photonic honeycomb lattice. Phys. Rev. Lett. 118, 107403 (2017).

    Article  ADS  Google Scholar 

  94. Umucalılar, R. O. & Carusotto, I. Fractional quantum Hall states of photons in an array of dissipative coupled cavities. Phys. Rev. Lett. 108, 206809 (2012).

    Article  ADS  Google Scholar 

  95. Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    Article  ADS  Google Scholar 

  96. Hafezi, M., Lukin, M. D. & Taylor, J. M. Non-equilibrium fractional quantum Hall state of light. New J. Phys. 15, 063001 (2013).

    Article  ADS  Google Scholar 

  97. Hormozi, L., Moller, G. & Simon, S. H. Fractional quantum Hall effect of lattice bosons near commensurate flux. Phys. Rev. Lett. 108, 256809 (2012).

    Article  ADS  Google Scholar 

  98. Zeuner, J. M. et al. Observation of a topological transition in the bulk of a non-Hermitian system. Phys. Rev. Lett. 115, 040402 (2015).

    Article  ADS  Google Scholar 

  99. Harari, G. et al. in Conference on Lasers and Electro-Optics, OSA Technical Digest paper FM3A.3 (Optical Society of America, 2016).

Download references

Acknowledgements

A.B.K. acknowledges the support of the National Science Foundation under grants no. CMMI-1537294 and no. EFRI-1641069. G.S. acknowledges the support of the Air Force Office of Scientific Research (AFOSR) under a grant no. FA9550-15-1-0075, and of the Army Research Office (ARO) under a grant no. W911NF-17-1-0479.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Grove School of Engineering, The City College of the City University of New York, New York, NY, USA

    Alexander B. Khanikaev

  2. Graduate Center of the City University of New York, New York, NY, USA

    Alexander B. Khanikaev

  3. School of Applied and Engineering Physics, Cornell University, Ithaca, New York, USA

    Gennady Shvets

Authors
  1. Alexander B. Khanikaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gennady Shvets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gennady Shvets.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khanikaev, A.B., Shvets, G. Two-dimensional topological photonics. Nature Photon 11, 763–773 (2017). https://doi.org/10.1038/s41566-017-0048-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-017-0048-5

This article is cited by

Search

Advanced search

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