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
Relevant articles
Open Access articles citing this article.
-
Hybrid topological photonic crystals
Nature Communications Open Access 25 July 2023
-
A topological nonlinear parametric amplifier
Nature Communications Open Access 24 November 2022
-
Topological polarization singular lasing with highly efficient radiation channel
Nature Communications Open Access 30 October 2022
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
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





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
Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological states in photonic systems. Nat. Phys. 12, 626–629 (2016).
Khanikaev, A. B. & Shvets, G. Two-dimensional topological photonics. Nat. Photon. 11, 763–773 (2017).
St-Jean, P. et al. Lasing in topological edge states of a one-dimensional lattice. Nat. Photon. 11, 651–656 (2017).
Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017).
Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).
Barik, S. et al. A topological quantum optics interface. Science 359, 666 (2018).
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).
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).
Leykam, D. & Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators. Phys. Rev. Lett. 117, 143901 (2016).
Bardyn, C.-E., Karzig, T., Refael, G. & Liew, T. C. H. Chiral Bogoliubov excitations in nonlinear bosonic systems. Phys. Rev. B 93, 020502 (2016).
Kartashov, Y. V. & Skryabin, D. V. Bistable topological insulator with exciton-polaritons. Phys. Rev. Lett. 119, 253904 (2017).
Zhou, X., Wang, Y., Leykam, D. & Chong, Y. D. Optical isolation with nonlinear topological photonics. New J. Phys. 19, 095002 (2017).
Fan, L. et al. An all-silicon passive optical diode. Science 335, 447–450 (2011).
Li, E., Eggleton, B. J., Fang, K. & Fan, S. Photonic Aharonov–Bohm effect in photon–phonon interactions. Nat. Commun. 5, E3225 (2014).
Shi, Y., Yu, Z. & Fan, S. Limitations of nonlinear optical isolators due to dynamic reciprocity. Nat. Photon. 9, 388–392 (2015).
Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).
Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).
Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).
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).
Poddubny, A., Miroshnichenko, A., Slobozhanyuk, A. & Kivshar, Y. Topological Majorana states in zigzag chains of plasmonic nanoparticles. ACS Photonics 1, 101 (2014).
Sinev, I. S. et al. Mapping plasmonic topological states at the nanoscale. Nanoscale 7, 11904 (2015).
Kruk, S. et al. Edge states and topological phase transitions in chains of dielectric nanoparticles. Small 13, 1603190 (2017).
Smirnova, D. & Kivshar, Y. S. Multipolar nonlinear nanophotonics. Optica 3, 1241–1255 (2016).
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).
Hadad, Y., Soric, J. C., Khanikaev, A. B. & Alù, A. Self-induced topological protection in nonlinear circuit arrays. Nat. Electron. 1, 178–182 (2018).
Shen, S.-Q. Topological Insulators. Dirac Equation in Condensed Matters (Springer, Heidelberg, 2013).
Rose, A., Huang, D. & Smith, D. R. Nonlinear interference and unidirectional wave mixing in metamaterials. Phys. Rev. Lett. 110, 063901 (2013).
Poutrina, E. & Urbas, A. Multipolar interference for non-reciprocal nonlinear generation. Sci. Rep. 6, 25113 (2016).
Alaee, R. et al. All-dielectric reciprocal bianisotropic nanoparticles. Phys. Rev. B 92, 245130 (2015).
Slobozhanyuk, A. et al. Three-dimensional all-dielectric photonic topological insulator. Nat. Photon. 11, 130–136 (2016).
O’Brien, K. et al. Predicting nonlinear properties of metamaterials from the linear response. Nat. Mater. 14, 379–383 (2015).
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).
Lu, L. et al. Experimental observation of Weyl points. Science 349, 622 (2015).
Wang, L. et al. Nonlinear wavefront control with all-dielectric metasurfaces. Nano Lett. 18, 3978–3984 (2018).
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
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
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
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41565-018-0324-7
This article is cited by
-
Unidirectional unpolarized luminescence emission via vortex excitation
Nature Photonics (2023)
-
Non-Hermitian topological phase transitions controlled by nonlinearity
Nature Physics (2023)
-
Hybrid topological photonic crystals
Nature Communications (2023)
-
Asymmetric parametric generation of images with nonlinear dielectric metasurfaces
Nature Photonics (2022)
-
Asymmetric topological pumping in nonparaxial photonics
Nature Communications (2022)