Structural color generation: from layered thin films to optical metasurfaces

2.1 CIE 1931 XYZ color space

The CIE 1931 XYZ color space is developed according to the color matching experiments containing all color sensations perceivable by a person with average vision [57, 58]. The tristimulus values, typically represented by X, Y, and Z coordinates, can be obtained by solving the corresponding integral equations (Eq. (1)) consisting of the color matching functions ( x ̄ ( λ ) , y ̄ ( λ ) and z ̄ ( λ ) , Figure 2(b)) [53, 59], relative spectral power distribution of the illuminating light source (I(λ)), and reflection or transmission spectrum of an object (R(λ)).

Where λ 1 , λ 2 is the spectrum range under study, and k is a normalizing factor defined as:

Standard illuminants D65, C, and E are the most frequently used light sources. D65 is a statistical representation of an average daylight with an associated color temperature of ∼6500 K. Illuminant C represents a daylight simulator with color temperature of ∼6774 K. Illuminant E is an equal-energy radiator with a color temperature of ∼5455 K.

The CIE 1931 XYZ chromaticity diagram (Figure 2(c)) is created as a perceptive color map that can contrast different color stimuli. Each point in the diagram denotes a certain color and the associated coordinate (x, y) can be obtained based on Eq. (3).

The color gradually changes from blue to green, and then to red when moving the coordinate point from the left bottom corner to the right bottom corner clockwise in the 1931 XYZ chromaticity diagram. It is worth noting that different kinds of color occupy areas with different sizes in this diagram (non-uniform color spacing). Also, the coordinate points closer to the diagram’s outer edge refer to colors of higher saturation, while points closer to the central point refer to colors of lower saturation. In the extreme case, the central point (x = 0.33, y = 0.33) denotes a white color.

The color gamut is usually shown by an enclosed area of the output colors from a device on the chromaticity diagram. The larger area the color gamut occupies, the wider color range the device can display [60–63]. A few frequently used color gamut standards, including NTSC (National Television System Committee) [64], sRGB (standard red green blue) [65, 66], Adobe RGB [67, 68], DCI-P3 (Digital Cinema Initiative) [69], and Rec. 2020 (ITU-R Recommendation BT. 2020) [70], are listed in Table 1. The triangular areas enclosed by the primary coordinates of these color gamut standards are plotted on CIE 1931 XYZ chromaticity diagram (Figure 2(c)).

Next, we will utilize the CIE 1931 XYZ chromaticity diagram to evaluate a group of colors that are based on different reflection spectra from the objects under study. For the ease of description, we choose to use a Gaussian-like distribution to construct the reflection spectrum from an object:

where, A represents the peak reflection intensity, λ refers to the incident wavelength, λ_c denotes the central wavelength of the reflection spectrum, and Δλ is the linewidth.

Three representative cases will be evaluated in the following discussion, which are (i) a group of reflection spectra with the same peak intensity and linewidth, but different central wavelengths; (ii) a group of reflection spectra with the same peak intensity and central wavelength, but different linewidths; and (iii) a group of reflection spectra with the same central wavelength and linewidth, but different peak intensities. In all cases, standard illuminant E is employed as the light source.

First, we will evaluate colors generated from a group of reflection spectra with the same peak intensity and linewidth, but different central wavelengths. The upper panel in Figure 2(d) plots seven different reflection spectra having identical reflection peak intensity (A = 1.0) and linewidth (Δλ = 20 nm), but different central wavelengths (λ_c = 420, 460, 500, 540, 580, 620, and 660 nm). As the central wavelength increases, the corresponding color coordinate point in the CIE 1931 XYZ diagram moves clockwise from the lower left corner to the upper left corner, and then to the lower right corner (Figure 2(d), lower panel). The associated color gradually varies from blue to green, and then to red. This indicates that the hue of a given color is largely determined by the central wavelength of its spectrum, and different areas in the CIE 1931 diagram correspond to colors of different hues.

Next, we will evaluate colors generated from reflection spectra with the same peak intensity and central wavelength, but different linewidths. Three different groups of reflection spectra are constructed (Figure 2(e), upper panel). For Group #1, #2, and #3, the peak intensities are all set as A = 1.0, and the central wavelengths are respectively set as λ_c = 460 nm, 540 nm, and 660 nm. Each group contains three reflection spectra of different linewidths (∆λ = 10 nm, 20 nm, 30 nm). As shown in the lower panel of Figure 2(e), the calculated color coordinate points from the same group occupy areas of similar hue on the CIE diagram. Moreover, colors associated with narrower reflection spectra are located closer to the edge of the diagram, exhibiting a higher saturation.

Finally, we will evaluate colors generated from reflection spectra with the same central wavelength and linewidth, but different peak intensities. Similar to the previous case, three groups of spectra are constructed (Figure 2(f), upper panel). For Group #1, #2, and #3, the linewidths are all set as ∆λ = 20 nm, and the central wavelengths are respectively set as λ_c = 460 nm, 540 nm, and 660 nm. Each group contains three reflection spectra of different peak intensities (A = 1.0, 0.8, and 0.6). As displayed in the lower panel of Figure 2(f), calculated color coordinates from the same group occupy identical point on the CIE diagram. Intuitively, colors associated with spectra of larger peak intensities should exhibit higher brightness levels. This indicates that the CIE 1931 chromaticity diagram is not capable of truthfully describing the brightness character of a color. In order to adequately describe all three characters (hue, saturation, and brightness) of a certain color, different color spaces need to be adopted. Next, we will describe one of those color spaces- the CIE 1976 L^*a^*b^* color space.

2.2 CIE 1976 L^*a^*b^* color space

The CIE 1976 L^*a^*b^* chromaticity diagram (Figure 3(a)) provides a 3D color map that enables an accurate measurement and comparison of all perceivable colors using three variables (i.e., L^*, a^*, and b^*). Different from the CIE 1931 XYZ color space, the L^*a^*b^* color space can properly represent all three characters (hue, saturation, and brightness) of a given color with a uniform color spacing. In other words, Euclidean distance between coordinate points in the L^*a^*b^* color space roughly corresponds to the amount of change humans perceive between different colors. Any point in the L^*a^*b^* 3D coordinate system can be described by three variables, L^*, a^*, and b^*, based on the following equations.

where

Figure 3:

CIE 1976 L^*a^*b^* color space. (a) The CIE 1976 L^*a^*b^* chromaticity diagram. Modified with permission [71]. Copyright 2014, Multidisciplinary Digital Publishing Institute. (b) The L^*, a^*, and b^* values in the CIE 1976 L^*a^*b^* color space. L^* represents the color’s brightness level, whose value varies from 0 to 100 as the brightness level increases from black to white. a^* and b^* represent the color’s chromaticity level, whose values range from −128 to 127 as the chromaticity level shifts from green to red alone the a* axis and from blue to yellow along the b* axis.

X, Y, and Z are the three tristimulus values obtained according to Eq. (1). X _n , Y _n , and Z _n describe a specified white achromatic reference illumination, and their values are associated with the employed white achromatic reference illuminant source. For the commonly used standard illuminant D65, X _n , Y _n , and Z _n are set as 95.0489, 100, and 108.884, respectively.

The L^*, a^*, and b^* values in the CIE 1976 L^*a^*b^* color space correspond to different characters of a given color. L^* represents the color’s brightness level, whose value varies from 0 to 100 as the brightness level increases from black to white. a^* and b^* represent the color’s chromaticity level, whose values range from −128 to 127 as the chromaticity level shifts from green to red alone the a^* axis and from blue to yellow along the b^* axis (Figure 3(b)). For colors having larger L^* values, the associated coordinate points are located on horizontal planes that are closer to the north pole in the L^*a^*b^* color space. In extreme cases, the coordinate point for a purely white color is located on the north pole (L^* = 100), while that for a purely black color is located on the south pole (L^* = 0). Colors with the same L^* values are located on the same horizontal plane. On a given horizontal plane, the distance from the center point represents the saturation level, or purity of a color. Coordinate points that are further away from the center point represent colors with higher saturation.

3.1 Thin-film-stack-based structural color generation

Transfer matrix method (TMM) [90–92] is one of the popular methods for analyzing the electromagnetic responses of a multilayer thin film structure, where 2 × 2 matrices are used to describe the light reflection (transmission) properties of stratified layers made of homogeneous materials.

Figure 4 shows the schematic drawing of a multilayer structure with m layers sandwiched between a semi-infinite ambient medium (layer 0) and a semi-infinite substrate (layer m + 1). A plane wave is incident from the ambient medium along the +x direction. For layer j, its thickness is denoted as d _j , and the complex index of refraction is represented by n ̃ j . The electrical field components at the input (ambient side), E 0 + and E 0 − , are related to the electrical field components at the output (substrate side), E m + 1 + and E m + 1 − , by the transfer matrix M:

where M can be written as:

Figure 4:

Schematic drawing of a multilayer thin film structure. The structure consists of m layers and is sandwiched between an ambient environment (layer 0) and a substrate (layer m + 1), both of which are considered to be semi-infinite. For layer j inside the thin film stack, its thickness is denoted as d_j and the complex index of refraction is represented by n ̃ j . The electrical field components propagating along the +x and −x directions are denoted as E j + and E j − , respectively. I represents the incident intensity, R and T, respectively denote the reflection and transmission intensity. Modified with permission [92]. Copyright 1999, American Institute of Physics.

Here, L _j is a layer matrix describing the light propagation through layer j, and is described by:

where

I _jk is an interface matrix describing light reflection and transmission at the interface between layer j and k, and is given by:

For an incident light with transverse electric (TE) polarization (electric field perpendicular to the plane of incidence), the reflection and the transmission coefficients, r _jk and t _jk , are expressed as:

For an incident light with transverse magnetic (TM) polarization (electric field parallel to the plane of incidence), r _jk and t _jk are expressed as:

Consider that when light is incident from the ambient side, there is no electrical field component propagating along the −x direction on the substrate side ( E m + 1 − = 0 ). Therefore, the complex reflection and transmission coefficients of the multilayer structure can be expressed as:

According to the Fresnel equations, the reflectivity R and transmittance T of the multilayer structure are:

Herein, n ̃ m + 1 is the refractive index of the substrate (layer m + 1), and θ_m+1 is the refraction angle on the output side (layer m + 1).

Fabry–Pérot cavity. FP cavity, whose basic form consists of an optically transparent dielectric medium sandwiched by two metallic mirrors, is one of the simplest resonators for generating structural colors [93–96]. A wide range of colors can be created by simply adjusting the dielectric layer thickness.

To gain a better understanding of its working mechanism, a standard FP cavity model is applied to analyze its operation [97]. The employed model is a symmetric FP cavity where a transparent dielectric layer is sandwiched between two identical metallic mirrors, and both the input and output sides have the same refractive indices (Figure 5(a)). Here, n and d denote the refractive index and thickness of the dielectric layer, respectively. For the ease of discussion, material absorption and dispersion of the dielectric layer is neglected. But the conclusions drawn from this simplified model also apply to more complicated cases where material absorption and dispersion exist.

Figure 5:

FP resonance for structural color generation. (a) Schematic diagram of a typical FP cavity model, which is composed of two metal mirrors and a dielectric layer between them. Here, n and d respectively represent refractive index and thickness of the dielectric layer. θ₁ and θ₂ represent angles of incidence and refraction at the metal/dielectric interface on the input side, respectively. (b) Schematic diagram of the Ag-SiO₂-Ag based FP cavity. Here, t, d, and h represent thickness of the top Ag, the middle SiO₂, and the bottom Ag layers, respectively. (c) Simulated reflectance spectra with the cavity length d ranging from 90 nm to 175 nm. The top and bottom Ag layer thicknesses are fixed as 30 and 100 nm, respectively. Modified with permission [101]. Copyright 2015, American Chemical Society. (d) Schematic diagram of the TiO₂-Ag-TiO₂-Ag based FP cavity for angle-robust structural color generation. (e) The calculated (dashed curves) and measured (solid curves) transmission spectra of the red, green and blue colors, where the TiO₂ cavity lengths are set as 100 nm, 75 nm, and 50 nm, respectively. Thicknesses of the over-coated TiO₂ layer, the top Ag layer, and the bottom Ag layer are respectively fixed as 60 nm, 23 nm, and 23 nm for all designs. (f) Angularly-resolved transmission spectra of the green-color device under p-polarized illumination. The device exhibits close-to-identical transmission spectra as the illumination angle increases up to 70°. Reproduced with permission [103]. Copyright 2015, Nature Publishing Group.

The reflectivity R_FP as well as the transmittance T_FP of a symmetric FP cavity can be written as [98, 99]:

where R is the reflection coefficient of the metal film, and δ is the total phase shift accumulated during a single round trip within the cavity [93, 100]. δ equals to δ _a + δ _b + δ_prop, where δ _a and δ _b denote the reflection phase shifts associated with the metal–dielectric interfaces, and δ_prop is the round-trip propagation phase shift in the cavity:

where θ₂ represents angle of refraction at the metal/dielectric interface. Compared to the propagation phase shift δ_prop, the reflection phase shifts, δ _a and δ _b , are relatively small in many cases. As a result, the total phase shift δ is mainly determined by δ_prop. Reflection minima (transmission maxima) occurs at certain incident wavelengths when the associated phase shift between two adjacent reflected (transmitted) lights is an integral number of 2π radians (i.e., δ = 2mπ). Increasing the dielectric layer thickness (d) leads to an increase of the phase shift for a given angle of incidence (Eq. (22)), and therefore, induces a shift in the cavity’s resonant wavelength. Consequently, diverse colors (resonance spectra) across the entire visible band can be easily achieved by adjusting the dielectric layer thickness.

Li and co-workers propose a stacked three-layer design for FP-cavity-based structural color generation [101]. The device is composed of a silicon dioxide (SiO₂) layer sandwiched by two silver (Ag) mirrors, with thicknesses of the top Ag, the middle SiO₂, and the bottom Ag layers, respectively, labeled as t, d, and h (Figure 5(b)). Ag is chosen for the metallic layer by its low extinction coefficient and absence of inter-band transition in the visible range. SiO₂ is chosen for the cavity layer by its high visible transparency. To construct reflection-mode devices, the bottom Ag layer is chosen to be optically opaque (h = 100 nm). By fixing the thickness of the top Ag layer (t = 30 nm) and adjusting that of the middle SiO₂ layer (d) from 90 nm to 175 nm, reflectance dips with central wavelengths gradually varying from 450 nm to 650 nm are obtained (Figure 5(c)). Transmission-mode colors can also be realized by reducing the thickness of the bottom Ag layer to 30 nm while maintaining the same top Ag layer thickness. Five different transmission spectra are obtained by adjusting the SiO₂ layer thickness (d) from 100 nm to 200 nm with a step of 25 nm. The obtained transmission resonance peaks are distributed across the whole visible range, and the measured curves exhibit a fair similarity to the simulated ones.

The afore-mentioned FP cavities generate pre-designed vivid colors under normal incidence. However, their resonant wavelengths exhibit a blue shift as the angle of incidence increases, leading to performance degradation and restricting the design’s usage in many displaying and imaging devices. One effective method to mitigate the angle-dependent issue of FP cavities is to employ high-refractive-index materials for the middle layer, such as silicon nitride (Si₃N₄) [102], titanium dioxide (TiO₂) [103], and tantalum pentoxide (Ta₂O₅) [104], etc. Figure 5(d) illustrates an angle-robust, transmission-type structural color design having a four-layer structure of TiO₂-Ag-TiO₂-Ag [103]. The bottom three layers of Ag, TiO₂ and Ag form an FP cavity with increased angular robustness. The thicknesses of both Ag layers are chosen to be 23 nm, while the thickness of the middle TiO₂ layer is adjusted to generate different transmitted colors. An additional 60 nm-thick TiO₂ layer is over-coated on top of the FP cavity to further alleviate the structure’s angle-sensitive response and simultaneously suppress light reflection from the structure. Transmission resonances with peak wavelengths of 636 nm, 541 nm, and 450 nm, which respectively correspond to eye-perceived red (R), green (G), and blue (B) colors, are achieved by setting the middle TiO₂ layer thickness as 100 nm, 75 nm, and 50 nm, respectively (Figure 5(e)). For a designed green-color device, its transmission spectrum is characterized at different angles of incidence ranging from 0° to 70°. The experimentally measured spectra exhibit close-to-identical transmission peaks around 541 nm (Figure 5(f)) for p-polarized incident light, verifying the device’s angle-robust response.

The angle-dependent response of an FP cavity can be explained using the afore-mentioned resonator model. For an FP cavity shown in Figure 5(a), the resonant wavelength of the reflection (transmission) spectrum is expressed as: λ r = 2 d ⋅ n 2 − si n 2 θ 1 . The variation in the resonant wavelength with respect to the change in angle of incidence can be written as:

It can be seen that the angular sensitivity of the device’s reflection (transmission) spectrum is, on one hand, proportional to the thickness of the middle dielectric layer (d), and on the other hand, inversely-proportional to the index of refraction of the middle dielectric layer (n). As we have discussed earlier, employing a high-refractive-index dielectric layer can effectively facilitate the device’s angularly-robust response. Next, we will show how reducing the cavity length would benefit the device’s performance.

One simple yet effective approach to construct an FP resonator with reduced cavity length is to deposit an ultrathin semiconductor layer (i.e., light-absorbing dielectric layer) on top of a metallic substrate [105–107]. Under such configuration, light reflections at both the bottom metal/semiconductor interface and the top medium (usually air)/semiconductor interface will generate nontrivial (neither 0 nor π) phase shifts. These nontrivial reflection phase shifts, together with the propagation phase shift inside the cavity, lead to resonance effects occurring in the ultrathin semiconductor layer. Kats and co-workers demonstrate an array of angle-insensitive structural colors generated from highly-absorbing amorphous Ge layers (with thicknesses varying from 7 nm to 25 nm) deposited on Au substrates [107]. For every 1 nm change in the Ge layer thickness, the measured reflection spectrum exhibits a ∼20 nm shift in its dip position. Moreover, the absorption band maintains its position for illumination angles up to 60° for both TE and TM polarized illumination. Lee and co-workers also demonstrate angle-insensitive transmission colors by sandwiching a thin amorphous silicon (α-Si) layer between two optically thin Ag layers (Figure 6(a)) [106]. To create red, green, and blue transmission colors (Figure 6(b)), thickness of the α-Si layer is set to be 28 nm, 15 nm, and 9 nm, respectively. In all designs, the thicknesses of both top and bottom Ag layers are fixed as 18 nm. As the extinction coefficient of α-Si is lower than that of Ge over the visible range, the corresponding devices exhibit resonance spectra of narrower bandwidth and higher efficiency. Similar to the afore-mentioned design using Ge as a lossy dielectric layer, the Ag/α-Si/Ag structure exhibits angle-robust transmission colors (Figure 6(c)).

Figure 6:

Absorbing material-based FP resonance for structural color generation. (a) Schematic diagram of the Ag/α-Si/Ag based FP cavity. (b) The measured transmission spectra of red, green, and blue colors under normal incidence. The α-Si layer thicknesses are, respectively, chosen as 28 nm (red), 15 nm (green), and 9 nm (blue). For all designs, the thicknesses of both the top and bottom Ag layers are set as 18 nm. (c) Measured angularly-resolved transmission spectra with the incident angle ranging from 0° to 70° under TM polarized illumination. Reproduced with permission [106]. Copyright 2014, American Institute of Physics. (d) Schematic diagram of the dielectric/bi-layer absorber/dielectric/metal (DADM) based FP cavity for high-purity additive color generation. (e) Left panel: simulated (solid curves) and measured (dashed curves) reflection spectra of the red, green, and blue colors. Insets: optical images of the fabricated RGB samples. Scale bars: 1.0 cm. Right panel: structural configurations of the three devices for RGB color generation. Modified with permission [104]. Copyright 2019, Wiley-VCH.

As can be seen from various studies mentioned earlier, an FP-cavity-based device typically generates subtractive colors (e.g., cyan, magenta, and yellow) in its reflection mode and additive colors (e.g., red, green, and blue) in transmission mode. This is due to the fact that resonance-induced absorption inside the FP cavity is usually narrowband. In order to realize additive reflection colors with high purity, constituent materials with high extinction coefficients are required for broadening the FP cavity’s absorption bandwidth. For such purpose, lossy metals (e.g., Ni, Ti, W, etc.) and semiconductors (e.g., Ge, α-Si, etc.) are typically chosen. For example, Yang and co-workers design asymmetric FP resonators to generate bright and pure additive reflection colors, which are based on a three-layer structure of Ni (6 nm), SiO₂, and Al (100 nm) on Si substrate [108]. The thin Ni layer works as a broadband absorber and the thick Al layer as a bottom reflective mirror. By adjusting thickness of the SiO₂ layer from 120 nm to 270 nm, different colors can be generated.

Yang and co-workers demonstrate another reflection-type device having a dielectric/bi-layer absorber/dielectric/metal (DADM) configuration (Figure 6(d)) to generate bright additive colors [104]. In this design, the FP cavity’s absorbing layer is made of two lossy media with different absorbing characteristics over the visible band. Combination of these two materials further enhances the device’s absorption bandwidth, and therefore, improves the reflection color’s purity. Moreover, the top dielectric layer acting as an antireflection (AR) coating can further reduce the intensity of undesired sideband reflection. A 100 nm-thick Al bottom mirror is used to provide high reflection and prevent light transmission, and loss-less Ta₂O₅ with high refractive index is used as both the dielectric layer and AR layer to promote the device’s angular insensitivity. RGB colors are achieved by properly choosing the two absorbing media and adjusting the thickness of each layer (Figure 6(e)).

Generally speaking, it is difficult to obtain structural colors with both high brightness and high purity using a single FP cavity, due to the intrinsic tradeoff between these two performance parameters and the limited degree of design freedom for single-FP-cavity devices. For example, the reflection (or transmission) intensity of off-resonance wavelength components needs to be suppressed as much as possible for improving the color purity. This can be achieved by increasing the thicknesses of absorbing layers or choosing materials with higher extinction coefficients. Unfortunately, the intensity of resonant peaks will be sacrificed at the same time, leading to degradation of the color brightness. To mitigate such issue, dual FP cavity-based devices have been exploited [76, 109, 110]. Lee and co-workers demonstrate efficient high-purity structural colors by employing a dual FP cavity [110]. The proposed device is composed of two cascaded identical FP cavities with metal–dielectric–metal structures, as well as a dielectric antireflection (AR) coating on each side (Figure 7(a)). Each FP cavity consists of two optically-thin Ag films and a zinc sulfide (ZnS) layer. Measured spectra under normal incidence display transmission peaks with efficiencies over 50% and off-resonance sidebands with largely suppressed intensities (Figure 7(b)). The associated images of fabricated samples display RGB colors with both high purity and brightness.

Figure 7:

Dual-FP cavity resonance for structural color generation. (a) Schematic representation of the dual-FP cavity with a ZnS antireflection (AR) coating on each side, where each cavity consists of two optically thin Ag films and a ZnS layer. (b) Measured transmission spectra (left panel) and optical images (right panel) of the fabricated samples. For each red (R), green (G), and blue (B) color device, thickness of the ZnS (Ag) layer is chosen as 104 (32), 70 (34), and 40 (28) nm, respectively. For each device, thickness of the ZnS AR coating is set as half of that of the ZnS layer inside the FP cavity. Modified with permission [110]. Copyright 2017, Wiley-VCH. (c) Schematic diagram of transmission-type structural color generation with a dual-FP cavity. (d) Measured transmission spectra (left panel) and optical images (right panel) of the fabricated samples. The thickness of each layer from top to bottom is chosen as 55 nm/30 nm/225 nm/13 nm/30 nm for the red-color device, 45 nm/35 nm/185 nm/5 nm/35 nm for the green-color device, and 35 nm/35 nm/140 nm/5 nm/35 nm for the blue-color device. Modified with permission [76]. Copyright 2019, Nature Publishing Group.

Another dual-cavity design of improved color purity using the high-order resonance suppression approach is proposed [76]. Figure 7(c) illustrates the schematic of the proposed device, which consists of an antireflection coating (ZnS) and a “compound dielectric layer” switched by two thin Ag mirrors, where the “compound dielectric layer” is made of ZnS, Ge, and ZnS. The designed FP cavity in the form of ZnS/Ag/ZnS/Ag/substrate has a relatively long cavity length, and thus, supports several high-order resonance modes which exhibit narrower linewidths compared to the fundamental resonance mode. Inserting a thin but highly-absorbing Ge layer into the cavity effectively eliminates the 5th order resonance mode (which occurs at the shorter wavelength range), while at the same time, barely affects the 3rd order FP resonance. Figure 7(d) displays three measured transmission spectra under normal incidence, which all exhibit sharp resonances with peak efficiencies over 50% as well as greatly suppressed sidebands. Photos of the fabricated devices exhibit red, green, and blue colors with fairly high purity.

Photonic crystal. Another approach for structural color generation is based on 1D photonic crystal (PC) resonators, which are composed of multiple thin films with alternating high and low index materials [111–113]. Various structural colors can be produced via properly adjusting the thickness of each layer. Lee and co-workers design a 1D PC device, which generates red color with high angular tolerance (up to ±70°) and polarization insensitivity [113]. Schematic diagram of the proposed device is shown in Figure 8(a), which is composed of alternating Si₃N₄ and α-Si thin films and two dielectric Si₃N₄ AR coatings. To generate a vivid red color (with central wavelength λ_c = 800 nm), thickness of each alternating layer inside the PC is designed to be one quarter wavelength (i.e., λ_c/4n). Based on this design rule, thicknesses of the Si₃N₄ (n = 2) and α-Si (n = 4) layers are set as 100 nm and 50 nm, respectively. Moreover, AR coatings on both the top and bottom sides are chosen to be 50 nm thick in order to suppress reflection of incident light with wavelengths ranging from 400 nm to 600 nm (Figure 8(b)). Figure 8(c) shows the optical images of a fabricated device under four oblique viewing angles. Vivid red colors are maintained over a wide angular range.

Figure 8:

1D photonic crystal resonance for structural color generation. (a) Schematic diagram of the proposed 1D photonic crystal for generating red color, which consists of alternating layers of α-Si and Si₃N₄ with a dielectric (Si₃N₄) AR coating on each side. (b) The reflection spectra with (red solid curve) and without (blue solid curve) the AR coating. (c) Optical images of a fabricated sample under four different viewing angles. Modified with permission [113]. Copyright 2015, Wiley-VCH. (d) Schematic diagram of the 1D photonic crystal-based device for reflective CMY color generation. The device is composed of PC stacks (alternating a-Si and Si₃N₄ layers) with additional three layers (thin Si₃N₄/a-Si/thick Si₃N₄) on top. (e) Total absorption and separated absorption in each α-Si layer over the visible band. (f) Calculated (yellow solid curve) and measured (yellow dashed curve) reflection spectra of the proposed device. The red curves are transmission spectra of the bottom PC stacks. Inset: optical image of a fabricated sample. Scale bar: 1 cm. Reproduced with permission [114]. Copyright 2019, Tsinghua University Press.

In spite of additive colors (such as the afore-mentioned red color), subtractive colors including cyan (C), magenta (M), and yellow (Y) can also be created using the 1D PC configuration [114]. Schematic diagram of a PC-based device is shown in Figure 8(d), which is composed of PC stacks (alternating a-Si and Si₃N₄ materials) with additional three layers (thin Si₃N₄/a-Si/thick Si₃N₄) incorporated on top of the device. This structure can be effectively simplified into an asymmetric FP cavity by treating the bottom PC stacks as a reflective mirror for the visible band. Cyan, magenta, and yellow colors are successfully created by properly designing thicknesses of the added thin Si₃N₄ and a-Si layers while maintaining high near-infrared (NIR) transmission (the red curves in Figure 8(f)) without changing the bottom PC stacks. To better understand the working principle of this design, a yellow-color device is analyzed as an example. The yellow color is created by suppressing light reflection within 400 nm–500 nm while maintaining high reflection intensity for the remaining visible spectrum. The reflection suppression for wavelengths between 400 nm and 500 nm is realized through the absorption in α-Si layers, especially the 1st α-Si layer (the red solid curve in Figure 8(e)). The device’s measured (yellow dashed curve) and calculated (yellow solid curve) reflection spectra are plotted in Figure 8(f), with the image of a vivid yellow-color sample shown in the inset. Furthermore, the proposed device exhibits great angular insensitivity (up to ±60°) for both TE and TM polarizations, benefiting from the employed high refractive index materials.

3.2 Subwavelength nanostructure array based structural colors

Subwavelength nanostructures support different kinds of resonances and have been widely employed for generating structural colors. Their reflection and transmission spectra, as well as electric and magnetic field profiles can be computed using various techniques such as finite difference time domain (FDTD) method, finite element method (FEM), and rigorous coupled wave analysis (RCWA). In the following part, we will elaborate on several representative resonance phenomena supported by subwavelength nanostructures and their applications in creating structural colors of diverse functionalities.

Guided mode resonance. Guided mode resonance (GMR) can be considered as a re-distribution of light-wave energy induced by the coupling between externally propagating diffracted light and modulated waveguide leakage wave [115–119]. When diffracted light from the grating is phase matched with the leaky mode supported by the waveguide, a sharp resonant reflection or transmission peak occurs with electric and magnetic fields well confined inside the waveguide layer. GMR usually exhibits narrow linewidth and high efficiency, and has been employed for structural color generation [81], [82], [83, 120].

Schematic diagram of a typical GMR-based structural color device is illustrated in Figure 9(a), which is composed of a grating layer, a waveguide layer, and a substrate. d_g and d_h represent depth of the grating and thickness of the planar waveguide layer, respectively. F denotes filling ratio of the grating, defined as the ratio of its width to period (Λ). The grating period is chosen to be smaller than the wavelength of incident beam, so that only the zeroth-order diffraction beam can propagate in free space while all higher-order diffraction beams are evanescent. In most cases, the medium on the incident side is air (with a refractive index of 1.0), and the substrate is glass (with a refractive index of ∼1.5). The waveguide layer is usually made of dielectric medium with high refractive index over the visible, such as titanium dioxide (TiO₂) [121, 122], hafnium oxide (HfO₂) [123, 124], silicon nitride (Si₃N₄) [81, 84, 125, 126], and zinc sulfide (ZnS) [127], to achieve high diffraction efficiency. Both dielectric and metallic materials can be employed to construct the subwavelength gratings. Figure 9(b) shows three reflection spectra generated from a GMR device consisting of TiO₂ gratings patterned over a thin TiO₂ homogeneous waveguide layer on a glass substrate. The perceived colors based on the reflectance spectra are shown in the insets, exhibiting R, G, and B colors of high purity and brightness.

Figure 9:

Guided mode resonance for structural color generation. (a) Schematic diagram of a representative GMR-based structural color device, consisting of a grating layer, a waveguide layer, and a substrate. d_g and d_h represent the grating depth and planar waveguide thickness, respectively. F denotes the grating filling ratio, defined as the ratio of its width to period. (b) Calculated reflection spectra of three GMR devices under normally-incident TM polarized light (with electric field oscillating perpendicular to the 1D grating). The device consists of TiO₂ gratings (d_g = 80 nm) patterned over a thin TiO₂ waveguide layer (d_h = 60 nm) on a glass substrate. The grating period (Λ) is respectively chosen as 260 nm, 340 nm, and 400 nm, while the filling ratio (F) is fixed as 0.5 for all three samples. Inset shows the perceived colors based on the reflectance spectra. (c) Schematic illustration of a transmission-type GMR-based structural color device, comprising an Ag grating layer, a SiO₂ buffer layer, a Si₃N₄ waveguide layer, and a glass substrate. (d) Calculated transmission spectra under TM polarized normal incidence. In the calculation, the filling ratio is fixed as 0.75, and the grating periods for RGB colors are respectively chosen as 280 nm, 340 nm, and 400 nm. Thicknesses of grating layer, the buffer layer, and the waveguide layer are set as 40 nm, 50 nm, and 100 nm, respectively. Modified with permission [128]. Copyright 2011, American Institute of Physics.

An example of transmission-type GMR-based structural color design is depicted in Figure 9(c), which is composed of a subwavelength Ag grating layer, a SiO₂ buffer layer, a Si₃N₄ waveguide layer, and a glass substrate [128]. The triple dielectric layer (SiO₂ buffer layer, Si₃N₄ waveguide layer, and glass substrate) forms a new hybrid waveguide, and the Ag grating layer provides additional momentum for an incident light to be coupled into the waveguide layer. As the grating period increases from 280 nm to 400 nm, three representative transmission spectra respectively for RGB colors are generated under normally-incident TM polarized light (Figure 9(d)). Compared to the afore-mentioned TiO₂-based device, this device’s peak diffraction efficiencies are less than 100% due to the absorption of Ag metallic gratings.

For a 1D subwavelength grating based GMR device, it exhibits different resonant characteristics and reflection (or transmission) spectra for illumination light polarized along and orthogonal to its grating axis [115]. Based on this principle, switchable structural colors can be obtained by varying the state of polarization of the incident light [82, 129]. For example, a polarization-state-controlled structural color device is proposed, consisting of a 40 nm-thick (H_g) 1D Al grating over a 100 nm-thick (H_c) Si₃N₄ planar waveguide layer (Figure 10(a)) [129]. When the state of polarization of the illumination beam is switched from TM to TE, the devices exhibit different transmitted colors (Figure 10(b)).

Figure 10:

Guided mode resonance for tunable structural color generation. (a) Schematic diagram of a GMR-based nanostructure for polarization-dependent structural color generation. The device is composed of a 40 nm thick (H _g ) Al grating layer, a 100-nm thick (H_C) Si₃N₄ waveguide layer and a glass substrate. Λ and W represent the period and width of the Al grating. TM polarization refers to the electrical field vector oscillating along θ = 0° direction, and TE polarization refers to the electrical field vector oscillating along θ = 90° direction. (b) SEM images of fabricated 1D-Al-grating based devices and the associated optical photos under TM- and TE-polarized illumination. Periods of the Al gratings are set as 280 nm, 340 nm, and 400 nm, respectively. The filling ratio is fixed as 0.5 for all samples. Modified with permission [129]. Copyright 2017, Nature Publishing Group. (c) Schematic diagram of a GMR-based device for angle-dependent structural color generation. The device consists of a 55 nm thick (d_g) TiO₂ grating, a 110 nm thick (d_wg) TiO₂ waveguide layer, and a glass substrate. θ _i and θ _o represent angles of the incidence and reflection, respectively. Here, refractive index of the lossless TiO₂ is set as 2.2 over the visible range. (d) Calculated reflection spectra under TM polarized illumination (electric field vector orthogonal to the grating). Angles of incidence for red, green, and blue colors are set as θ _i = 50°, 20° and 0°, respectively. The TiO₂ grating has a period of 260 nm and a filling ratio of 0.5.

In spite of obtaining different colors by modulating the state of polarization, tunable structural colors can also be generated through varying the angle of incidence of the illumination light [115]. This angle-dependent spectral feature can be explained in terms of the propagation constant (β) of the wave vector [130]:

where m denotes the diffraction order and θ is the angle of incidence. As θ increases, propagation constant corresponding to the backward-diffracted wave vector (m = −1) decreases while propagation constant corresponding to the forward-diffracted wave vector (m = +1) increases. Moreover, λ _r is inversely-proportional to β. As a result, the resonant wavelength varies with the incident angle θ, leading to diverse color generation. A GMR-based angle-dependent structural color device is proposed, consisting of a subwavelength grating layer (TiO₂), a waveguide layer (TiO₂), and a glass substrate (Figure 10(c)). Three distinct reflection curves corresponding to red, green, and blue colors are generated under TM polarized illumination (electric field vector oscillating orthogonal to the grating) from the same structure, by setting the illumination angle θ _i as 50°, 20°, and 0°, respectively (Figure 10(d)).

Plasmon resonance. Plasmon polaritons are electromagnetic oscillations bound to metal–dielectric interfaces. They can be further categorized into two types: surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs), where SPPs refer to propagating polaritons that travel along metal–dielectric interfaces, and LSPs refer to electron oscillations that are bound to the surfaces of isolated metallic nanostructures [131]. By their unique properties such as subwavelength confinement and large field enhancement, plasmon polaritons have found various applications in imaging, sensing, lasing, energy harvesting, and spectrum filtering [132–141]. Researchers have explored various plasmonic structures for vivid structural color generation and we will elaborate on some representative examples in the following text.

Transmission-type, subtractive colors with peak intensities of ∼70% have been realized by a plasmonic device with an ultrathin nanostructured metallic film [142]. Figure 11(a) shows the schematic drawing of the designed structure, consisting of a 30 nm-thick, 1D Ag nano-grating array on a glass substrate. The device exhibits enhanced reflection as well as absorption at its resonant wavelength when illuminated by a normally-incident, TM polarized light (electric filed along the x-axis), leading to a dip in the device’s transmission spectrum. Three distinct transmission colors of yellow, magenta, and cyan can be produced by fixing the grating’s filling ratio as 0.5 and setting its period respectively as 230 nm, 270 nm, and 350 nm (Figure 11(b)).

Figure 11:

Plasmon resonance for structural color generation. (a) Schematic diagram of a 1D plasmonic nanostructure, consisting of 30 nm-thick Ag nano-gratings arrayed over a period of P on a glass substrate. (b) Left panel: experimentally measured transmission spectra under normally-incident, TM polarized light. For the three transmission colors of yellow, magenta, and cyan, the grating’s filling ratio is fixed at 0.5 while its period is set as 230 nm, 270 nm, and 350 nm, respectively. Right panel: corresponding SEM images. Scale bar: 1 μm. Reproduced with permission [142]. Copyright 2013, Nature Publishing Group. (c) Schematic diagram of a 2D plasmonic nanostructure, consisting of 40 nm thick (H_g) Al nano-patches on a glass substrate. (d) Left panel: Transmission spectra of three different samples measured under illumination light of different polarization directions. Periods of the Al nano-patches are chosen as 400 nm, 340 nm, and 260 nm, respectively, and the filling ratio (W/P) is fixed as 0.5. Right panel: corresponding SEM images and generated colors (insets) of the three samples. Modified with permission [143]. Copyright 2014, American Chemical Society.

The afore-mentioned 1D metallic grating based structural color device exhibits a high polarization-sensitive response, which is undesirable for various imaging and sensing applications. To reduce sensitivity to the polarization state of illuminating light, 2D symmetric nanostructure arrays can be employed. A representative metasurface design composed of 2D arrays of aluminum (Al) nano-patches on a glass substrate is illustrated in Figure 11(c) [143]. Similar to the 1D metallic grating, different transmission colors can be obtained by varying the period of 2D symmetric nano-patches (Figure 11(d)). Moreover, the device exhibits close-to-invariant transmission spectra as polarization state of the incident light varies.

The spectral responses as well as generated colors of SPP-based plasmonic devices usually exhibit high sensitivity to the incident angle of the illumination light. This is due to the fact that different frequency components of the incident light are coupled to the SPPs as the angle of incidence varies [144]. Such angular sensitivity largely limits the device’s application in various fields such as displaying and imaging. To mitigate the above issue, structural colors that are based on LSPs have been explored.

Figure 12(a) illustrates the schematic of an angle-independent plasmonic device which relies on LSPs, as well as an SEM image of a fabricated sample [145]. In this design, an optically-opaque Ag layer is conformally coated onto a subwavelength-pitch fused silica (SiO₂) grating. Instead of relying on coupling the incident light energy into the grating-assisted SPP mode, geometric parameters of the 1D grating (width, height, and pitch) are deliberately chosen such as the incident light energy is trapped inside the isolated nano-slit and coupled to a metal–insulator–metal Fabry–Pérot (MIMFP) mode, a localized resonant mode facilitated by the light funneling effect [146–148] (Figure 12(b)). As the angle of incidence varies, the device exhibits close-to-identical subtractive colors in reflection (Figure 12(c)). It is worth noting that although this device is designed to operate only under TM polarized illumination (magnetic field oscillating along the grating direction) due to the employed 1D grating structure, both polarization- and angle-insensitive devices based on similar working principles can be realized by employing 2D subwavelength grating structures [86, 149].

Figure 12:

Plasmon resonance for angle-insensitive structural color generation. (a) Schematic diagram of a metallic nanoslit-based angle-insensitive structural color device, where an optically-opaque Ag layer is conformally coated on a 1D subwavelength-pitch fused silica grating layer. The associated SEM image of a fabricated device is displayed in the inset. (b) Polarization charge and Poynting vector distribution of light funneled into a nano-slit, represented by the red–blue surface plot and purple arrows, respectively. (c) The angularly-resolved reflection spectra of a device under TM polarized illumination (magnetic field oscillating along the grating direction). The period, width, and height of the grating are respectively chosen as 180 nm, 50 nm, and 130 nm. The device exhibits almost-identical subtractive colors as the angle of incidence varies. Modified with permission [145]. Copyright 2013, Nature Publishing Group. (d) Schematic illustration of a metal-insulator-metal (MIM) configuration for angle-insensitive structural color generation. The unit cell consists of a circular Au nanodisk, a continuous Au layer, and a SiO₂ layer in between. (e) SEM image of a fabricated sample consisting of arrays of 270 nm-diameter Au nanodisks. Inset is the associated optical photo. (f) A colored logo of the University of Southern Denmark, created using the designed MIM plasmonic structures. Modified with permission [153]. Copyright 2014, American Chemical Society.

Metal–insulator–metal (MIM) configurations which support gap-plasmon resonance (GPR), a representative kind of LSPs, have also been employed to realize angle-independent structural color devices [85, 150–152]. Schematic diagram of a GPR-based device is illustrated in Figure 12(d). Each unit cell consists of an Au nano-disk hovering on a continuous Au film with a thin SiO₂ film sandwiched between them [153]. A subwavelength period of 340 nm is chosen to minimize high-order diffraction from the structure under normal incidence. Different GPRs of resonant frequencies over the whole visible range can be realized by tuning diameter of the Au nano-disk as well as thickness of the SiO₂ dielectric layer. The SEM image of a fabricated sample consisting of 270 nm-diameter Au nano-disk arrays is displayed in Figure 12(e), showing high-fidelity circular disk patterns. The inset is an associated optical photo, exhibiting a homogeneous generated color. Using the designed plasmonic structures, a high-quality and fine-resolution colored University of Southern Denmark logo is successfully fabricated (Figure 12(f)).

Mie resonance. Mie scattering theory can describe the light scattering behavior of a particle with size similar to or larger than the wavelength of incident light [154–156]. It applies to scattering objects with various shapes and different constituent materials (such as dielectrics, metals, as well as semiconductors). The theory also accommodates cases of incident light with a wide range of frequencies. Over recent years, all-dielectric Mie resonators have been exploited for generating structural colors with high spatial resolution, low optical loss, and robust angular insensitivity [25, 88, 89].

Both individual nanosphere and nanowire made of Si have been demonstrated for displaying distinct colors [157–159]. However, in many cases, the generated colors can only be observed under dark-field illumination due to the low scattering efficiency of an individual Mie resonator. To enhance the scattering efficiency, many researchers have explored devices made of arrays of Mie resonators [160–164]. For example, Park and co-workers develop transmission-type structural colors based on periodically arranged Si resonators [165]. Figure 13(a) illustrates the schematic of the proposed device, which is composed of arrays of α-Si:H nanodisks on a glass substrate. Polymethyl methacrylate (PMMA), which has a refractive index around 1.49 in the visible and serves as an index-matching layer, is employed to fill in the gap between adjacent Si nanodisks. The incident light can be filtered into distinct colors based on the electric dipole (ED) and magnetic dipole (MD) resonances supported within α-Si:H nanodisks via Mie scattering. Figure 13(b) shows the spectra of three different transmission-type colors (yellow, magenta, and cyan). The nanodisk height for all three colors is fixed as 80 nm, while the lattice spacing and the diameter respectively changes from 150 nm to 370 nm and from 80 nm to 170 nm.

Figure 13:

Si based Mie resonance for structural color generation. (a) Schematic illustration of Mie resonators for transmission-type structural color generation, where each unit consists of a 2D α-Si:H nanodisk arrayed on a glass substrate. The nanodisks are embeded inside PMMA. (b) Calculated (dashed curves) and measured (solid curves) transmission spectra of yellow, magenta, and cyan colors. Insets: photos of the generated colors. The height of the nanodisk is fixed as 80 nm, and its period (diameter) is chosen as 150 nm (80 nm), 330 nm (130 nm) and 379 nm (170 nm) to generate the yellow, magenta, and cyan color, respectively. Reproduced with permission [165]. Copyright 2017, Nature Publishing Group. (c) Schematic illustration of Mie resonators for reflection-type structural color generation. The device is composed of arrays of Si nanodisks on a sapphire substrate, over-coated with a refractive index matching layer (PMMA or DMSO). (d) Experimentally measured reflection spectra of the 100-nm thick Si metasurfaces with different lattice sizes (Diameter (R), Period (l)). Insets: recorded colors under bright-field microscope. Modified with permission [166]. Copyright 2020, Nature Publishing Group.

In addition to transmission-type colors, Si-based Mie resonators can also produce reflection-type structural colors. For instance, Yang and co-workers demonstrate reflective RGB colors by exploiting Si-based resonators [166]. Schematic diagram of the proposed device is shown in Figure 13(c), which consists of periodic arrays of Si nanodisks on a sapphire substrate and a refractive index matching layer (PMMA or DMSO (dimethyl sulfoxide)). Both the resonant bandwidth and off-resonance intensity of the reflection spectrum are sufficiently suppressed due to the reduced refractive index contrast between the sapphire substrate and refractive index matching layer. Consequently, structural colors with high purity and large gamut are generated. Meanwhile, the intrinsic high refractive index of Si facilitates a diffraction-limit spatial resolution of the generated colors. Figure 13(d) shows the measured reflection spectra of an array of samples and the associated microscope images. Various structural colors ranging from red to blue are generated by fixing the height of Si nanodisk as 100 nm, and adjusting its diameter (lattice spacing) from 180 nm (320 nm) to 60 nm (110 nm).

Si-based Mie resonators, however, suffer from severe absorption loss in the visible band (especially in the blue region), leading to generated colors with limited efficiency and broadened bandwidth. To mitigate such limitation, alternative dielectric materials with both high refractive index and low absorption loss over the visible, such as TiO₂, Si₃N₄, and ZnS, have been exploited for creating high-performance structural color devices [167–170]. Among various materials, TiO₂ has been widely accepted as a good candidate by its high refractive index and zero absorption loss over the visible. For example, Sun and co-workers demonstrate distinct colors by utilizing TiO₂-based resonators [168]. Figure 14(a) shows the schematic diagram of the proposed device composed of arrays of TiO₂ blocks on an ITO (15 nm in thickness) coated glass substrate, where the cross-section of each block is a trapezoid with the trapezoidal corner around 72°. The periodic arrays of TiO₂ blocks generate distinct structural colors via both ED and MD resonances. Meanwhile, the proposed device exhibits a weak angle-dependent feature (Figure 14(b)). The peak wavelengths of the reflection spectra are maintained within 450–470 nm as the incident angle increases from 0° to 60°.

Figure 14:

TiO₂ based Mie resonance for structural color generation. (a) Schematic diagram of the TiO₂-based metasurface, consisting of arrays of TiO₂ blocks on a glass substrate. Here, p, w, g and t represent the period, the bottom square width, the gap between the adjacent units, and the block height, respectively. Cross-section of each block is a trapezoid with the trapezoidal corner around 72°. (b) Angularly-resolved reflection spectra under s-polarized illumination. Inset shows the angle and polarization direction of the incident light. Reproduced with permission [168]. Copyright 2017, American Chemical Society. (c) Schematic illustration of the multi-dielectric-stack metasurface, where each nanopillar is made of a vertically stacked 100 nm-thick (H₁) SiO₂ capping layer, a 140 nm-thick (H₂) TiO₂ spacer layer, and a 60 nm-thick (H₃) Si₃N₄ bottom layer. (d) Simulated reflection spectrum of an array of stacked-layer nanoblocks, which have a period of 350 nm and width of 200 nm. Insets show the magnetic field distribution (|H|) at 480 nm (orange dashed box) and 535 nm (gray dashed box). Reproduced with permission [167]. Copyright 2019, American Chemical Society.

Yang and co-workers propose another design that can realize structural colors with high purity based on resonators having a multi-dielectric-stack configuration [167]. Figure 14(c) illustrates the schematic diagram of the proposed device, which is composed of stacked-layer nanoblocks arrayed over a silica substrate. Each nanoblock is made of a vertically stacked 100 nm-thick (H₁) SiO₂ capping layer, a 140 nm-thick (H₂) TiO₂ spacer layer, and a 60 nm-thick (H₃) Si₃N₄ bottom layer. In contrast to the all-TiO₂ structure, this stacked-layer structure exhibits reflection spectrum with suppressed high order resonance and therefore, generates colors with improved saturation. Such improvement is due to the fact that the SiO₂ layer and the Si₃N₄ layer, acting as index matching layers, suppress the excitation of multipolar modes at shorter wavelengths. Figure 14(d) shows the simulated reflection spectrum of the proposed device, exhibiting only one resonant peak at 535 nm. The magnetic field distribution (|H|) at 480 nm shown in the inset (orange dashed box) further illustrates the suppressed resonance at shorter wavelengths.

4.1 Optimization-based approaches

Particle swarm optimization (PSO) and genetic algorithm (GA) are two most widely used optimization algorithms for the design of structural color devices. Both methods aim to minimize the difference between the targeted color and the color generated by the designed nanostructure. We will elaborate on these two methods in the following part.

Particle swarm optimization. Particle swarm optimization (PSO), as one representative bio-inspired algorithm, has been employed for designing metasurfaces of complicated configurations [172, 182]. In order to identify a globally optimized design that adjusts the merit function to an appropriate value, PSO first creates a set of particles with randomly-distributed initial positions. The coordinates of each particle’s position correspond to a specific group of design parameters. During the optimization process, each particle’s position is updated with a velocity determined by the position the particle itself has encountered and the best position found by all particles. The quality of each position is then evaluated by EM simulation. After sufficient rounds of iteration, the positions of all particles will converge to the same value, and an optimized design is obtained.

PSO has been successfully employed in the design task of guided mode resonance (GMR) based structural color metasurfaces [182]. For the GMR 1D grating structure shown in Figure 16(a), its thickness (d), grating period (Λ), and filling ratio (F) are the three design parameters used in the PSO process. During the optimization process, each particle’s position (described with the aforementioned parameters, d, Λ, and F) is updated according to a fitness function defined as a root mean square error function between the target reflection spectrum and the designed counterpart by PSO. After 6000 rounds of iteration, an optimized set of structure parameters (d = 335.9 nm, Λ = 279.1 nm, F = 783.0 nm) is obtained, which generates reflection spectrum (solid curve in Figure 16(b)) in good correspondence to the target one (dotted curve in Figure 16(b)).

Figure 16:

Optimization-based approaches for structural color device design. (a) Schematic diagram of a guided mode resonance grating structure. Three optimization parameters used in the PSO process are the grating thickness (d), period (Λ), and filling ratio (F). (b) Target reflection spectrum (dotted curve) and calculated reflection spectrum (solid curve) based on the optimized device parameters through PSO. Modified with permission [182]. Copyright 2007, Optica Publishing Group. (c) GA-based optimization for structural color generation. Optimizing the design parameters of the multiple-meta-atom metasurface leads to a better purity for green color compared to the single-meta-atom metasurface. Modified with permission [185]. Copyright 2020, American Chemical Society.

Genetic algorithm. Similar to PSO, genetic algorithm (GA) is also a bio-inspired optimization algorithm and maintains a group of intermediate designs throughout its optimization process [183, 184]. Instead of mimicking the swarming behavior of flocks or fish, GA models the natural selection procedure based on carefully designed selection, crossover, and mutation rules. In each round of iteration, GA first computes the fitness scores of a set of solutions. Solutions with higher fitness scores will be selected with a higher probability to proceed to the next crossover step. During crossover, selected solutions from the previous step are randomly paired to generate offspring solutions with a small probability of mutation, where some design parameters are randomly changed by chance. Such iterative selection–crossover–mutation process will repeat until a convergence criterion is met.

Liu and co-workers employ GA for designing multiplexed metasurfaces, whose unit cell consists of multiple meta-atoms [185]. For a conventional metasurface device, its unit cell is usually composed of only one meta-atom. This makes the design relatively simple and straightforward, but at the same time, limits the device performance for certain structural color applications (Figure 16(c)). Although extending metasurface design from single meta-atom to multiple meta-atoms could potentially improve the device performance, the substantially increased number of parameters makes traditional design methodology relying on physical intuition and parameter sweeping impractical. With the aid of GA optimization, the researchers successfully obtain multiplexed metasurface designs that can generate high-purity red, green, and yellow colors. These multiplexed metasurfaces all contain four metal disks in each unit cell. During the GA optimization process, the unit cell period (T), height (H) and diameter (D) of the disk, and thickness (T) of the dielectric layer underneath the metal disks are optimized to minimize the Euclidean distance between the designed color and the color target in the CIE diagram.

GA can also be employed for multi-objective optimization, where several potentially conflicting merit functions are being maximized at the same time [173, 184]. Wiecha and co-workers apply non-dominated sorting genetic algorithm II (NSGA-II), a widely used multi-objective GA method, for designing dielectric metasurfaces with polarization-multiplexed resonances [173]. The antenna structure consists of unit cells with four rectangular Si blocks. By optimizing the design parameters including the position A, length L, and width W of each Si block, the authors aim to maximize the antenna scattering efficiency for perpendicular polarization states at two different wavelengths λ _x = 550 nm and λ _y = 450 nm, which are conflicting design goals. Starting with a set of random designs, NSGA-II successfully identifies a design that maximizes the overall scattering efficiency for both polarization states.

4.2 Machine learning-based approaches

Machine learning-based methods for structural color design can be grouped into model-based optimization (MBO), generative modeling (GM), and reinforcement learning (RL). MBO first trains a forward surrogate model that can efficiently predict the color of a certain design. Then, EM simulations are replaced by the trained surrogate model to speed up the structural color design process. Unlike MBO, GM directly learns a conditional distribution of design parameters given a color target. A diverse set of designs can be sampled from the learned conditional distribution. Most MBO and GM methods rely on static datasets, which may not lead to a satisfying design performance when the color target differs too much from the training data distribution. RL methods overcome this limitation by actively exploring the design space through a user-defined reward function that measures the quality of various designs.

Model-based optimization. In model-based optimization, a surrogate forward model that can predict the color based on the design parameters is first trained on a dataset containing an array of designs and associated color labels. Afterwards, a search process or another machine learning model is used for querying the surrogate forward model to find the optimal set of design parameters.

Huang and co-workers train kernel ridge regression models to predict the CIE xy coordinates for dielectric ring arrays (Figure 17(a)) and dielectric pyramid arrays with different design parameters [186]. The trained models are later used as the surrogate models to replace the computationally-expensive EM simulation. With the surrogate models, the authors search the optimal design parameters that can lead to the target design with a simple greedy search process, which iteratively updates each design parameter and evaluates the design’s performance based on the surrogate models. Deep neural networks have also been trained as surrogate models to predict the structural color given device parameters during fabrication. Baxter and co-workers train neural networks to predict the RGB values of plasmonic nanoparticles (Figure 17(b)) based on laser machining parameters [175]. Similarly, a greedy search process is later applied to find the laser machining parameters that can produce the desired color.

Figure 17:

Machine learning-based approaches for structural color design. (a) Dielectric ring structure for structural color generation. The inner diameter d, outer diameter D, and the inter-ring gap g are predicted for a given color target. Reproduced with permission [186]. Copyright 2019, Royal Society of Chemistry. (b) Laser-induced nanoparticles for structural color generation. The optimal laser machining parameters are optimized with a deep neural network model. Reproduced with permission [175]. Copyright 2019, Nature Publishing Group. (c) Silicon nanorod structure designed by tandem networks. The design parameters are the diameter D, height H, gap G, and period P. Modified with permission [174]. Copyright 2019, Wiley-VCH. (d) Free-form silicon metasurface structure designed by GANs. Modified with permission [191]. Copyright 2021, Wiley. (e) Silicon nanorod structure designed by the reinforcement learning algorithm. Reproduced with permission [195]. Copyright 2019, Optica Publishing Group. (f) Neural network architectures for tandem networks (top left), Variational autoencoders (VAEs, top right), and generative adversarial networks (GANs, bottom). Modified with permission [192]. Copyright 2022, China Science Publishing and Media (CSPM) LTD.

Instead of relying on searching the input space of a trained forward model, Gao and co-workers apply a tandem network that combines a forward model and an inverse model to predict the metasurface designs (Figure 17(c)) for user-specified CIE xyY coordinates [174]. Specifically, the forward model and the inverse model are trained in two separate steps. After the forward model is trained, its parameters would be fixed when training the inverse model. The tandem network has recently been improved by using the L^*a^*b^* target to allow more uniform color design accuracy [95], and introducing a mean squared error regularizer to avoid outputting infeasible designs [176]. Roberts and co-workers augment the labeled data with unlabeled synthetic data containing only the CIE xy coordinates to improve the inverse design accuracy [187]. In addition to patterned metasurfaces, tandems networks have also been used for the inverse structural color designs based on nanoparticles [188].

Generative models. Variational autoencoders (VAEs) [189] and generative adversarial networks (GANs) [190] are both popular generative modeling methods. They directly learn the conditional distribution of design parameters for the target color. A diverse set of solutions can be sampled from the learned conditional distribution. Han and co-workers train GANs for designing transmissive metasurface color filters based on free-form meta-atoms (Figure 17(d)) [191]. Their results show that GANs can output free-form metasurface designs for a wide range of possible transmission spectra within a few seconds. Ma and co-workers compare the performance of both VAEs and GANs against the tandem network, an MBO method, on designing nanopillar structures and free-form structures all based on Si [192]. Neural network architectures of all three models are shown in Figure 17(f). The authors find that generative models including VAEs and GANs outperform tandem networks in terms of design diversity, which helps users to select designs that are more amenable to fabrication process. In addition, the authors show that the design accuracy of generative models can be improved by sampling multiple designs and verifying the sampled designs through EM simulation. Ren and co-workers also present similar findings in their recent work comparing the performance of various deep learning models for artificial electromagnetic material inverse design [193].

Reinforcement learning. Most model-based optimization and generative modeling methods are trained with static datasets, which may end up with sub-optimal design accuracy when the color target deviates too much from the training data distribution. Reinforcement learning (RL) addresses this issue by actively collecting additional data through a trial-and-error learning process [194]. Similar to optimization-based approaches, RL also requires an iterative color property evaluation through the design process. However, RL improves upon conventional optimization-based approaches by learning a mapping between the color target and the optimal design parameters through intelligently exploring. As more data are explored through the learning process, RL can gradually acquire a more efficient strategy for designing a wide variety of colors. Sajedian and co-workers apply RL to design silicon metasurfaces that can generate targeted CIE xyz coordinates (Figure 17(e)) [195]. Wang and co-workers develop an RL approach that allows designing multilayer thin-film based structures with a variable number of constituent layers [196]. The developed method has been used for designing a 14-layer broadband absorber exhibiting a close-to-perfect black color.

4.3 Comparison between optimization and machine learning based approaches

Both optimization and machine learning approaches have advantages and disadvantages when applied to the structural color design task. The significant difference between optimization-based approaches and machine learning-based approaches is whether a model is learned through the design process. Learning a model allows one to efficiently predict the design for an unseen color target, while optimization-based approaches always require a time-consuming iterative search process for every new design target. However, collecting a large dataset for training accurate machine learning models is not trivial. If the researchers expect to only solve for a handful of designs, optimization-based inverse design approaches could be more practical. When many designs are needed (e.g., finding structures for reconstructing all color pixels in a high-resolution image), synthesizing datasets for training machine learning models becomes worthwhile because the dataset generation process is a one-time cost. As more and more new design targets are encountered, machine learning-based approaches can save significantly more time than optimization-based approaches.

In addition to efficiency, researchers should also consider the design accuracy of different inverse design methods (Figure 18). Because optimization-based approaches and RL involve iterative dataset collection that allows an active design space exploration, they are often more accurate than static model-based methods. Additionally, advanced RL methods could perform better than conventional optimization-based approaches [196]. However, both approaches are slow due to the requirement of iterative EM simulation. Thus, if researchers value efficiency more than accuracy, MBO or GMs should be used for the design process, while PSO, GA, and RL are more suitable for obtaining highly accurate designs for a small set of color targets. Moreover, we believe that combining optimization and machine learning to form a hybrid method may bring the best of both worlds. Wang and co-workers recently propose a method that combines a neural network model and PSO for efficient structural color design [197]. The proposed method can provide designs for an array of multilayer thin films to reconstruct images with more than 200,000 pixels within few hours.

Figure 18:

Comparison between different inverse design methods for structural color generation in terms of accuracy and computational efficiency.

5.1 Multi-layer thin film based structural colors

Structural colors based on multilayer thin films are commonly fabricated using an array of vacuum-based thin film deposition methods, including physical vapor deposition (e.g., thermal/electron-beam evaporation, magnetron sputtering, etc.) [198–203], chemical vapor deposition (e.g., low pressure chemical vapor deposition-LPCVD, plasma enhanced chemical vapor deposition-PECVD, etc.) [204–206], and atomic layer deposition (ALD) [207–209]. To further reduce the fabrication cost and avoid the need for vacuum-based systems, alternative thin film deposition methods have been explored. Examples include electrochemical deposition and self-assembly method. Moreover, to realize monolithic color integration, planar thin film structures with different constituent layer thicknesses need to be fabricated over the same substrate. Towards this goal, various lithography techniques have been employed together with the afore-mentioned thin film deposition techniques.

Electrochemical deposition. Electrochemical deposition (electrodeposition) is a process of coating conductive or semi-conductive materials onto substrates using an electric field and redox reaction [210–212]. The employed electrochemical cells generally consist of a pair of electrodes and electrolyte solution in between. When a voltage is applied on the electrodes and an induced current passes through the electrolyte solution, metal ions in the electrolyte solution become solid metals and subsequently, get deposited on the cathode surface. Electrochemical deposition can be performed under mild conditions and allows precise growth of layers with nanometer thicknesses onto surfaces with arbitrary shapes.

Ji and co-workers report a simple and low-cost electrodeposition procedure under ambient condition (T < 50°) for fabricating metal–dielectric–metal (MDM) FP-type structural colors [213]. The device is composed of two Au films separated by a Cu₂O layer, and is coated on a heavily-doped n-type crystalline Si substrate (Figure 19(a)). The employed electrochemical cell (Figure 19(b)) has three electrodes, which are the reference electrode, the working electrode (n-type Si substrate), and the counter electrode (Pt mesh). A cross-sectional SEM image of one fabricated sample is displayed in Figure 19(c), showing the thickness of each electrodeposited layer. By fixing the top (bottom) Au layer thickness as 15 nm (40 nm) and setting Cu₂O layer thickness respectively to 70 nm, 45 nm, and 20 nm, three reflection colors (cyan, magenta, and yellow) are realized. Measured reflection spectra from the fabricated samples show good correspondence to numerically calculated ones (Figure 19(d)). Benefiting from the high refractive index of Cu₂O (n ∼ 2.5 in the visible range), the reflection spectra show robust angular insensitivity. In addition, to demonstrate the technique’s capability of depositing onto irregular-shape surfaces, the Au/Cu₂O/Au stacks are coated onto stainless-steel spoons. Figure 19(e) shows the glossy and uniform colors from the layers on the curved surfaces of spoons.

Figure 19:

Electrochemical deposition for fabricating multi-layer thin film based structural colors. (a) Schematic diagram of the FP cavity with an Au-Cu₂O-Au configuration over a heavily n-doped crystalline Si substrate. (b) A standard three-electrode electrochemical cell setup, consisting of a reference electrode, a working electrode, and a counter electrode. (c) Cross-sectional SEM image of a fabricated sample, showing the thickness of each electrodeposited layer. (d) Simulated (solid curves) and measured (dashed curves) reflection spectra from the cyan-, magenta-, and yellow-color samples. Insets are the associated optical images (∼1.5 cm × 1.0 cm). (e) Photos of the colored stainless-steel spoons with the electrodeposited multilayer thin films. Reproduced with permission [213]. Copyright 2019, American Chemical Society.

Self-assembly. Self-assembly method can be regarded as a process to organize components of a system (such as molecules, polymers, colloids, and macroscopic particles) into ordered or functional structures using local interactions among these components [214–216]. Self-assembly approaches have been shown as simple and cost-effective methods for scalable production of structural color devices [217–220].

Inspired by the self-assembled melanosomes in avian feathers which produce vivid colors (Figure 20(a)), Xiao and co-workers construct colored thin films through an evaporation based self-assembly process [217]. The device fabrication process consists of two main steps, which are synthetic melanin nanoparticle (SMNP) synthesis and evaporation based self-assembly. The SMNPs are synthesized through oxidation and self-polymerization of dopamine molecules at room temperatures in a solution consisting of water, ethanol, and ammonia. The sizes of synthesized SMNPs are determined by the molar ratio of ammonia and dopamine hydrochloride. In the self-assembly step, a clean silicon wafer is held vertically in the prepared solution at 60 °C until all its solvent contents are evaporated. A coated SNMP layer with an averaged particle diameter of 146 ± 15 nm is then obtained, and the associated SEMs are displayed in Figure 20(b). Nanometer-scale cracks, which result from film shrinkage during the evaporation process, are found to be evenly distributed in the obtained film. Measured (red curve) and simulated (black curve) reflectance spectra of a fabricated red-color sample are displayed in Figure 20(c). The two curves show good correspondence with each other, both of which exhibit two distinct peaks in the visible range with the primary one centered around 675 nm.

Figure 20:

Self-assembly approach for fabricating multi-layer thin film based structural colors. (a) Photo of a bird. The color in its feather is produced by the self-assembled melanosomes. (b) Cross-sectional and top-view SEM images of a fabricated sample composed of synthetic melanin nanoparticle films. (c) Measured (red curve) and simulated (black curve) reflection spectra of a red-color sample under normal incidence. Inset shows the associated optical image. Modified with permission [217]. Copyright 2015, American Chemical Society. (d) Schematic of the fabrication process of PDA@SiO₂ array via the spraying-drying method. (e) Optical images of the fabricated devices. Particle sizes of the PDA@SiO₂ are around 172, 193, 204, 215, 232, and 252 nm (upper panel, left to right) and 264, 273, 286, 291, 309, and 323 nm (lower panel, left to right). (f) Photos of multicolor Chinese opera facial makeups fabricated on four different substrates. Reproduced with permission [218]. Copyright 2018, Royal Society of Chemistry.

Liu and co-workers demonstrate another efficient approach for constructing non-iridescent structural colors by assembling self-adhesive poly-dopamine (PDA) coated SiO₂ nanoparticles (PDA@SiO₂) via a spraying-drying method (Figure 20(d)) [218]. PDA, produced by the autoxidation of dopamine (DA), can adhere to most commonly-used substrates with high strength. Different colors can be generated by altering the size of the silica core, content of the PDA, as well as arrangement of the PDA@SiO₂. Optical images of fabricated samples are displayed in Figure 20(e), where the samples exhibit non-iridescent structural colors with hue ranging from blue to purple-red as the size of PDA@SiO₂ increases. Multicolor patterns of a Chinese opera facial makeup are fabricated on four different substrates using this method (Figure 20(f)), showing the method’s good compatibility with various substrate types.

Monolithic color integration. One way to create different colors over the same substrate using the multilayer thin film structures (i.e., realizing monolithic color integration) is to create stepwise micro- or nano-cavities. Towards such goal, grayscale lithography [221–224] and nanoimprint lithography [225–230] have been exploited. During the device fabrication process, a thickness-modulated photoresist is commonly employed either as the dielectric layer in the cavity or as the etching mask to transfer the stepwise thickness profile onto the underneath dielectric layer.

Grayscale lithography is a commonly used approach to produce three-dimensional (3D) structures at both the micro- and nano-scale. Figure 21(a) illustrates the manufacturing flow of a full-color FP-based device using the direct-write grayscale lithography [231]. Each individual color pixel is composed of a bottom Al mirror, a middle HSQ layer, and a top Ni layer (Figure 21(b)). Different colors are obtained by adjusting thickness of the middle HSQ dielectric layer (i.e., the device’s cavity length). The bottom Al layer is first deposited onto a Si substrate through electron-beam evaporation. Then, a layer of negative tone electron beam resist (hydrogen silsesquioxane-HSQ) is spun coated over the Al layer. By setting a proper exposure dose during the grayscale patterning process and optimizing the subsequent development condition, HSQ layers with different thicknesses are patterned simultaneously. Finally, a thin Ni layer is deposited on the substrate. Using this method, a full-color microscale painting which reproduces of Vincent van Gogh’s “Still Life: Vase with Twelve Sunflowers” is obtained (Figure 21(c)).

Figure 21:

Grayscale lithography for monolithic color integration using multilayer thin film structures. (a) Schematic illustration of the direct write grayscale lithography for fabricating FP cavities with different cavity thicknesses. (b) Schematic diagram of monolithic full-color printing based on grayscale-patterned asymmetric FP resonators. Each individual color pixel is composed of an Al back reflector, an HSQ dielectric layer, and a Ni top layer. (c) Full-color reproduction of Vincent van Gogh’s “Still Life: Vase with Twelve Sunflowers”. Reproduced with permission [231]. Copyright 2017, Wiley-VCH. (d) Schematic representation of the grayscale stencil lithography which can generate patterns of spatially-varying thicknesses with a single shadow mask. (e) Schematic diagram of the FP cavity based device, which is composed of TiO₂/Pt/TiO₂/Ag stacked thin films on a Si substrate. (f) Experimental deposition results of reflective color arrays. Reproduced with permission [232]. Copyright 2020, Optica Publishing Group.

Besides the direct-write grayscale lithography, grayscale stencil lithography with a single shadow mask has been used for creating stepwise cavity thicknesses for multilayer thin film based structural colors (Figure 21(d)) [232]. Steady or movable shadow masks made of semiconductors or metals are used to define the open areas for material deposition. The total amount of deposited materials over a certain substrate area is determined by the filling ratio of aperture arrays in the customized stencil. Multispectral reflective structural color filter arrays have been successfully fabricated using this method. Figure 21(e) shows the configuration of this multilayer device, which consists of TiO₂/Pt/TiO₂/Ag thin films on a Si substrate. The thicknesses of both TiO₂ layers can be tuned from 0 to 150 nm during fabrication, generating a palette with a wide range of reflective colors (Figure 21(f)).

Nanoimprint lithography (NIL) transfers patterns from the mold into the target material through mechanical pressing, with the aid of heating or ultraviolet irradiation. By preparing molds with spatially-varying depth profiles, NIL can be utilized for fabricating FP-based structural color devices with diverse dielectric thicknesses on the same substrate. Baek and co-workers employ NIL to fabricate FP-based structural colors (Figure 22(a)), which are composed of two Ag mirrors and a dielectric medium sandwiched in between (Figure 22(b)) [233]. Key fabrication steps include bottom Cr/Ag layer deposition onto the Si substrate, pattern transfer through UV NIL, and top Ag layer deposition. Photo of a fabricated device in the form of colored letters is displayed in Figure 22(c). In addition, roll-to-roll (R2R) NIL has attracted great attention by its advantages of reduced cost and enhanced throughput compared with conventional NIL [234–236], and has shown great potential in creating large-scale structural color devices. Recently, a R2R-based physical vapor deposition process has been employed for manufacturing the “structural blue paint” used in Toyota Lexus LC Structural Blue Edition [237, 238].

Figure 22:

UV nanoimprint lithography (NIL) for monolithic color integration using multilayer thin film structures. (a) Fabrication process of FP cavities with different cavity thicknesses using NIL. (b) Schematic representation of the multicolor asymmetric FP absorbers integrated on the same substrate. Each absorber consists of a top semitransparent metallic layer (Ag), a middle dielectric layer of spatially-varying thickness (p-BMA (poly benzyl methacrylate)), and a bottom reflection layer (Ag). (c) Photo of a fabricated sample in the form of colored letters. Modified with permission [233]. Copyright 2020, IOP Publishing.

5.2 Subwavelength nanostructure array based structural colors

Electron-beam lithography (EBL) followed by thin-film deposition and (or) etching is one of the most frequently used methods to fabricate subwavelength nanostructure based structural color devices [239–242]. In such process, patterns of the designed nanostructures are first created in the resist layer by EBL. Subsequently, those patterns are transferred to the device’s constituent materials through lift-off, etching, or a combination of two. Recently, a resist-based Damascene process has been demonstrated to fabricate high-aspect-ratio dielectric metasurfaces, where the device pattern is first defined in the resist layer through EBL, and then transferred to the dielectric material through low-temperature atomic layer deposition (ALD) followed by back-etching [243–247]. Although EBL exhibits great flexibility and high resolution in fabricating devices of various structures and materials, its high cost and low throughput have impeded the method’s usage for many practical applications. To mitigate the above issues, several alternative methods have been exploited for fabricating subwavelength nanostructure based structural color devices. Examples include self-assembly, nanoimprint lithography, fluid-guided printing, and digital inkjet printing. We will give a detailed discussion in the following parts.

Self-assembly. In addition to fabricating planar multilayer thin film structures, cost-effective self-assembly method can also be utilized to create large-area periodic subwavelength nanostructures [248–251]. Figure 23(a) shows the fabrication process of arrays of Al-based disks, dome-rings, and rings using a colloidal self-assembly method [252]. In this process, HSQ is first spin-coated onto a Si substrate. Then a self-assembled monolayer of polystyrene (PS) spheres is formed atop the spin-coated HSQ film. Afterwards, oxygen-based deep RIE is performed using the PS spheres as etching mask to remove the HSQ in the exposed area over the substrate. Depending on the etching condition, the PS spheres can be fully removed or partially etched. Subsequently, a 15 nm-thick Al layer is deposited on the substrate to create Al disk or Al dome-ring arrays. By sonicating the dome-ring sample in DI wafer for ∼30 min, Al ring arrays can be obtained. SEMs of fabricated samples are displayed in Figure 23(b)–23(d), showing periodically arranged Al disks, dome-rings, and rings, respectively.

Figure 23:

Self-assembly approach for fabricating subwavelength nanostructure array based structural colors. (a) Schematic flow chart for creating arrays of Al disks, dome-rings, and rings assisted by a bottom-up self-assembly process. (b)–(d) SEM images of the fabricated Al disks, dome-dings, and dings, respectively. Modified with permission [252]. Copyright 2016, American Chemical Society. (e) Schematic representation of self-assembled Al particles atop an oxide spacer and Al mirror. (f) Photos (left column) and SEM images (right column) of three samples respectively exhibiting yellow, magenta, and cyan colors. (g) Histogram of the particle sizes obtained from the fabricated samples. Reproduced with permission [253]. Copyright 2020, National Academy of Sciences.

Self-assembled metallic nanoparticles can also exhibit colors with robust angular sensitivity and high purity [253]. Figure 23(e) shows a plasmonic color device having a dense array of Al nanoparticles formed atop an oxide-coated Al backplate. Arrays of closely-packed Al particles are created in an ultrahigh vacuum electron beam evaporator through a temperature and pressure dependent thin film growth mechanism. Shapes of the obtained particles depend on the equilibrium condition between the Al’s free energy and interfacial stress with substrate. Large-scale samples showing yellow, magenta, and cyan colors are fabricated (Figure 23(f), left panel), of which the associated mass equivalent thicknesses are, respectively, 4 nm, 8 nm, and 12 nm. As observed from both the SEMs (Figure 23(f), right panel) and particle size histograms (Figure 23(g)), the size of Al particles increases as the sample’s reflection spectrum moves to the longer wavelength range.

Nanoimprint lithography. Nanoimprint lithography (NIL) can also be employed for fabricating nanostructure-based structural color devices [254, 255]. Flexible wafer-scale polarization-dependent structural color devices, which consist of Ag-TiO₂ composite nanowires, are fabricated through NIL and electron-beam evaporation (Figure 24(a)) [256]. In the NIL process, imprint resin is first coated on the Si stamp having line patterns. Then, a polymethyl methacrylate (PMMA) film is covered on the resin. After UV curing, the whole PMMA-patterned resin structure is peeled off the Si stamp. Finally, Ag and TiO₂ thin films are sequentially coated onto the patterned resin surface. SEM image of one fabricated sample and photo of a large-area color sample are respectively displayed in Figure 24(b) and (c). A similar fabrication process has been applied for creating 2D plasmonic color filters (Figure 24D), comprising Al metallic disks on top of dielectric nano-pillars (Figure 24(e)) [257]. A thick protective coating layer is deposited on top of the fabricated device to protect it against environmental damage. Photos of a colored sample before and after the coating are shown in Figure 24(f) and (g), respectively. Compared to the as-fabricated sample, the coating-protected sample shows a redshift in its color due to an increase in the effective refractive index of the nanostructures’ surrounding environment.

Figure 24:

Nanoimprint lithography for fabricating subwavelength nanostructure array based structural colors. (a) Fabrication process of large-scale, flexible, and polarization-dependent structural colors with composite nanowire structures. (b) and (c) SEM and photo of a fabricated sample. Modified with permission [256]. Copyright 2018, American Chemical Society. (d) Fabrication scheme of 2D plasmonic nanostructures. (e) Cross-sectional SEM image of a fabricated sample, showing the PMMA polymer pillar array covered by a metallic Al layer. (f) and (g) Optical images of a fabricated sample without (f) and with (g) the protective coating (Ormocomp, Micro resist technology GmbH). Modified with permission [257]. Copyright 2014, American Chemical Society.

Fluid-guided printing. Fluid-guided printing [258, 259] is another method for fabricating large-scale structural color devices. The fabrication flow of a Selenium (Se)-based structural color device is illustrated in Figure 25(a) [259]. First, a flexible PDMS template is replicated from a groove-shaped Si substrate. Then, Se is evaporated onto the patterned PDMS template. When Se is heated above its glass transition temperature, the resulting material flow leads to the structure’s downsizing and shaping with the guidance of the template. After cooling down to room temperature for ∼5 min, high refractive index (n ∼ 2.79) Se microline arrays are formed on the substrate. The sample’s reflection spectrum exhibits a high angular sensitivity due to the high refractive index of Se and the associated strong optical confinement effect inside the fabricated structure. The sample’s dark-field optical microscopy image and 3D height profile are shown in Figure 25(b), showing the structure’s uniform orientation and smooth edge.

Figure 25:

Fluid-guided printing for fabricating subwavelength nanostructure array based structural colors. (a) Schematic illustration of the fluid-guided printing process for preparing selenium microarrays. The fabricated device exhibits an angle-dependent coloration appearance. (b) Top panel: dark-field optical microscope image of the Se microline arrays. Inset: the associated SEM image. Bottom panel: 3D optical profile image of a fabricated sample. Modified with permission [259]. Copyright 2021, Elsevier.

Digital inkjet printing. Digital inkjet printing [260–262] with transparent inks has also been exploited for creating full-color and high-photorealistic structural color devices (Figure 26(a)) [263]. During the printing process, microdomes with different sizes are prepared by a droplet-by-droplet method (Figure 26(b)). Controlling both the ink volume and the substrate wettability leads to the total internal reflection (TIR) effect inside the microdome occurring at different wavelengths, which consequently results in different reflection colors from the printed sample. Vivid structural colors with controlled gamut, saturation and brightness have been realized by properly programming the arrangement of different microdomes during the inkjet printing process. Figure 26(c) shows the top-view and cross-sectional SEM images of printed microdome arrays with different diameters, which all exhibit a symmetrical morphology with smooth surface. Figure 26(d) shows the optical images of generated colors (red, blue, and green) from arrays of microdomes with diameters of 16.2 μm, 20.3 μm, and 23.5 μm, respectively. Measured reflection spectra are displayed in Figure 26(e).

Figure 26:

Digital inkjet printing for fabricating subwavelength nanostructure array based structural colors. (a) The process of structural-color printing with a single transparent polymer ink. (b) Schematic illustration of the droplet-by droplet printing process. (c) Top-view (left) and cross-sectional (right) SEM images of printed microdomes with different diameters. (d) Dark-field optical micrographs of the microdomes observed from the bare-glass side. (e) Reflection spectra of the printed structural-color panel at the macroscale. Inset shows the associated optical images. Scale bar: 1 mm. Modified with permission [263]. Copyright 2021, American Association for the Advancement of Science.