# Three-dimensional all-dielectric photonic topological insulator

## Abstract

The discovery of two-dimensional topological photonic systems has transformed our views on the propagation and scattering of electromagnetic waves, and the quest for similar states in three dimensions is open. Here, we theoretically demonstrate that it is possible to design symmetry-protected three-dimensional topological states in an all-dielectric platform, with the electromagnetic duality between electric and magnetic fields being ensured by the structure design. Magneto-electrical coupling plays the role of a synthetic gauge field that determines a topological transition to an ‘insulating’ regime with a complete three-dimensional photonic bandgap. We reveal the emergence of surface states with conical Dirac dispersion and spin-locking, and we numerically confirm robust propagation of the surface states along two-dimensional domain walls with first-principles studies. The proposed system represents a table-top platform capable of emulating the relativistic dynamics of massive Dirac fermions and the surface states can be interpreted as Jackiw–Rebbi states bound to the interface separating domains with particles of opposite masses.

## Access options

from\$8.99

All prices are NET prices.

## References

1. 1

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

2. 2

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

3. 3

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

4. 4

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

5. 5

Prodan, E. & Prodan, C. Topological phonon modes and their role in dynamic instability of microtubules. Phys. Rev. Lett. 103, 248101 (2009).

6. 6

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

7. 7

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

8. 8

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

9. 9

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

10. 10

Kane, C. L. & Lubensky, T. C. Topological boundary modes in isostatic lattices. Nat. Phys. 10, 39–45 (2014).

11. 11

Süsstrunk, R . & Huber, S. D. Observation of phononic helical edge states in a mechanical topological insulator. Science 349, 47–50 (2015).

12. 12

Xiao, M. et al. Geometric phase and band inversion in periodic acoustic systems. Nat. Phys. 11, 240–244 (2015).

13. 13

Yang, Z. et al. Topological acoustics. Phys. Rev. Lett. 114, 114301 (2015).

14. 14

Khanikaev, A. B., Fleury, R., Mousavi, S. H. & Alù, A. Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice. Nat. Commun. 6, 8260 (2015).

15. 15

Lu, L. et al. Experimental observation of Weyl points. Science 349, 622–624 (2015).

16. 16

Nash, L. M. et al. Topological mechanics of gyroscopic metamaterials. Proc. Natl Acad. Sci. USA 112, 14495–14500 (2015).

17. 17

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

18. 18

Wang, P., Lu, L. & Bertoldi, K. Topological phononic crystals with one-way elastic edge waves. Phys. Rev. Lett. 115, 104302 (2015).

19. 19

Mousavi, S. H., Khanikaev, A. B. & Wang, Z. Topologically protected elastic waves in phononic metamaterials. Nat. Commun. 6, 8682 (2015).

20. 20

Slobozhanyuk, A. P., Poddubny, A. N., Miroshnichenko, A. E., Belov, P. A. & Kivshar, Y. S. Subwavelength topological edge states in optically resonant dielectric structures. Phys. Rev. Lett. 114, 123901 (2015).

21. 21

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

22. 22

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

23. 23

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).

24. 24

Huber, S. D. Topological mechanic. Nat. Phys. 12, 621–623 (2016).

25. 25

Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological states in photonic systems. Nat. Phys. 12, 626–629 (2016).

26. 26

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

27. 27

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).

28. 28

Lu, L. et al. Symmetry-protected topological photonic crystal in three dimensions. Nat. Phys. 12, 337–340 (2016).

29. 29

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

30. 30

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

31. 31

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).

32. 32

Fleury, R., Khanikaev, A. & Alu, A. Floquet topological insulators for sound. Nat. Commun. 7, 11744 (2016).

33. 33

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

34. 34

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

35. 35

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

36. 36

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

37. 37

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

38. 38

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).

39. 39

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

40. 40

Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).

41. 41

Jahani, S. & Jacob, Z. All-dielectric metamaterials. Nat. Nanotech. 11, 23–36 (2016).

42. 42

Ringel, Z., Kraus, Y. E. & Stern, A. Strong side of weak topological insulators. Phys. Rev. B 86, 045102 (2012).

43. 43

Bliokh, K. Y., Smirnova, D. & Nori, F. Quantum spin Hall effect of light. Science 348, 1448–1451 (2015).

44. 44

Schnyder, A. P., Ryu, S., Furusaki, A. & Ludwig, A. W. W. Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008).

45. 45

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

46. 46

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

47. 47

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

48. 48

Jackiw, R. & Rebbi, C. Solitons with fermion number 1/2. Phys. Rev. D 13, 3398–3409 (1976).

## Acknowledgements

The authors are grateful to L. Lu and A. Poddubny for many enlightening comments, useful discussions and suggestions. This work was supported by the National Science Foundation (CMMI-1537294 and EFRI-1641069). Research was partly carried out at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-SC0012704. This work was partially supported by the Australian Research Council. A.S. and A.B.K. acknowledge that the large scale numerical simulations were supported by the Russian Science Foundation (grant no.16-19-10538). A.S. acknowledges support from the IEEE MTT-S and Photonics Graduate Fellowships.

## Author information

Authors

### Contributions

All authors contributed extensively to the work presented in this paper.

### Corresponding author

Correspondence to Alexander B. Khanikaev.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 1529 kb)

## Rights and permissions

Reprints and Permissions

Slobozhanyuk, A., Mousavi, S., Ni, X. et al. Three-dimensional all-dielectric photonic topological insulator. Nature Photon 11, 130–136 (2017). https://doi.org/10.1038/nphoton.2016.253

• Accepted:

• Published:

• Issue Date:

• ### Three-Dimensional Visualization Algorithm Simulation of Construction Management Based on GIS and VR Technology

• Shuhong Xu
•  & Wei Wang

Complexity (2021)

• ### Superscattering, Superabsorption, and Nonreciprocity in Nonlinear Antennas

• Lin Cheng
• , Rasoul Alaee
• , Akbar Safari
• , Lei Zhang
•  & Robert W. Boyd

ACS Photonics (2021)

• ### Nonspecular effects in the vicinity of a photonic Dirac point

• Qiang Yang
• , Wenhao Xu
• , Shizhen Chen
• , Shuangchun Wen
•  & Hailu Luo

Physical Review A (2021)

• ### Dielectric Resonant Metaphotonics

• Kirill Koshelev
•  & Yuri Kivshar

ACS Photonics (2021)

• ### An elastic higher-order topological insulator based on kagome phononic crystals

• Zhen Wang
•  & Qi Wei

Journal of Applied Physics (2021)