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.

  • Letter
  • Published:

Nonlinear light generation in topological nanostructures

Abstract

Topological photonics has emerged as a route to robust optical circuitry protected against disorder1,2 and now includes demonstrations such as topologically protected lasing3,4,5 and single-photon transport6. Recently, nonlinear optical topological structures have attracted special theoretical interest7,8,9,10,11, as they enable tuning of topological properties by a change in the light intensity7,12 and can break optical reciprocity13,14,15 to realize full topological protection. However, so far, non-reciprocal topological states have only been realized using magneto-optical materials and macroscopic set-ups with external magnets4,16, which is not feasible for nanoscale integration. Here we report the observation of a third-harmonic signal from a topologically non-trivial zigzag array of dielectric nanoparticles and the demonstration of strong enhancement of the nonlinear photon generation at the edge states of the array. The signal enhancement is due to the interaction between the Mie resonances of silicon nanoparticles and the topological localization of the electric field at the edges. The system is also robust against various perturbations and structural defects. Moreover, we show that the interplay between topology, bi-anisotropy and nonlinearity makes parametric photon generation tunable and non-reciprocal. Our study brings nonlinear topological photonics concepts to the realm of nanoscience.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Fig. 1: Nonlinear parametric generation of light from topological zigzag arrays.
Fig. 2: Experimental observations of the third-harmonic signal from zigzag arrays.
Fig. 3: Topological protection of the edge states against disorder.
Fig. 4: Spectral and directional control of the third-harmonic hot spots.
Fig. 5: Theoretical analysis of the control of THG hotspots in zigzag arrays.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

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

    Article  CAS  Google Scholar 

  2. Khanikaev, A. B. & Shvets, G. Two-dimensional topological photonics. Nat. Photon. 11, 763–773 (2017).

    Article  CAS  Google Scholar 

  3. St-Jean, P. et al. Lasing in topological edge states of a one-dimensional lattice. Nat. Photon. 11, 651–656 (2017).

    Article  CAS  Google Scholar 

  4. Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017).

    Article  CAS  Google Scholar 

  5. Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).

    Article  Google Scholar 

  6. Barik, S. et al. A topological quantum optics interface. Science 359, 666 (2018).

    Article  CAS  Google Scholar 

  7. Hadad, Y., Khanikaev, A. B. & Alù, A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials. Phys. Rev. B 93, 155112 (2016).

    Article  Google Scholar 

  8. Solnyshkov, D. D., Nalitov, A. V. & Malpuech, G. Kibble–Zurek mechanism in topologically nontrivial zigzag chains of polariton micropillars. Phys. Rev. Lett. 116, 046402 (2016).

    Article  CAS  Google Scholar 

  9. Leykam, D. & Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators. Phys. Rev. Lett. 117, 143901 (2016).

    Article  Google Scholar 

  10. Bardyn, C.-E., Karzig, T., Refael, G. & Liew, T. C. H. Chiral Bogoliubov excitations in nonlinear bosonic systems. Phys. Rev. B 93, 020502 (2016).

    Article  Google Scholar 

  11. Kartashov, Y. V. & Skryabin, D. V. Bistable topological insulator with exciton-polaritons. Phys. Rev. Lett. 119, 253904 (2017).

    Article  Google Scholar 

  12. Zhou, X., Wang, Y., Leykam, D. & Chong, Y. D. Optical isolation with nonlinear topological photonics. New J. Phys. 19, 095002 (2017).

    Article  Google Scholar 

  13. Fan, L. et al. An all-silicon passive optical diode. Science 335, 447–450 (2011).

    Article  Google Scholar 

  14. Li, E., Eggleton, B. J., Fang, K. & Fan, S. Photonic Aharonov–Bohm effect in photon–phonon interactions. Nat. Commun. 5, E3225 (2014).

    Article  Google Scholar 

  15. Shi, Y., Yu, Z. & Fan, S. Limitations of nonlinear optical isolators due to dynamic reciprocity. Nat. Photon. 9, 388–392 (2015).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Blanco-Redondo, A. et al. Topological optical waveguiding in silicon and the transition between topological and trivial defect states. Phys. Rev. Lett. 116, 163901 (2016).

    Article  Google Scholar 

  20. Poddubny, A., Miroshnichenko, A., Slobozhanyuk, A. & Kivshar, Y. Topological Majorana states in zigzag chains of plasmonic nanoparticles. ACS Photonics 1, 101 (2014).

    Article  CAS  Google Scholar 

  21. Sinev, I. S. et al. Mapping plasmonic topological states at the nanoscale. Nanoscale 7, 11904 (2015).

    Article  CAS  Google Scholar 

  22. Kruk, S. et al. Edge states and topological phase transitions in chains of dielectric nanoparticles. Small 13, 1603190 (2017).

  23. Smirnova, D. & Kivshar, Y. S. Multipolar nonlinear nanophotonics. Optica 3, 1241–1255 (2016).

    Article  CAS  Google Scholar 

  24. 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).

    Article  Google Scholar 

  25. Hadad, Y., Soric, J. C., Khanikaev, A. B. & Alù, A. Self-induced topological protection in nonlinear circuit arrays. Nat. Electron. 1, 178–182 (2018).

    Article  Google Scholar 

  26. Shen, S.-Q. Topological Insulators. Dirac Equation in Condensed Matters (Springer, Heidelberg, 2013).

  27. Rose, A., Huang, D. & Smith, D. R. Nonlinear interference and unidirectional wave mixing in metamaterials. Phys. Rev. Lett. 110, 063901 (2013).

    Article  Google Scholar 

  28. Poutrina, E. & Urbas, A. Multipolar interference for non-reciprocal nonlinear generation. Sci. Rep. 6, 25113 (2016).

    Article  CAS  Google Scholar 

  29. Alaee, R. et al. All-dielectric reciprocal bianisotropic nanoparticles. Phys. Rev. B 92, 245130 (2015).

    Article  Google Scholar 

  30. Slobozhanyuk, A. et al. Three-dimensional all-dielectric photonic topological insulator. Nat. Photon. 11, 130–136 (2016).

    Article  Google Scholar 

  31. O’Brien, K. et al. Predicting nonlinear properties of metamaterials from the linear response. Nat. Mater. 14, 379–383 (2015).

    Article  Google Scholar 

  32. Kujala, S., Canfield, B. K., Kauranen, M., Svirko, Y. & Turunen, J. Multipole interference in the second-harmonic optical radiation from gold nanoparticles. Phys. Rev. Lett. 98, 167403 (2007).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  34. Wang, L. et al. Nonlinear wavefront control with all-dielectric metasurfaces. Nano Lett. 18, 3978–3984 (2018).

Download references

Acknowledgements

The authors acknowledge financial support from the Australian Research Council and the Strategic Fund of the Australian National University. A part of this research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. Numerical calculations were supported in part by the Ministry of Education and Science of the Russian Federation (Zadanie no. 3.2465.2017/4.6) and the Russian Foundation for Basic Research (grant no. 18-02-00381). A.P. and A.Sl. acknowledge partial support from the Russian Foundation for Basic Research (grant no. 18-32-20065). Y.K. thanks H. Atwater, B. Kanté, D. Leykam and E. Poutrina for discussions.

Author information

Authors and Affiliations

Authors

Contributions

S.K., A.Sl. and Y.K. conceived the idea. S.K., A.Sh. and B.L.-D. performed the experimental measurements. A.P. and D.S. developed the discrete dipole theoretical model. D.S., L.W. and A.Sl. performed numerical calculations. I.K. and S.K. fabricated the samples. Y.K. supervised the project. All authors contributed to the discussion of results and manuscript preparation.

Corresponding author

Correspondence to Yuri Kivshar.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Notes 1–6; supplementary figures 1–12

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kruk, S., Poddubny, A., Smirnova, D. et al. Nonlinear light generation in topological nanostructures. Nature Nanotech 14, 126–130 (2019). https://doi.org/10.1038/s41565-018-0324-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-018-0324-7

This article is cited by

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