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 data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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).
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.
The authors declare no competing interests.
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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
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