Skip to main content

Thank you for visiting 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.

Giant broadband refraction in the visible in a ferroelectric perovskite


In principle, materials with a broadband giant index of refraction (n > 10) overcome chromatic aberration and shrink the diffraction limit down to the nanoscale, allowing new opportunities for nanoscopic imaging1. They also open alternative avenues for the management of light to improve the performance of photovoltaic cells2. Recent advances have demonstrated the feasibility of a giant refractive index in metamaterials at microwave and terahertz frequencies3,4, but the highest reported broadband index of refraction in the visible is n < 5 (ref. 5). Here, we report a ferroelectric perovskite with an index of refraction of n > 26 across the entire visible spectrum and demonstrate its behaviour using white-light and laser refraction and diffraction experiments. The sample, a solid-solution K0.997Ta0.64Nb0.36:Li0.003 (KTN:Li) perovskite6,7,8,9,10,11,12, has a naturally occurring room-temperature phase that propagates visible light along its normal axis without significant diffraction or chromatic dispersion, irrespective of beam size, intensity and angle of incidence.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


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

Fig. 1: Giant refraction.
Fig. 2: White-light experiments.
Fig. 3: Monochromatic experiments and the physical origin of GR.

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.


  1. Hell, S. W. Far-field optical nanoscopy. Science 316, 1153–1158 (2007).

    Article  ADS  Google Scholar 

  2. Brongersma, M. L., Cui, Y. & Fan, S. Light management for photovoltaics using high-index nanostructures. Nat. Mater. 13, 451–460 (2014).

    Article  ADS  Google Scholar 

  3. Chang, T. et al. Broadband giant-refractive-index material based on mesoscopic space-filling curves. Nat. Commun. 7, 12661 (2016).

    Article  ADS  Google Scholar 

  4. Choi, M. et al. A terahertz metamaterial with unnaturally high refractive index. Nature 470, 369–374 (2011).

    Article  ADS  Google Scholar 

  5. Palik, E. D. Handbook of Optical Constants of Solids (Academic Press, Cambridge, 1998).

    Chapter  Google Scholar 

  6. Cohen, R. E. Origin of ferroelectricity in perovskite oxides. Nature 358, 136–138 (1992).

    Article  ADS  Google Scholar 

  7. Bokov, A. A. & Ye, Z. G. Dielectric relaxation in relaxor ferroelectrics. J. Adv. Dielectrics 2, 1241010 (2012).

    Article  Google Scholar 

  8. Shvartsman, V. V. & Lupascu, D. C. Lead-free relaxor ferroelectrics. J. Am. Ceram. Soc. 95, 1–26 (2012).

    Article  Google Scholar 

  9. Burschka, J. et al. Sequential deposition as a route to high-performance perovskite-sensitized solar cells. Nature 499, 316–319 (2013).

    Article  ADS  Google Scholar 

  10. Rahaman, M. M., Imai, T., Sakamoto, T., Tsukada, S. & Kojima, S. Fano resonance of Li-doped KTa1–xNbxO3 single crystals studied by Raman scattering. Sci. Rep. 6, 23898 (2016).

    Article  ADS  Google Scholar 

  11. Kutnjak, Z. & Pirc, R. Specific heat anomaly in relaxor ferroelectrics and dipolar glasses. J. Appl. Phys. 121, 105107 (2017).

    Article  ADS  Google Scholar 

  12. Tan, P. et al. Field-driven electro-optic dynamics of polar nanoregions in nanodisordered KTa1−xNbxO3 crystal. Appl. Phys. Lett. 111, 012903 (2017).

    Article  ADS  Google Scholar 

  13. Pierangeli, D. et al. Super-crystals in composite ferroelectrics. Nat. Commun. 7, 10674 (2016).

    Article  ADS  Google Scholar 

  14. Ferraro, M. et al. Observation of polarization-maintaining light propagation in depoled compositionally disordered ferroelectrics. Opt. Lett. 42, 3856–3859 (2017).

    Article  ADS  Google Scholar 

  15. Zhang, X. et al. Abnormal optical anisotropy in correlated disorder KTa1–xNbxO3:Cu with refractive index gradient. Sci. Rep. 8, 2892 (2018).

    Article  ADS  Google Scholar 

  16. Niu, S. et al. Giant optical anisotropy in a quasi-one-dimensional crystal. Nat. Photon. 12, 392–396 (2018).

    Article  ADS  Google Scholar 

  17. DelRe, E., Spinozzi, E., Agranat, A. J. & Conti, C. Scale-free optics and diffractionless waves in nanodisordered ferroelectrics. Nat. Photon. 5, 39–42 (2011).

    Article  ADS  Google Scholar 

  18. DelRe, E. et al. Subwavelength anti-diffracting beams propagating over more than 1,000 Rayleigh lengths. Nat. Photon. 9, 228–232 (2015).

    Article  ADS  Google Scholar 

  19. Di Mei, F. et al. Intrinsic negative mass from nonlinearity. Phys. Rev. Lett. 116, 153902 (2016).

    Article  ADS  Google Scholar 

  20. Chang, Y. C., Wang, C., Yin, S., Hoffman, R. C. & Mott, A. G. Giant electro-optic effect in nanodisordered KTN crystals. Opt. Lett. 38, 4574–4577 (2013).

    Article  ADS  Google Scholar 

  21. Pierangeli, D. et al. Observation of an intrinsic nonlinearity in the electro-optic response of freezing relaxors ferroelectrics. Opt. Mater. Express 4, 1487–1493 (2014).

    Article  ADS  Google Scholar 

  22. Gunter, P. & Hiugnard, J. P. (eds) Photorefractive Materials and Their Applications I (Springer, New York, 2006).

    Google Scholar 

  23. DelRe, E., Di Porto, P. & Crosignani, B. Photorefractive solitons and their underlying nonlocal physics. Progr. Opt. 53, 153–200 (2009).

    Article  ADS  Google Scholar 

  24. Aieta, F., Kats, M. A., Genevet, P. & Capasso, F. Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science 347, 1342–1345 (2015).

    Article  ADS  Google Scholar 

  25. Mansfield, S. M. & Kino, G. S. Solid immersion microscope. Appl. Phys. Lett. 57, 2615–2616 (1990).

    Article  ADS  Google Scholar 

  26. Pendry, J. B., Schrurig, D. E. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  27. Born, M. & Wolf, E. Principles of Optics (Cambridge Univ. Press, Cambridge, 2005).

    Google Scholar 

  28. Stranks, S. D. & Snaith, H. J. Metal-halide perovskites for photovoltaic and light-emitting devices. Nat. Nanotech. 10, 391–401 (2015).

    Article  ADS  Google Scholar 

  29. Chang, D. E., Vuletic, V. & Lukin, M. D. Quantum nonlinear optics—photon by photon. Nat. Photon. 8, 685–694 (2014).

    Article  ADS  Google Scholar 

  30. Caspani, L. et al. Integrated sources of photon quantum states based on nonlinear optics. Light Sci. Appl. 6, e17100 (2017).

    Article  Google Scholar 

  31. Yariv, A. Quantum Electronics (John Wiley & Sons, New York, 1967).

  32. Parravicini, J., DelRe, E., Agranat, A. J. & Parravicini, G. B. Liquid-solid directional composites and anisotropic dipolar phases of polar nanoregions in disordered perovskites. Nanoscale 9, 9572 (2017).

    Article  Google Scholar 

  33. Bons, P. C., de Haas, R., de Jong, D., Groot, A. & van der Straten, P. Quantum enhancement of the index of refraction in a Bose–Einstein condensate. Phys. Rev. Lett. 116, 173602 (2016).

    Article  ADS  Google Scholar 

Download references


The authors acknowledge funding from grants Sapienza 2016/2017 and Lazio Innova 2017. A.J.A. acknowledges the support of the Peter Brojde Center for Innovative Engineering.

Author information

Authors and Affiliations



F.D.M. and E.D. conceived and designed the experiments. F.D.M., L.F., M.F., D.P., P.D.P. and E.D. carried out the investigation and the experiments. A.J.A. designed and grew the crystal samples. All authors discussed the results and wrote the paper.

Corresponding author

Correspondence to F. Di Mei.

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

This file contains additional photographs and analysis.

Supplementary Video 1

A sequence of videos of the giant refraction effect.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Di Mei, F., Falsi, L., Flammini, M. et al. Giant broadband refraction in the visible in a ferroelectric perovskite. Nature Photon 12, 734–738 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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