Scalable, ultra-resistant structural colors based on network metamaterials

Structural colors have drawn wide attention for their potential as a future printing technology for various applications, ranging from biomimetic tissues to adaptive camouflage materials. However, an efficient approach to realize robust colors with a scalable fabrication technique is still lacking, hampering the realization of practical applications with this platform. Here, we develop a new approach based on large-scale network metamaterials that combine dealloyed subwavelength structures at the nanoscale with lossless, ultra-thin dielectric coatings. By using theory and experiments, we show how subwavelength dielectric coatings control a mechanism of resonant light coupling with epsilon-near-zero regions generated in the metallic network, generating the formation of saturated structural colors that cover a wide portion of the spectrum. Ellipsometry measurements support the efficient observation of these colors, even at angles of 70°. The network-like architecture of these nanomaterials allows for high mechanical resistance, which is quantified in a series of nano-scratch tests. With such remarkable properties, these metastructures represent a robust design technology for real-world, large-scale commercial applications.


INTRODUCTION
Billions of years ago, green algae originated life, changing the face of the earth from gray to green and paving the way for the life forms we see today 1 . Since then, living organisms have extensively used color for a variety of purposes, ranging from communication to self-defense, from reproduction to camouflage 2 . The enormous variety of colors, such as the sapphire blue wings of the Morpho butterfly 3,4 and the thermochromic coloration of the chameleon 5 , has stimulated the interest of researchers dating back to seventeenth century, when Hooke theorized about the origin of color in the brilliant feathers of peacocks and ducks 6 . Many of these colors do not originate from pigments or dyes but are 'structural', resulting from the interaction of light with self-assembled structures of living organisms 4,7,8 .
The engineering of structural colors from artificial photonic structures has attracted conspicuous interest in research due to the many applications that can potentially be opened by this technology 5,[9][10][11][12][13][14][15][16][17] . Structural colors based on photonic crystals and metamaterials have been explored, showing very promising results, including the possibility to create colors at the diffraction limit 15 . A major challenge is overcoming the problems of limited scalability and lack of robustness, which affect the real-world applicability of photonic crystals and classical metamaterials. It is therefore highly desirable to investigate new approaches that can transform these initial breakthroughs into real-world applications.
In the following, we describe a new biomimetic material that overcomes the aforementioned challenges, introducing a new type of structural coloration that is highly scalable and extremely robust. This nanomaterial takes inspiration from subwavelength nanoscale networks identified in the feathers of Cotinga maynana, a South American bird 18 . The non-iridescent blue color of the feathers is produced by an aperiodic nanoporous keratin network with a typical feature size smaller than 200 nm. This lightweight network has extraordinary optical properties that cannot be explained by classical Rayleigh/Mie scattering and are strongly related to the short-range order of the nano-network of the barbs 19 . The interaction of light waves with complex materials has already been reported to have a series of fascinating dynamics, ranging from energy harvesting to ultra-dark nanomaterials and beyond 7,11,[20][21][22][23][24][25][26][27] . Taking inspiration from the Cotinga maynana feathers as an example in nature of a networkbased optical nanomaterial, we create complex nano-photonic structures that combine a cellular metallic network 28,29 with subwavelength coatings made by lossless dielectrics. This material combination provides significant advantages for real-world applications: it is suited for large-scale fabrication and is lightweight and mechanically robust, combining the high-yield strength to low density ratio of a cellular metallic network with the resistance to wear that alumina offers 30 . Optically, the interface of such a metallic nanoscale network and the lossless dielectric can be considered as electromagnetically 'weakly' rough and an inhomogeneous mixture of dielectric/metal and dielectric/air regions. In this scenario, the component of the wavevector parallel to the interface is not conserved, resulting in a highly spatially dependent electromagnetic response. Taking advantage of such a complex light-matter interaction, we illustrate here how to create colors with remarkable properties.

Sample preparation and characterization
PtYAl layers of 300-nm thickness were deposited at room temperature by magnetron co-sputtering onto SiN x /Si substrates that were precleaned using isopropanol and acetone. Subsequently, the films were dealloyed in 4 M NaOH at room temperature for 60 s and then rinsed with deionized water. The morphological analysis of the samples was studied via scanning electron microscopy assisted by focused ion beam etching (FIB). The compositional analysis was performed by Rutherford backscattering spectrometry. Detailed information is given in the Supplementary Information. In this work, the Savannah atomic layer deposition (ALD) from Ultratech/Cambridge NanoTech (Waltham, MA, USA) was used to deposit Al 2 O 3 coatings on the dealloyed metal nanowire networks. During the ALD deposition of Al 2 O 3 , a pulse time of 0.15 s and a purge time of 30 s for both trimethylaluminium and water were used. The base pressure was 500 mTorr, and the working temperature was 250°C. The growth rate was~0.1 nm per cycle. For creating colored graphic arts, the 60-nm-thick Al 2 O 3 film was deposited via radio frequency (RF) sputtering at room temperature using a sputtering tool (AJA International, Scituate, MA, USA). The electromagnetic reflectance of the coated samples was measured using a variable-angle spectroscopic ellipsometer from J.A. Woollam Co. (Lincoln, NE, USA) and a NanoCalc thin film reflectometry setup (Ocean Optics Inc., Dunedin, FL, USA). The dielectric constant of the Al 2 O 3 coating deposited by ALD was determined using a Cauchy model by analyzing a 53-nm-thick Al 2 O 3 coating deposited on a Si wafer. The scratch tests were performed using an Anton Paar TriTec Nano Scratch Tester (Anton Paar TriTec SA, Peseux, Switzerland).

Finite-difference time-domain (FDTD) simulations
Numerical simulations were carried out using our parallel code NANOCPP, which is a highly scalable (up to hundreds of thousands CPU) Maxwell equation solver, able to include dispersive materials with arbitrary dispersion curves 20 . To build a realistic model for our sample, we considered a metallic structure whose profile was extracted from the morphological analysis of the samples (FIB) shown in Figure 1a. The dispersion parameters of the various materials were taken from direct measurements. Light impinging on the sample was simulated within the transmitted field/scattered field formulation 20 , which allows the detailed modeling of plane wave input excitations on the samples.

Material design and color characterization
We selected dealloying to assemble a nanoscale metallic network with controllable features. This method, first proposed by Raney to synthesize metal catalysts 31 , utilizes the selective dissolution of the less noble constituent of an alloy during wet etching. In our experiments, 300-nm-thick Pt .14 Y .06 Al .80 thin films were deposited on an amorphous Si 3 N 4 /Si substrate. Although immersing the film in a 4 M aqueous solution of NaOH for 60 s, the less noble Al in the Pt-alloy thin film is subsequently removed, and the remaining metal reorganizes into a network with an open porosity. Characteristic geometrical features of the network can be altered by changing the etching time, the etchant concentration or the initial composition of the thin film [32][33][34][35][36] .
In a second step, the nanomaterial is coated with an ultra-thin layer of Al 2 O 3 using ALD. The coating thickness is increased stepwise in a range from 7 to 53 nm. We characterized the growth of the subwavelength Al 2 O 3 coatings by Rutherford backscattering spectroscopy and FIB-assisted scanning electron microscopy (see Supplementary Information). A three-dimensional image of the Pt .56 Y .26 Al .18 network, experimentally obtained using FIB thin film tomography, is displayed in Figure 1a.
In a final series of experiments, we characterized the optical response of the network metamaterial for different thicknesses of the dielectric layer Al 2 O 3 . These experiments unveiled a very interesting mechanism of structural coloration from the nanowire network, as shown in Figure 1b. By changing the coating thickness, we observed the formation of a multitude of colors spanning from yellow, orange and red to, finally, blue. The same physical effect with the optical response blue-shifted and smaller color range was observed for a Pt-Al network (see Supplementary Information and Supplementary  Fig. S9). Conversely, when the same coatings were deposited on a dense PtYAl metal thin film, no particular color was produced (see Supplementary Information and Supplementary Fig. S5). The colors observed in the metallic network were saturated and go even slightly beyond the red green blue gamut in the CIE chromaticity diagram (Figure 1c).
To illustrate that these colors were consistently observed by varying Al 2 O 3 layer thickness, we compared experimental results with theoretical predictions based on finite-difference time-domain (FDTD) simulations. For the latter, we used a two-dimensional section of the FIB tomography of the sample illustrated in  Figure 1d, which illustrates the color palette that can be observed when the thickness of Al 2 O 3 increases.
To emphasize that the structural coloration in these nanoplasmonic structures can be achieved by various deposition techniques, we also fabricated a structural colored graphic arts by using physical vapor deposition. Figure 2 depicts an example created by combining a dealloyed network metamaterial with an RF-sputtered 60-nm-thick Al 2 O 3 coating and photolithography using a Heidelberg μPG501 optical direct writing system. The bicolored graphic art combines a highly uniform structural color (blue) with a metallic white color (dense film). The material choice for the coating layer is not limited to Al 2 O 3 a lossless dielectric. Dielectric coatings with and without losses could, in principle, be used to alter the plasmonic response and finally change the structural coloration. Another approach to altering the color impression, especially its saturation, is to change the number of trapping sites within the network metamaterial, for example, by reducing the metamaterial thickness.

Robustness of structural colors from metamaterial networks
To quantify the mechanical robustness of these colors, we resort to nano-scratch resistance testing (Figure 3a), which is an ideal technique to characterize the adhesion failure of coatings. A detailed description of the experimental procedure we used is given in the Supplementary Information. Figure 3b reports optical micrographs of four representative nano-scratch tests. The wear resistance of a dense PtYAl film with and without a 28-nm-thick Al 2 O 3 coating is compared with a porous nanoscale Pt network coated with 28 and 53 nm of Al 2 O 3 , respectively. The critical load causing delamination of the coated network metamaterial is almost two times higher than the corresponding dense metallic film ( Figure 2b) and 20% higher than the dense metallic film coated with 28-nm-thick Al 2 O 3 . Considering the 53% porosity in the nanoscale network, the observed increase in wear resistance is remarkable and indicates an enhanced strength-to-density ratio 37 corresponding to a significant reduction of overall weight of the coating. Figure 4 illustrates s-polarized reflectivity spectra at normal ( Figure 4a) and oblique (Figure 4b-4e) incidence for different alumina coating thickness. Figure 4a demonstrates that the formation of colors originates from a large red shift of the reflectivity response of the nanomaterial, observed when the Al 2 O 3 layer changes thickness. The corresponding FDTD results are reported in Figure 4f. FDTD simulations quantitatively reproduce well the experimental results, confirming the principal role of the Al 2 O 3 coating layer in red-shifting the spectral response of the material. A small variation of only 30 nm in the Al 2 O 3 thickness shifts the reflectivity minimum of~350 nm. Reflectivity spectra of the material are stable and do not show significant variations up to incident angles of 70°, which still provide reflectivity minima as low as o1% (Figure 4b-4e). The mean angular Scalable, ultra-resistant structural colors H Galinski et al dispersion of the reflectance minimum has been determined from the reflectance spectra obtained by ellipsometry. The mean angular dispersion is independent of the coating thickness and the reflectance minimum blue shifts with − 1.0 ± 0.3 nm per degree. These experiments show that the structural colors observed in Figure 1 are noniridescent, that is, robust against large changes of the incident angle.
Structural coloration from localized surface states in complex epsilon-near-zero (ENZ) materials In this section, we analyze in more detail the mechanisms by which structural colors are created and observed in the metallic network of Figure 1. When polychromatic light impinges on the structure of Figure 1a, the interaction between light and matter generates surface plasmon polaritons (SPP) 38 , which are surface waves localized at the metal-dielectric interface of the structure 7 . In our samples (Figure 5a), the motion of SPP develops along complex trajectories in space due to a strongly disordered metallic profile, (Figure 5a, inset). It is convenient to study this motion in a new curvilinear system, whose axes are parallel to the spatial trajectories of SPP. To this extent, we introduce a new set of coordinates, (ψ, φ), which are conformal to the disordered surface of the metal. Figure 5a shows how these coordinates appear in the original space. (x,y), whereas Figure 5b shows how the original structure appears in the space (ψ, φ), which we identify as the 'plasmonic reference'. In the plasmonic reference, the motion of    (Figure 5b, inset). When we change spatial coordinates in any electromagnetic system, Maxwell equations remain invariant if we introduce an inhomogeneous refractive index distribution that makes the two reference systems equivalent 39,40 . The pseudocolor plot in Figure 5b shows the spatial distribution of the inhomogeneous index, n(ψ, φ), computed by using transformation optics (see Supplementary  Information). The index, n(ψ, φ), is associated with the coordinate transformation introduced in Figure 5b and acts as a counterpart of the metallic geometry of Figure 5a, which does not exist in Figure 5b, as the metal surface is flattened out. The two structures of Figure 5a and 5b are exactly equivalent: when light propagates in one or another, it follows the same dynamics. This is an exact result of Maxwell equations that contains no approximation. This result also implies that when light impinges on the structure of Figure 5a, it happens to propagate in the medium of Figure 5b. The calculation of a conformal grid for the disordered surface of Figure 5a requires a new formulation of optical conformal mapping, which we recently developed, and allows for the generation of conformal grids for arbitrary structures with arbitrary-large numerical precision. This approach is relatively involved, and it will be discussed in a future work. The plasmonic reference of Figure 5b illustrates in clear form the effects of disorder, which introduce a strong modulation of the refractive index in the proximity of the metallic surface at ψ = 0, generating a network of epsilon-near-zero (ENZ) regions, separated by areas of high refractive index (Figure 5b). As observed in the insets of Figure 5a and 5b (dashed lines), ENZ regions are created in the points where the metallic surface is convex, whereas high dielectric permittivities originate in the points where the surface is concave. When waves propagate into an ENZ material, the phase velocity diverges, thus creating standing waves with infinite wavelengths [41][42][43] . When SPP waves propagate in the nanowire network of Figure 5a, they 'see' the equivalent medium illustrated in Figure 5b and become trapped in the ENZ regions, thereby generating a set of quasi-localized states. We illustrated these dynamics by a series of FDTD simulations. Figure 6a presents a magnified version of Figure 4a, showing FDTDcalculated reflectivity spectra for different thicknesses of the Al 2 O 3 layer. FDTD results corresponding to different combinations of alumina thicknesses and input wavelengths are summarized in Figure 6b-6j. When light impinges on the disordered metallic structure (Figure 6b), some energy is scattered back, generating components along all directions in space, whereas the remainder is coupled into SPP waves. As illustrated in Figure 6c-6e, which show FDTD-calculated electromagnetic energy density distributions, SPP waves are completely localized in the proximity of different convex points of the surface, exactly where the ENZ regions are formed. FDTD simulations show that different wavelengths are trapped in different ENZ regions of the metal, demonstrating that the ENZ network formed in Figure 5b does not possess a particular length scale and that it traps equivalently all input wavelengths. The absence of a characteristic scale is expected from the strongly disordered surface modulation of the sample, which possesses an abundant variety of different curvatures (Figure 5a) and therefore of ENZ regions with different extensions (Figure 5b). These ENZ regions trap polychromatic light very efficiently, as observed from the flat reflectivity response of Figure 6a (Figure 1a). When light impinges on this structure, it excites the propagation of SPP waves, which move along the complex surface of the metal (a, inset). This motion is conveniently described in a curvilinear reference (φ, ψ), which provides a conformal map of the metallic surface of the sample (solid red line). In the transformed space, (φ, ψ) (b), SPP waves appear to propagate inside an inhomogeneous material with refractive index, n(φ, ψ), on the line at ψ = 0 (c, inset). The material, n(φ, ψ), models the effects of the metallic geometry of a, which is flattened out in transformed space, (φ, ψ). The two systems of a and b are exactly the same for light propagation. The equivalent structure of b demonstrates a complex network of ENZ structures (b, dark blue area), which are created by points of convex metallic curvature (right inset). 2D, twodimensional.
Scalable, ultra-resistant structural colors H Galinski et al energy propagation in the structure, we also plotted the flow of electromagnetic energy in the structure, computed from the Poynting vector of the electromagnetic field (Figure 6f). This is represented with a specific line integral convolution technique, which clearly visualizes the energy flow, characterized by complex patterns with a nontrivial vorticity. When we deposited a small layer of Al 2 O 3 on top of the metal, the scattering dynamics changed abruptly (Figure 6g). In this situation, a portion of scattered wavevectors were reflected inside the alumina layer, thus generating a series of additional scattering events in the Al 2 O 3 . Wavevectors propagating at an angle, θ, (see Figure 6g) larger than the critical angle, y c ¼ arcsin nAIR where λ 0 is the wavelength of a reflectivity minimum corresponding to a coating thickness, d 0 . Figure 6l compares

CONCLUSIONS
We have experimentally demonstrated a new design concept to create robust and saturated structural colors in metasurfaces composed of metallic nanowire networks with ultra-thin, lossless dielectric coatings. Using a combination of analytical and numerical techniques, we illustrated that these colors are the result of the resonant coupling of light with surface plasmons that are localized in equivalent ENZ regions formed in the metallic network. This mechanism is not constrained for large angles as high as 70°, allowing for efficient trapping of light over a broad wavelength range in the visible region. The combination of mechanical robustness and color saturation in an extremely lightweight structure makes these structural colors suitable for real-world industrial applications, such as automotive vehicles or airplanes, for which the weight is directly related to the fuel economy. As discussed in the introduction, achieving a scalable fabrication is a key problem in structural color printing. On the basis of our experiments, it is evident that our metasurfaces have shown a wide color capability without the need for electron beam lithography or other complex fabrication procedures. Our structures, in fact, are based on simple wet-chemistry and coating technologies, which can produce robust colors on large spatial scales. In addition to such fundamental advances, our design concept has the potential to enrich the application of metasurfaces to areas in which large active regions are mandatory, such as efficient light trapping layers in photovoltaic cells. Although a deeper discussion of this topic is beyond the scope of this paper, we can introduce some important points. On the basis of our theory and experiments, we demonstrated that it is possible to control the response of an optical material by 'engineering' the connectivity of a network of ENZ nanostructures created in a random metallic structure. From the results of Figure 6, we observed that this approach allows for strong localization of optical radiation in nanoscale regions located well outside the metal, completely absorbing incoming optical photons in a specific bandwidth (Figure 6j and 6k). This approach can potentially enhance the absorption power of ultrathin absorbers, which can take advantage of the formation of localized spots and harvest a significant portion of light energy in nm-thick film structures. The current photovoltaic technology employs Si absorbers of~100 μm thickness, whereas other solution-processed materials with high manufacturability and low cost, such as quantum dots, require film thickness 41 μm to efficiently absorb all incoming photons. Our metastructures can considerably scale down these thicknesses, stimulating new research aimed at developing innovative materials for renewable energy harvesting.