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The visual appearances of disordered optical metasurfaces



Nanostructured materials have recently emerged as a promising approach for material appearance design. Research has mainly focused on creating structural colours by wave interference, leaving aside other important aspects that constitute the visual appearance of an object, such as the respective weight of specular and diffuse reflectances, object macroscopic shape, illumination and viewing conditions. Here we report the potential of disordered optical metasurfaces to harness visual appearance. We develop a multiscale modelling platform for the predictive rendering of macroscopic objects covered by metasurfaces in realistic settings, and show how nanoscale resonances and mesoscale interferences can be used to spectrally and angularly shape reflected light and thus create unusual visual effects at the macroscale. We validate this property with realistic synthetic images of macroscopic objects and centimetre-scale samples observable with the naked eye. This framework opens new perspectives in many branches of fine and applied visual arts.

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Fig. 1: Prediction of the visual appearance of macroscopic objects covered by disordered metasurfaces.
Fig. 2: Engineering of individual particles.
Fig. 3: Engineering of a layered substrate.
Fig. 4: Engineering of structural correlations.
Fig. 5: Experimental demonstration of the diffuse halo due to short-range structural correlations.

Data availability

The datasets underlying the figures of the current study are available either in the Zenodo repository,, or from the corresponding authors upon reasonable request.

Code availability

The codes used to compute the scattering diagrams of particles and to generate the synthetic images in this study are publicly available at and, respectively. Additional codes used in this study are available from the corresponding authors upon reasonable request.


  1. Vukusic, P. & Sambles, J. R. Photonic structures in biology. Nature 424, 852–855 (2003).

    CAS  Article  Google Scholar 

  2. Kinoshita, S. Structural Colors in the Realm of Nature (World Scientific, 2008).

  3. Shopsowitz, K. E., Qi, H., Hamad, W. Y. & MacLachlan, M. J. Free-standing mesoporous silica films with tunable chiral nematic structures. Nature 468, 422–425 (2010).

    CAS  Article  Google Scholar 

  4. Parker, R. M. et al. The self-assembly of cellulose nanocrystals: hierarchical design of visual appearance. Adv. Mater. 30, 1704477 (2018).

    Article  CAS  Google Scholar 

  5. Chan, C. L. C. et al. Visual appearance of chiral nematic cellulose-based photonic films: angular and polarization independent color response with a twist. Adv. Mater. 31, 1905151 (2019).

    CAS  Article  Google Scholar 

  6. Takeoka, Y., Honda, M., Seki, T., Ishii, M. & Nakamura, H. Structural colored liquid membrane without angle dependence. ACS Appl. Mater. Interfaces 1, 982–986 (2009).

    CAS  Article  Google Scholar 

  7. Park, J.-G. et al. Full-spectrum photonic pigments with non-iridescent structural colors through colloidal assembly. Angew. Chem. Int. Ed. 53, 2899–2903 (2014).

    CAS  Article  Google Scholar 

  8. Goerlitzer, E. S., Klupp Taylor, R. N. & Vogel, N. Bioinspired photonic pigments from colloidal self-assembly. Adv. Mater. 30, 1706654 (2018).

    Article  CAS  Google Scholar 

  9. Goodling, A. E. et al. Colouration by total internal reflection and interference at microscale concave interfaces. Nature 566, 523–527 (2019).

    CAS  Article  Google Scholar 

  10. Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

    CAS  Article  Google Scholar 

  11. Arbabi, A., Horie, Y., Bagheri, M. & Faraon, A. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937–943 (2015).

    CAS  Article  Google Scholar 

  12. Kuznetsov, A. I., Miroshnichenko, A. E., Brongersma, M. L., Kivsha, Y. S. & Luk’yanchuk, B. Optically resonant dielectric nanostructures. Science 354, aag2472 (2016).

    Article  CAS  Google Scholar 

  13. Lalanne, P. & Chavel, P. Metalenses at visible wavelengths: past, present, perspectives. Laser Photon. Rev. 11, 1600295 (2017).

    Article  CAS  Google Scholar 

  14. Zhu, X., Yan, W., Levy, U., Mortensen, N. A. & Kristensen, A. Resonant laser printing of structural colors on high-index dielectric metasurfaces. Sci. Adv. 3, e1602487 (2017).

    Article  CAS  Google Scholar 

  15. Kristensen, A. et al. Plasmonic colour generation. Nat. Rev. Mater. 2, 16088 (2017).

    CAS  Article  Google Scholar 

  16. Stewart, J. W., Akselrod, G. M., Smith, D. R. & Mikkelsen, M. H. Toward multispectral imaging with colloidal metasurface pixels. Adv. Mater. 29, 1602971 (2017).

    Article  CAS  Google Scholar 

  17. Peng, J. et al. Scalable electrochromic nanopixels using plasmonics. Sci. Adv. 5, eaaw2205 (2019).

    CAS  Article  Google Scholar 

  18. Daqiqeh Rezaei, S. et al. Nanophotonic structural colors. ACS Photon. 8, 18–33 (2021).

    CAS  Article  Google Scholar 

  19. Hunter, R. S. & Harold, R. W. The Measurement of Appearance (John Wiley & Sons, 1987).

  20. Fleming, R. W., Dror, R. O. & Adelson, E. H. Real-world illumination and the perception of surface reflectance properties. J. Vis. 3, 357–368 (2003).

    Article  Google Scholar 

  21. Pharr, M., Jakob, W. & Humphreys, G. Physically Based Rendering: From Theory to Implementation (Morgan Kaufmann, 2016).

  22. Nicodemus, F. E., Richmond, J. C., Hsia, J. J., Ginsberg, I. W. & Limperis, T. Geometrical Considerations and Nomenclature for Reflectance NBS Monograph 160 (National Bureau of Standards, 1977).

  23. Stam, J. Diffraction shaders in Proc. 26th Annual Conference on Computer Graphics and Interactive Techniques 101–110 (Addison Wesley, 1999).

  24. Cuypers, T., Haber, T., Bekaert, P., Oh, S. B. & Raskar, R. Reflectance model for diffraction. ACM Trans. Graph. 31, 122 (2012).

    Article  Google Scholar 

  25. Musbach, A., Meyer, G., Reitich, F. & Oh, S. Full wave modelling of light propagation and reflection. Comput. Graph. Forum 32, 24–37 (2013).

    Article  Google Scholar 

  26. Holzschuch, N. & Pacanowski, R. A two-scale microfacet reflectance model combining reflection and diffraction. ACM Trans. Graph. 36, 66 (2017).

    Article  Google Scholar 

  27. Belcour, L. & Barla, P. A practical extension to microfacet theory for the modeling of varying iridescence. ACM Trans. Graph. 36, 65 (2017).

    Article  Google Scholar 

  28. Werner, S., Velinov, Z., Jakob, W. & Hullin, M. B. Scratch iridescence: wave-optical rendering of diffractive surface structure. ACM Trans. Graph. 36, 207 (2017).

    Article  Google Scholar 

  29. Weyrich, T., Peers, P., Matusik, W. & Rusinkiewicz, S. Fabricating microgeometry for custom surface reflectance. ACM Trans. Graph. 28, 32 (2009).

    Article  Google Scholar 

  30. Levin, A. et al. Fabricating BRDFs at high spatial resolution using wave optics. ACM Trans. Graph. 32, 144 (2013).

    Article  Google Scholar 

  31. Tsang, L. & Kong, J. A. Scattering of Electromagnetic Waves (John Wiley & Sons, 2004).

  32. Maile, F. J., Pfaff, G. & Reynders, P. Effect pigments: past, present and future. Prog. Org. Coat. 54, 150–163 (2005).

    CAS  Article  Google Scholar 

  33. Schertel, L. et al. The structural colors of photonic glasses. Adv. Optical Mater. 7, 1900442 (2019).

    Article  CAS  Google Scholar 

  34. Hunter, R. S. et al. Methods of Determining Gloss NBS RP 958 (National Bureau of Standards, 1937).

  35. Elfouhaily, T. M. & Guérin, C.-A. et al. A critical survey of approximate scattering wave theories from random rough surfaces. Waves Random Media 14, R1–R40 (2004).

    Article  Google Scholar 

  36. Hong, K. Multiple scattering of electromagnetic waves by a crowded monolayer of spheres: application to migration imaging films. J. Opt. Soc. Am. 70, 821–826 (1980).

    CAS  Article  Google Scholar 

  37. García-Valenzuela, A., Gutiérrez-Reyes, E. & Barrera, R. G. Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles. J. Opt. Soc. Am. A 29, 1161–1179 (2012).

    Article  Google Scholar 

  38. Loiko, N. A., Miskevich, A. A. & Loiko, V. A. Incoherent component of light scattered by a monolayer of spherical particles: analysis of angular distribution and absorption of light. J. Opt. Soc. Am. A 35, 108–118 (2018).

    CAS  Article  Google Scholar 

  39. Sasihithlu, K., Dahan, N., Hugonin, J.-P. & Greffet, J.-J. A surface-scattering model satisfying energy conservation and reciprocity. J. Quant. Spectrosc. Radiat. Transf. 171, 4–14 (2016).

    CAS  Article  Google Scholar 

  40. Holsteen, A. L., Raza, S., Fan, P., Kik, P. G. & Brongersma, M. L. Purcell effect for active tuning of light scattering from semiconductor optical antennas. Science 358, 1407–1410 (2017).

    CAS  Article  Google Scholar 

  41. Wang, B. & Zhao, C. The dependent scattering effect on radiative properties of micro/nanoscale discrete disordered media. Annu. Rev. Heat. Transf. 23, 231–353 (2020).

    CAS  Article  Google Scholar 

  42. Vynck, K. et al. Light in correlated disordered media. Preprint at (2021).

  43. Piechulla, P. M. et al. Tailored light scattering through hyperuniform disorder in self-organized arrays of high-index nanodisks. Adv. Optical Mater. 9, 2100186 (2021).

    CAS  Article  Google Scholar 

  44. Sterl, F., Herkert, E., Both, S., Weiss, T. & Giessen, H. Shaping the color and angular appearance of plasmonic metasurfaces with tailored disorder. ACS Nano 15, 10318–10327 (2021).

    Article  CAS  Google Scholar 

  45. Akselrod, G. M. et al. Large-area metasurface perfect absorbers from visible to near-infrared. Adv. Mater. 27, 8028–8034 (2015).

    CAS  Article  Google Scholar 

  46. Florescu, M., Torquato, S. & Steinhardt, P. J. Designer disordered materials with large, complete photonic band gaps. Proc. Natl Acad. Sci. USA 106, 20658–20663 (2009).

    CAS  Article  Google Scholar 

  47. Salvalaglio, M. et al. Hyperuniform monocrystalline structures by spinodal solid-state dewetting. Phys. Rev. Lett. 125, 126101 (2020).

    CAS  Article  Google Scholar 

  48. Hsu, C. W. et al. Transparent displays enabled by resonant nanoparticle scattering. Nat. Commun. 5, 3152 (2014).

    Article  CAS  Google Scholar 

  49. Andkjær, J., Johansen, V. E., Friis, K. S. & Sigmund, O. Inverse design of nanostructured surfaces for color effects. J. Opt. Soc. Am. B 31, 164–174 (2014).

    Article  CAS  Google Scholar 

  50. Auzinger, T., Heidrich, W. & Bickel, B. Computational design of nanostructural color for additive manufacturing. ACM Trans. Graph. 37, 159 (2018).

    Article  Google Scholar 

  51. Yang, J., Hugonin, J. P. & Lalanne, P. Near-to-far field transformations for radiative and guided waves. ACS Photon. 3, 395–402 (2016).

    CAS  Article  Google Scholar 

  52. Baus, M. & Colot, J.-L. Thermodynamics and structure of a fluid of hard rods, disks, spheres, or hyperspheres from rescaled virial expansions. Phys. Rev. A 36, 3912 (1987).

    CAS  Article  Google Scholar 

  53. Langlais, M., Hugonin, J.-P., Besbes, M. & Ben-Abdallah, P. Cooperative electromagnetic interactions between nanoparticles for solar energy harvesting. Opt. Express 22, A577–A588 (2014).

    CAS  Article  Google Scholar 

  54. Jouanin, A., Hugonin, J. P. & Lalanne, P. Designer colloidal layers of disordered plasmonic nanoparticles for light extraction. Adv. Funct. Mater. 26, 6215–6223 (2016).

    CAS  Article  Google Scholar 

  55. Bertrand, M., Devilez, A., Hugonin, J.-P., Lalanne, P. & Vynck, K. Global polarizability matrix method for efficient modeling of light scattering by dense ensembles of non-spherical particles in stratified media. J. Opt. Soc. Am. A 37, 70–83 (2020).

    Article  Google Scholar 

  56. Malitson, I. H. Interspecimen comparison of the refractive index of fused silica. J. Opt. Soc. Am. 55, 1205–1209 (1965).

    CAS  Article  Google Scholar 

  57. Green, M. A. & Keevers, M. J. Optical properties of intrinsic silicon at 300 K. Prog. Photovolt. Res. Appl. 3, 189–192 (1995).

    CAS  Article  Google Scholar 

  58. Johnson, P. B. & Christy, R.-W. Optical constants of the noble metals. Phys. Rev. B 6, 4370 (1972).

    CAS  Article  Google Scholar 

  59. BMW M3 E46 (Blend Swap; accessed 27 April 2022);

  60. High-Resolution Light Probe Image Gallery (Institute for Creative Technologies, accessed 27 April 2022);

  61. Green Point Park (Poly Haven, accessed 27 April 2022);

  62. Meng, J., Simon, F., Hanika, J. & Dachsbacher, C. Physically meaningful rendering using tristimulus colours. Computer Graph. Forum 34, 31–40 (2015).

    CAS  Article  Google Scholar 

  63. Walter, B., Marschner, S. R., Li, H. & Torrance, K. E. Microfacet models for refraction through rough surfaces In Eurographics Symposium on Rendering (eds Kautz, J. & Pattanaik, S.) 195–206 (The Eurographics Association, 2007).

  64. Johnson, P. & Christy, R. Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd. Phys. Rev. B 9, 5056 (1974).

    CAS  Article  Google Scholar 

  65. Kajiya, J. T. The rendering equation. In Proc. 13th Annual Conference on Computer Graphics and Interactive Techniques 143–150 (1986).

  66. Kalos, M. H. & Whitlock, P. A. Monte Carlo Methods 2nd edn (Wiley VCH, 2008).

  67. Wyszecki, G. & Stiles, W. S. Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd edn (John Wiley & Sons, 1982).

  68. Amendment 1—Multimedia Systems and Equipment, Colour Measurement and Management, Part 2-1: Colour Management—Default RGB Colour Space, sRGB IEC 61966-2-1:1999/AMD1:2003 (IEC, 2003);

  69. Parker, S. G. et al. OptiX: a general purpose ray tracing engine. ACM Trans. Graph. 29, 66 (2010).

    Article  Google Scholar 

  70. Keller, A. et al. The iRay light transport simulation and rendering system. In ACM SIGGRAPH 2017 Talks 1–2 (Association for Computing Machinery, 2017).

  71. Bridson, R. Fast Poisson disk sampling in arbitrary dimensions. ACM SIGGRAPH Sketches 22-es (Association for Computing Machinery, 2007).

  72. Patel, M. Poisson-disc-sampling: Matlab script for n-dimensional Poisson-disc sampling. GitHub (2016).

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We are grateful to P. Barla (INRIA Bordeaux Sud-Ouest, Talence, France) for very stimulating and fruitful discussions on the BRDF model and the interpretation of visual appearances. P. Barla declined being an author of the present work for ecological reasons. P.L. acknowledges F. Carcenac (LAAS) for his attention and diligence in fabricating the metasurfaces under the RENATECH program of CNRS. X.G. and P.L. acknowledge P. Bouyer (LP2N) for inspiring discussions at the initial stage of the project. K.V. and P.L. acknowledge J.-P. Hugonin (LCF) for his help in the development of the full-wave simulation tool used to test the model accuracy. P.L. thanks L.-E. Bataille, P. Teulat, A. Tizon and L. Bellando for their help in developing the goniospectrometer set-up. P.L. and A.A. acknowledge J. Leng (LOF) for giving free access to the solar simulator and B. Simon (LP2N) for fruitful discussions on the experimental measurements. This work received financial support from the French State and the Région Nouvelle-Aquitaine under the CPER project ‘CANERIIP’, from CNRS through the MITI interdisciplinary programmes, and from the French National Agency for Research (ANR) under the projects ‘NanoMiX’ (ANR-16-CE30-0008), ‘VIDA’ (ANR-17-CE23-0017) and ‘NANO-APPEARANCE’ (ANR-19-CE09-0014).

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Authors and Affiliations



K.V. elaborated the BRDF model with feedbacks from R.P. and P.L., performed the electromagnetic calculations and compiled the numerical BRDF data. R.P. and A.D. developed and used the rendering tools to obtain the appearance of nanostructured objects. K.V. and P.L. developed the full-wave simulation tool used to test the BRDF model accuracy. A.A. and P.L. developed the experimental setups. A.A. performed the experimental measurements and calibrated photographs. All authors discussed the results and their interpretation, and contributed to writing the manuscript.

Corresponding authors

Correspondence to Kevin Vynck or Philippe Lalanne.

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Competing interests

The authors declare the following competing interests: patent deposited on the control of visual appearance with disordered metasurfaces (applicants: Université de Bordeaux, Centre National de la Recherche Scientifique (CNRS), Institut d’Optique Théorique et Appliquée and Université Paris-Saclay; inventors: K.V., R.P., X.G. and P.L.; filing date, 1 February 2021; application no. FR 2100948]. The remaining authors declare no competing interests.

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Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Visual impact of dielectric particle size on diffuse and specular colours.

Decomposition in diffuse and specular components of the visual appearance of spherical probes for metasurfaces made of Si particles (of varying radii) on a glass substrate with f = 0.1 and p = 0.1. Compared to Fig. 2 in the main text, a new structure is shown (r = 70 nm).

Extended Data Fig. 2 Visual impact of spacing layer thickness on diffuse iridescence.

Visual appearance of spherical probes for metasurfaces made of Ag particles of radius r = 90 nm on a SiO2/Si substrate with varying h with f = 0.1 and p = 0.1. Two additional images (h = 200 and 400 nm) are shown compared to Fig. 3e of the main text. One observes the progressive formation of diffuse colours as h increases.

Extended Data Fig. 3 Visual impact of particle density ρ and correlation degree p.

Visual appearance of spherical probes for metasurfaces made of Ag particles of radius r = 90 nm on glass at various densities and correlation degrees. The extent of the region where the scattered intensity is suppressed, near the specular direction, strongly depends on the particle density, being small (resp. large) at low (resp. high) densities. This dependence is explained by the invariance of the structure factor with qa. Smaller densities imply larger values of a, meaning a larger accessible range of the structure factor.

Extended Data Fig. 4 Visual impact of particle density ρ and correlation degree p for dielectric metasurfaces.

Same as the Extended Data Fig. 3 for Si particles of radius r = 70 nm. These metasurfaces are comparable (though not strictly equivalent) to those fabricated and characterized experimentally, enabling a qualitative comparison of the visual appearances reported in Fig. 5 of the main text. Similarly to the experiment, the green diffuse colour stems from the Mie resonances of the individual particles (see also the Extended Data Fig. 1) and short-range correlations lead to a suppression of the diffuse intensity near the specular direction (covering the same apparent region on the object surface as in the Extended Data Fig. 3, since the structure factors are strictly identical).

Extended Data Fig. 5 Richness of the visual appearances of a disordered metasurface in different lighting environments.

Rendered images of the same common object (a car), whose body is covered by the same disordered metasurface made of Ag particles (radius r = 90 nm) on tinted glass with surface coverage f = 0.1 and correlation degree p = 0.5. The visual appearances markedly differ with the lighting environment. In low spatial frequency environments (i.e., nearly Lambertian illumination such as under a cloudy sky), the object acquires a nearly uniform colour, except near shadows (see, e.g., under the rear view mirror in the left image). In higher spatial frequency environments, the object recovers vivid colours. This great variability can be attributed to the peculiar “diffuse halo” effect, which depends strongly on the direction of the light source and viewpoint.

Extended Data Fig. 6 Persistent visual effects due to structured substrates and correlated disorder.

Compared to the rendered images in Fig. 1 of the main text in which the lighting is given by an environment map, here we simulate the entire environment. Light sources are rectangular windows placed all around the car and with Lambertian angular emission and a flat spectrum over the visible range (standard illuminant E). We investigate four metasurfaces made of either Si or Ag particles, on either a glass substrate or a SiO2/Si substrate (h = 400 nm), at a particle density ρ = 5 μm−2 and correlation degree p = 0.5. The rendered images are given for three different viewpoints. For unstructured substrates (first three rows), the dominant diffuse colour is driven by the resonances of the individual particles (similarly to the rendered images of Fig. 2 in the main text) and structural correlations create important colour variations under certain viewpoints. When adding a structured substrate (last row), diffuse iridescence introduces a new panel of colours that are clearly visible from all viewpoints.

Supplementary information

Supplementary Information

Supplementary Notes 1–5, Figs. 1–19 and Tables I–IV.

Supplementary Video 1

Visual effects created by disordered metasurfaces with controlled parameters.

Supplementary Video 2

Effect of the lighting environment on the diffuse halo effect.

Supplementary Video 3

Experimental observation of the diffuse halo effect on centimetre-scale metasurface samples.

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Vynck, K., Pacanowski, R., Agreda, A. et al. The visual appearances of disordered optical metasurfaces. Nat. Mater. (2022).

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