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.

Solution-processed inorganic perovskite crystals as achromatic quarter-wave plates


Waveplates are widely used in photonics to control the polarization of light1,2. Often, they are fabricated from birefringent crystals that have different refractive indices along and normal to the crystal axis. Similar optical components are found in the natural world, including the eyes of mantis shrimp3,4 and the iridescence of giant clams5, fish6 and plants7. Optical retardation in biology relies on sophisticated self-assembly, whereas man-made systems comprise multiple-layered materials8,9,10,11. Here we report a discovery that bridges these two design principles. We observe wideband achromatic retardation in the visible and near-infrared (532–800 nm) regions for Cs4PbBr6 perovskite crystals embedded with CsPbBr3 nanocrystals. We explain our observations as matched dispersions of the refractive indices of the ordinary and extraordinary rays caused by the ordered embedding of the nanocrystals in the host. The wideband performance and ease of fabrication of these perovskite materials are attractive for future applications.

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

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: Illustration of crystal birefringence and the samples of Cs4PbBr6 crystals without and with embedded CsPbBr3 NCs.
Fig. 2: The measurement setup and the results of polarization modulation.
Fig. 3: The analysis of the degree of polarization measurements with fitting results.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


  1. Mitchell, S. An achromatic three-quarter wave plate for ultra-violet. Nature 212, 65–66 (1966).

    Article  ADS  Google Scholar 

  2. Samoylov, A. V., Samoylov, V. S., Vidmachenko, A. P. & Perekhod, A. V. Achromatic and super-achromatic zero-order waveplates. J. Quant. Spectrosc. Radiat. Transf. 88, 319–325 (2004).

    Article  ADS  Google Scholar 

  3. Roberts, N. W., Chiou, T. H., Marshall, N. J. & Cronin, T. W. A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region. Nat. Photonics 3, 641–644 (2009).

    Article  ADS  Google Scholar 

  4. Daly, I. M. et al. Dynamic polarization vision in mantis shrimps. Nat. Commun. 7, 12140 (2016).

    Article  ADS  Google Scholar 

  5. Holt, A. L., Vahidinia, S., Gagnon, Y. L., Morse, D. E. & Sweeney, A. M. Photosymbiotic giant clams are transformers of solar flux. J. R. Soc. Interface 11, 20140678 (2014).

    Article  Google Scholar 

  6. Feller, K. D., Jordan, T. M., Wilby, D. & Roberts, N. W. Selection of the intrinsic polarization properties of animal optical materials creates enhanced structural reflectivity and camouflage. Philos. Trans. R. Soc. Lond. B 372, 20160336 (2017).

    Article  Google Scholar 

  7. Jacobs, M. et al. Photonic multilayer structure of Begonia chloroplasts enhances photosynthetic efficiency. Nat. Plants 2, 16162 (2016).

    Article  Google Scholar 

  8. Saha, A., Bhattacharya, K. & Chakraborty, A. K. Achromatic quarter-wave plate using crystalline quartz. Appl. Opt. 51, 1976–1980 (2012).

    Article  ADS  Google Scholar 

  9. Nagai, M. et al. Achromatic THz wave plate composed of stacked parallel metal plates. Opt. Lett. 39, 146–149 (2014).

    Article  ADS  Google Scholar 

  10. Nagai, M. et al. Achromatic wave plate in THz frequency region based on parallel metal plate waveguides with a pillar array. Opt. Express 23, 4641–4649 (2015).

    Article  ADS  Google Scholar 

  11. Karimi, E. et al. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light Sci. Appl. 3, e167 (2014).

    Article  Google Scholar 

  12. Smartt, R. N. & Steel, W. H. Birefringence of quartz and calcite. J. Opt. Soc. Am. 49, 710–712 (1959).

    Article  ADS  Google Scholar 

  13. Beckers, J. M. Achromatic linear retarders. Appl. Opt. 10, 973–975 (1971).

    Article  ADS  Google Scholar 

  14. Mcintyre, C. M. & Harris, S. E. Achromatic wave plates for visible spectrum. J. Opt. Soc. Am. 58, 1575–1580 (1968).

    Article  ADS  Google Scholar 

  15. Koester, C. J. Achromatic combinations of half-wave plates. J. Opt. Soc. Am. 49, 405–409 (1959).

    Article  ADS  Google Scholar 

  16. Boulbry, B., Bousquet, B., Le Jeune, B., Guern, Y. & Lotrian, J. Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range. Opt. Express 9, 225–235 (2001).

    Article  ADS  Google Scholar 

  17. Peng, W. et al. Solution-Grown Monocrystalline hybrid perovskite films for hole-transporter-free solar cells. Adv. Mater. 28, 3383–3390 (2016).

    Article  Google Scholar 

  18. Chen, Z. et al. Thin single crystal perovskite solar cells to harvest below-bandgap light absorption. Nat. Commun. 8, 1890 (2017).

    Article  ADS  Google Scholar 

  19. Cao, Y. et al. Perovskite light-emitting diodes based on spontaneously formed submicrometre-scale structures. Nature 562, 249–253 (2018).

    Article  ADS  Google Scholar 

  20. Chen, M., Shan, X., Geske, T., Li, J. & Yu, Z. Manipulating ion migration for highly stable light-emitting diodes with single-crystalline organometal halide perovskite microplatelets. ACS Nano 11, 6312–6318 (2017).

    Article  Google Scholar 

  21. Hu, X. et al. Direct vapor growth of perovskite CsPbBr3 nanoplate electroluminescence devices. ACS Nano 11, 9869–9876 (2017).

    Article  Google Scholar 

  22. Liu, Y. et al. Thinness- and shape-controlled growth for ultrathin single-crystalline perovskite wafers for mass production of superior photoelectronic devices. Adv. Mater. 28, 9204–9209 (2016).

    Article  ADS  Google Scholar 

  23. Zhang, Q., Ha, S. T., Liu, X., Sum, T. C. & Xiong, Q. Room-temperature near-infrared high‑Q perovskite whispering-gallery planar nanolasers. Nano Lett. 14, 5995–6001 (2014).

    Article  ADS  Google Scholar 

  24. Ye, H. Y. et al. Metal-free three-dimensional perovskite ferroelectrics. Science 361, 151–155 (2018).

    Article  ADS  Google Scholar 

  25. Chen, X. M. et al. Centimeter-sized Cs4PbBr6 crystals with embedded CsPbBr3 nanocrystals showing superior photoluminescence: nonstoichiometry induced transformation and light-emitting applications. Adv. Funct. Mater. 28, 1706567 (2018).

    Article  Google Scholar 

  26. Zhang, Z. J. et al. Aqueous solution growth of millimeter-sized nongreen-luminescent wide bandgap Cs4PbBr6 bulk crystal. Cryst. Growth Des. 18, 6393–6398 (2018).

    Article  Google Scholar 

  27. Møller, C. K. On the structure of caesium hexahalogeno-plumbates (II). Matemat. Fysis. Meddel. 32, 1–27 (1959).

    Google Scholar 

  28. Powell, J. A. Refractive-index and birefringence of 2H silicon-carbide. J. Opt. Soc. Am. 62, 341–344 (1972).

    Article  ADS  Google Scholar 

  29. Walsh, T. E. Birefringence of cadmium sulfide single-crystals. J. Opt. Soc. Am. 62, 81–83 (1972).

    Article  ADS  Google Scholar 

  30. Kadro, J. M., Nonomura, K., Gachet, D., Gratzel, M. & Hagfeldt, A. Facile route to freestanding CH3NH3PbI3 crystals using inverse solubility. Sci. Rep. 5, 11654 (2015).

    Article  ADS  Google Scholar 

  31. Tan, J. C., Saines, P. J., Bithell, E. G. & Cheetham, A. K. Hybrid nanosheets of an inorganic–organic framework material: facile synthesis, structure, and elastic properties. ACS Nano 6, 615–621 (2012).

    Article  Google Scholar 

  32. Olivares, J. & Cabrera, J. M. Guided modes with ordinary refractive-index in proton-exchanged LiNbO3 wave-guides. Appl. Phys. Lett. 62, 2468–2470 (1993).

    Article  ADS  Google Scholar 

  33. Smith, D. S., Riccius, H. D. & Edwin, R. P. Refractive-indexes of lithium-niobate. Opt. Commun. 17, 332–335 (1976).

    Article  ADS  Google Scholar 

  34. Zhang, F. et al. Brightly luminescent and color-tunable colloidal CH3NH3PbX3 (X = Br, I, Cl) quantum dots: potential alternatives for display technology. ACS Nano 9, 4533–4542 (2015).

    Article  Google Scholar 

Download references


This work was supported by the National Natural Science Foundation of China (61722502, 61727808 and 12074037), the National Natural Science Foundation of China and Research Grants Council Joint Research Scheme (51761165021). G.D.S. acknowledges the Bio-Inspired Energy Program of CIFAR. We thank C. Ding for measuring the Tyndall light scattering, Y. Ge for fabricating the CdxZn1−xSeyS1−y@silica monolith, E. H. Sargent and R. Quintero-Bermudez for structural analysis, K. Shi for helpful discussions on the polarization measurement. We would like to thank BIT Experimental Center of Advanced Materials for providing the experimental equipments.

Author information

Authors and Affiliations



H.Z. conceived and supervised the project. X.C., W.-g.L. and J.T. fabricated the materials. X.C., W.-g.L. and Y.W. carried out the spectroscopic measurements. Y.Z. proposed the theoretical model and performed the fitting. H.Z., G.D.S., X.C., Y.W. and Y.Z. wrote the manuscript with contribution from all the authors.

Corresponding authors

Correspondence to Yongyou Zhang or Haizheng Zhong.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Photonics thanks Daniela Täuber and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–23, Discussion and Tables 1 and 2.

Source data

Source Data Fig. 2

Source data for Fig. 2.

Source Data Fig. 3

Source data for Fig. 3.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, X., Lu, Wg., Tang, J. et al. Solution-processed inorganic perovskite crystals as achromatic quarter-wave plates. Nat. Photon. 15, 813–816 (2021).

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