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Asymmetric parametric generation of images with nonlinear dielectric metasurfaces


Subwavelength dielectric resonators assembled into metasurfaces have become a versatile tool for miniaturizing optical components approaching the nanoscale1,2,3. An important class of metasurface functionalities is associated with asymmetry in both the generation and transmission of light with respect to reversals of the positions of emitters and receivers4,5,6. The nonlinear light–matter interaction in metasurfaces7,8,9 offers a promising pathway towards miniaturization of the asymmetric control of light. Here we demonstrate asymmetric parametric generation of light in nonlinear metasurfaces. We assemble dissimilar nonlinear dielectric resonators into translucent metasurfaces that produce images in the visible spectral range on being illuminated by infrared radiation. By design, the metasurfaces produce different and completely independent images for the reversed direction of illumination, that is, when the positions of the infrared emitter and the visible light receiver are exchanged. Nonlinearity-enabled asymmetric control of light by subwavelength resonators paves the way towards novel nanophotonic components via dense integration of large quantities of nonlinear resonators into compact metasurface designs.

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Fig. 1: Concept of asymmetric parametric generation of images with a nonlinear metasurface.
Fig. 2: Optical properties of a metasurface unit cell.
Fig. 3: Symmetric linear and asymmetric nonlinear spectral response of a uniform metasurface.
Fig. 4: Set of resonators with dissimilar asymmetric parametric generation of light.
Fig. 5: Asymmetric parametric generation of images with nonlinear metasurfaces.

Data availability

All data in this study are available within the paper and the Supplementary Information. Additional information will be provided by S.K. and L.W. on reasonable request.

Code availability

The code used for modelling the data is available for download at Additional information will be provided by L.W. on reasonable request.


  1. Kruk, S. S. & Kivshar, Y. S. Functional meta-optics and nanophotonics governed by Mie resonances. ACS Photonics 4, 2638–2649 (2017).

    Article  Google Scholar 

  2. Chen, W. T., Zhu, A. Y. & Capasso, F. Flat optics with dispersion-engineered metasurfaces. Nat. Rev. Mater. 5, 604–620 (2020).

    Article  ADS  Google Scholar 

  3. Kamali, S. M., Arbabi, E., Arbabi, A. & Faraon, A. A review of dielectric optical metasurfaces for wavefront control. Nanophotonics 7, 1041–1068 (2018).

    Article  Google Scholar 

  4. Gallo, K., Assanto, G., Parameswaran, K. R. & Fejer, M. M. All-optical diode in a periodically poled lithium niobate waveguide. Appl. Phys. Lett. 79, 314–316 (2001).

    Article  ADS  Google Scholar 

  5. Lepri, S. & Casati, G. Asymmetric wave propagation in nonlinear systems. Phys. Rev. Lett. 106, 164101 (2011).

    Article  ADS  Google Scholar 

  6. Biancalana, F. All-optical diode action with quasiperiodic photonic crystals. J. Appl. Phys. 104, 93113 (2008).

    Article  Google Scholar 

  7. Li, G., Zhang, S. & Zentgraf, T. Nonlinear photonic metasurfaces. Nat. Rev. Mater. 2, 17010 (2017).

    Article  ADS  Google Scholar 

  8. Krasnok, A., Tymchenko, M. & Alù, A. Nonlinear metasurfaces: a paradigm shift in nonlinear optics. Mater. Today 21, 8–21 (2017).

    Article  Google Scholar 

  9. Zubyuk, V., Carletti, L., Shcherbakov, M. & Kruk, S. Resonant dielectric metasurfaces in strong optical fields. APL Mater. 9, 060701 (2021).

    Article  ADS  Google Scholar 

  10. Schlickriede, C. et al. Imaging through nonlinear metalens using second harmonic generation. Adv. Opt. Mater. 30, 1703843 (2018).

    Article  Google Scholar 

  11. D’Aguanno, G. et al. Nonlinear topological transitions over a metasurface. Phys. Rev. B 100, 214310 (2019).

    Article  ADS  Google Scholar 

  12. Huang, Z., Baron, A., Larouche, S., Argyropoulos, C. & Smith, D. R. Optical bistability with film-coupled metasurfaces. Opt. Lett. 40, 5638–5641 (2015).

    Google Scholar 

  13. Divitt, S., Zhu, W., Zhang, C., Lezec, H. J. & Agrawal, A. Ultrafast optical pulse shaping using dielectric metasurfaces. Science 364, 890–894 (2019).

    Article  ADS  Google Scholar 

  14. Koshelev, K. et al. Subwavelength dielectric resonators for nonlinear nanophotonics. Science 367, 288–292 (2020).

    Article  ADS  Google Scholar 

  15. Bender, N. et al. Observation of asymmetric transport in structures with active nonlinearities. Phys. Rev. Lett. 110, 234101 (2013).

    Article  ADS  Google Scholar 

  16. Shitrit, N. et al. Asymmetric free-space light transport at nonlinear metasurfaces. Phys. Rev. Lett. 121, 046101 (2018).

    Article  ADS  Google Scholar 

  17. Mahmoud, A. M., Davoyan, A. R. & Engheta, N. All-passive nonreciprocal metastructure. Nat. Commun. 6, 8359 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Kim, K. H. Asymmetric second-harmonic generation with high efficiency from a non-chiral hybrid bilayer complementary metasurface. Plasmonics 16, 77–82 (2021).

    Article  Google Scholar 

  20. Lawrence, M., Barton, D. R. & Dionne, J. A. Nonreciprocal flat optics with silicon metasurfaces. Nano Lett. 18, 1104–1109 (2018).

    Article  ADS  Google Scholar 

  21. Jin, B. & Argyropoulos, C. Self-induced passive nonreciprocal transmission by nonlinear bifacial dielectric metasurfaces. Phys. Rev. Appl. 13, 054056 (2020).

    Article  ADS  Google Scholar 

  22. Cheng, L. et al. Superscattering, superabsorption and nonreciprocity in nonlinear antennas. ACS Photonics 8, 585–591 (2021).

    Article  Google Scholar 

  23. Asadchy, V. S., Díaz-Rubio, A. & Tretyakov, S. A. Bianisotropic metasurfaces: physics and applications. Nanophotonics 7, 1069–1094 (2018).

    Article  Google Scholar 

  24. Kruk, S. et al. Nonlinear light generation in topological nanostructures. Nat. Nanotechnol. 14, 126–130 (2019).

    Article  ADS  Google Scholar 

  25. Zhao, Y., Belkin, M. A. & Alù, A. Twisted optical metamaterials for planarized ultrathin broadband circular polarizers. Nat. Commun. 3, 870 (2012).

    Article  ADS  Google Scholar 

  26. Svirko, Y., Zheludev, N. & Osipov, M. Layered chiral metallic microstructures with inductive coupling. Appl. Phys. Lett. 78, 498–500 (2001).

    Article  ADS  Google Scholar 

  27. Menzel, C. et al. Asymmetric transmission of linearly polarized light at optical metamaterials. Phys. Rev. Lett. 104, 253902 (2010).

    Article  ADS  Google Scholar 

  28. Pfeiffer, C., Zhang, C., Ray, V., Guo, L. J. & Grbic, A. High performance bianisotropic metasurfaces: asymmetric transmission of light. Phys. Rev. Lett. 113, 023902 (2014).

    Article  ADS  Google Scholar 

  29. Ra’Di, Y., Asadchy, V. S. & Tretyakov, S. A. Tailoring reflections from thin composite metamirrors. IEEE Trans. Antennas Propag. 62, 3749–3760 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  30. Albooyeh, M., Alaee, R., Rockstuhl, C. & Simovski, C. Revisiting substrate-induced bianisotropy in metasurfaces. Phys. Rev. B 91, 195304 (2015).

    Article  ADS  Google Scholar 

  31. Zhirihin, D. V. et al. Photonic spin Hall effect mediated by bianisotropy. Opt. Lett. 44, 1694–1697 (2019).

    Article  ADS  Google Scholar 

  32. Gorlach, A. A., Zhirihin, D. V., Slobozhanyuk, A. P., Khanikaev, A. B. & Gorlach, M. A. Photonic Jackiw-Rebbi states in all-dielectric structures controlled by bianisotropy. Phys. Rev. B 99, 205122 (2019).

    Article  ADS  Google Scholar 

  33. Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater. 12, 233–239 (2012).

    Article  ADS  Google Scholar 

  34. Albooyeh, M. et al. Purely bianisotropic scatterers. Phys. Rev. B 94, 245428 (2016).

    Article  ADS  Google Scholar 

  35. Ra’Di, Y. & Tretyakov, S. A. Balanced and optimal bianisotropic particles: maximizing power extracted from electromagnetic fields. New J. Phys. 15, 053008 (2013).

    Article  ADS  MATH  Google Scholar 

  36. Grahn, P., Shevchenko, A. & Kaivola, M. Electromagnetic multipole theory for optical nanomaterials. New J. Phys. 14, 093033 (2012).

    Article  ADS  MATH  Google Scholar 

  37. Multipole Analysis of Electromagnetic Scattering (COMSOL. 2015);

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We thank V. Asadchy, A. Alu, C. Caloz, A. Poddubny, D. Smirnova, K. Simovski, I. Shadrivov and S. Tretyakov for numerous stimulating discussions. We acknowledge the use of the nanofabrication facility at Paderborn University and acknowledge the Australian National Fabrication Facility, ACT Node, for access to the electron microscope. S.S.K. acknowledges support from the Alexander von Humboldt Foundation, the Australian Research Council (DE210100679) and the EU Horizon 2020 research and innovation programme (grant no. 896735). Z.D. acknowledges help from F. Tjiptoharsono with the fabrication etching recipe. T.Z. acknowledges funding by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 724306) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation; TRR142, no. 231447078, project B09). L.W. acknowledges support from the National Key R&D Program of China (2020YFB1806603), the National Natural Science Foundation of China (grant no. 62101127), the Natural Science Foundation of Jiangsu Province of China (BK20200393), SC project of Jiangsu Province (JSSCBS20210116) and the Fundamental Research Funds for the Central Universities (2242022R10025). Y.K. acknowledges support from the Strategic Fund of the Australian National University, the Australian Research Council (grant no. DP210101292) and the US Army International Office (grant no. FA520921P0034).

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Authors and Affiliations



S.S.K. and L.W. conceived the idea. L.W. performed theoretical calculations. B.S., Z.D. and S.S.K. fabricated the samples. S.S.K. and L.W. performed experimental measurements. J.Y., T.Z. and Y.K. contributed to data analysis and to supervision of the project. S.S.K. wrote the first version of the manuscript. All co-authors contributed extensively to writing and to revisions of the manuscript.

Corresponding authors

Correspondence to Sergey S. Kruk, Lei Wang or Yuri Kivshar.

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Nature Photonics thanks Christos Argyropoulos, Yuanmu Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–4, Discussion and Tables 1–7.

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Kruk, S.S., Wang, L., Sain, B. et al. Asymmetric parametric generation of images with nonlinear dielectric metasurfaces. Nat. Photon. 16, 561–565 (2022).

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