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The visual appearances of disordered optical metasurfaces

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Abstract

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, https://doi.org/10.5281/zenodo.6327176, 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 https://doi.org/10.5281/zenodo.3609149 and https://mrf-devteam.gitlab.io/mrf/main.md.html, respectively. Additional codes used in this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

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

Authors

Contributions

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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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). https://doi.org/10.1038/s41563-022-01255-9

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