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.

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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


  1. Nonlinear Physics Centre, Australian National University, Canberra, Australian Capital Territory, Australia

    • Sergey Kruk
    • , Alexander Poddubny
    • , Daria Smirnova
    • , Lei Wang
    •  & Yuri Kivshar
  2. ITMO University, St Petersburg, Russia

    • Alexander Poddubny
    • , Alexey Slobozhanyuk
    •  & Yuri Kivshar
  3. Ioffe Institute, St Petersburg, Russia

    • Alexander Poddubny
  4. Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod, Russia

    • Daria Smirnova
  5. Lomonosov Moscow State University, Moscow, Russia

    • Alexander Shorokhov
  6. Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    • Ivan Kravchenko
  7. Laser Physics Centre, Australian National University, Canberra, Australian Capital Territory, Australia

    • Barry Luther-Davies


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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.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Yuri Kivshar.

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    Supplementary Notes 1–6; supplementary figures 1–12

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