Color appears in every aspect of human life. In comparison with chemical dyes, structural colors usually have a more sustainable appearance, more eco-friendly manufacturing processes, and more abundant resources, making them attractive in fields like anticounterfeiting^[1], decoration^[2], display devices^[3], and solar cell panels^[4]. So far, two main ways have been applied to generate structural colors. One is the metasurface method^[5–7], using technologies such as ion beam etching and photolithography to construct periodic microstructures on different substrates. It is highly flexible in model design, and colors obtained are generally of nice quality. However, the cost from a series of complicated processes is still high. To address this, the other one, which is based on multilayered thin films, was developed^[8–10]. At the interfaces of different materials, visible light is scattered, interfered, and finally comes out with a specific spectral line shape to achieve various colors. It is simple in process and proper for massive manufacturing. The current mainstream thin-film design involves employing an asymmetric Fabry–Perot (F–P) cavity, coupled with antireflective (AR) units or ultrathin absorptive layers. However, stuck with a limited choice in structure, performance, such as high brightness and saturation, often cannot be simultaneously achieved. There are still problems to be solved in the multilayered thin-film structural colors.

Fano resonance is a promising choice to solve the above-mentioned questions because of its narrowband reflection spikes and lowest energy to zero. It was first discovered in 1935 by Beutler, and after that, Fano gave a theoretical explanation from the perspective of quantum mechanics, which is the superposition of quantum states including the bound state and the continuum state^[11]. Prior to being utilized in structural coloration, Fano resonance, owing to its sharp peaks or dips and high sensitivity to the environment, has been extensively employed in optical sensors. It was not until 2015 when Regan et al.^[12] introduced a zigzag metasurface at the Conference on Lasers and Electro-Optics (CLEO), which resulted in two narrowband reflection peaks at 330 and 480 nm with a peak reflectance reaching up to 33%, that the potential value of Fano resonance in the field of structural coloration was elucidated. In subsequent years, researchers have utilized various metasurface structures to achieve improved structural colors, such as Yang et al.^[13] who designed a columnar metasurface. The calculated peak reflectance of his design reaches up to 100% and covers 57% of the CIE color space. However, it was EIKabbash et al. in 2021 who first introduced the multilayered thin films based on Fano resonance^[14], which eliminates the need for photolithography and offers a simpler manufacturing process. A four-layer thin-film structure was constructed with three materials. The top two layers made of a lossy material and a highly reflective metal acts as the broadband absorber. When it couples with the left part, Fano resonance is achieved, making these thin films selectively reflect certain frequencies just as the DBRs do but with a narrower bandwidth. They did not extensively explore the color performance of this structure; instead, they found its unique properties of transmitting and reflecting the same color. Later in 2023, they processed further and began to explore the advantages of this structure in constructing high-saturation and wide-gamut colors^[15]. A silica cap was put on top of the original film stacks, which suppressed the sideband reflection of different colors, especially the ones whose center wavelength located in the long wave range, such as green and red. These thin films, therefore, are of high color purity (99%) and present full gamut (61% of the CIE color space). Moreover, the actual fabricated samples exhibit high brightness, with peak reflectance gradually increasing from 63% at ∼420nm to 83% at ∼650nm. However, there still remains a scarcity of research on the Fano resonance phenomenon in multilayered thin films that offer relatively simpler fabrication processes.

In this paper, we investigated the coupling between different continuum states and the bound states, and proposed a simple multilayered structure with excellent color performance, such as high saturation, high brightness, and wide color gamut. It was found that the asymmetric lines of the Fano resonance seem to result from the superposition of phase mutations. Phase abrupt changes in the bound state will superimpose on the continuous state, thus forming a peak and a valley in the spectrum at the same time in a short wavelength range. In addition, four structures forming different continuous states were investigated. Among them, the cavity-like unit proposed here exhibits the lowest energy, ensuring the reflected colors produce the weakest background scattering light, less than 8%, and then high saturation. The essence lies in the moderate absorption and high refractive index of Ge2Sb2Te5 (GST) layer. It traps light in the first three layers and slowly absorbs it. This is not just for a particular color with certain center wavelength. As the thickness of the dielectric layer changes, various colors with dim background can be created. And the reflection peak of the entire film stack stays as high as 80%; the bandwidth increases slightly from 50 to 70 nm in the whole visible range from 400 to 800 nm. As for color diversity, the film stack proposed here has a much larger gamut than any other structures. It covers 56.7% of the CIE color space in the chromaticity diagram, which is 125% of the Adobe RGB (45.2%). Even with just one film layer changed, 47.1% is achieved. Also, in experiments, by applying fewer oxygen-dependent materials, such as LaTiO3 and MgF2, highly matched samples with simulation were successfully prepared. The peak reflectance ranges from a minimum of 78% for blue to a maximum of 82% for green.

The schematic graph in Fig. 1(a) illustrates the Fano resonance optical coatings (FROCs) proposed here, which is an MD2MD1A structure, namely metal/dielectric 2/metal/dielectric 1/absorptive material. When visible light passes through the first three layers: MD1A, it undergoes partial absorption and reflection, resulting in a wideband reflection with smooth fluctuations in its spectrum. This represents the continuum state or the background. Simultaneously, light transmitted is coupled into unit: MD2M, an asymmetric F–P cavity that exhibits high-quality Q resonance and confines the frequency range. This is known as the bound state. These two parts interfere with each other outside the first surface, giving rise to what is called Fano resonance. It is found that material selection plays an important part in utilizing the advantages of Fano resonance. In the unit, the metal layers can be a combination of Al, Ag, Ti or other metals. To effectively bind light in the cavity and obtain a narrow frequency range, Ag was used because of its relatively high reflection. In addition, the dielectric layer D2 should be highly transparent at visible wavelengths to lower energy loss, considering the light oscillating back and forth in the cavity. Materials such as TiO2, SiO2, and LaTiO3 can be used. In experiments, we found that the use of LaTiO3, a material with less dependence on oxygen, is more suitable for actual production. As for TiO2 and SiO2, extra oxygen input was needed in preparation processes and an obvious decrease of reflection was observed. As shown in Fig. 1(b), reflectance of the same structure using TiO2 or LaTiO3 materials as the transparent layer D2 is plotted. The material type and thickness of other layers remained unchanged. For simulation (figures on the left), substitution of materials in D2 brings no significant difference in reflectance peak. However, facts during fabrication considered, the peak reflectance of film stacks using TiO2 is reduced from 80% to 40% while LaTiO3 decreased slightly. Considering the fact that during the fabrication, apart from the oxygen pressure, all other conditions remained the same, this reflectance decrease may be caused by the oxidation of metal layers. In terms of the unit MD1A, its main task is to reduce the background light. And here, in order to enhance its function, a cavity-like structure composed of three layers was adopted. It is MD1A in which the metal layer is shared with the MD2M unit by using Ag, MgF2 material acts as the dielectric D1 and GST the absorptive layer. GST is phase change material with appropriate and uniform absorption and a high refractive index. With this material, background light can be effectively trapped and absorbed in this film stack, improving the color saturation.

Similar to traditional multilayered structures, we can also use the effective interface method to analyze the regulatory characteristics of Fano resonance on light^[16]. From this theory, the total Fresnel reflection coefficient of a model, shown in Fig. 1(c), can be simplified into two interfaces and described as the following: $$\begin{gathered} r=r1∓t1+t1−r2−e−2iδ+t1+r2−r1+r2−t1−e−4iδ+⋯t1+r2−r1+r2−r1+r2−t1−e−6iδ+⋯ \\ =r1∓(t1+t1−r2−e−2iδ)1−r2−r1+e−2iδ, \end{gathered}$$(1)=>|r1−|eiφ1+|A|eiφ*,(2)where rn and tn represent the reflection coefficient and transmission coefficient of the nth interface, respectively, and δ represents the phase difference between the two interfaces. Worth noticing is that both two terms in Eq. (1) are complex, which means that this formula can be simplified as Eq. (2), a commonly used expression in physical optics. It describes the phenomenon when two beams of light intervene with each other. In a multilayered thin-film system, one is the reflected part from the interface between air and the first layer, and the other comes from deeper interfaces. Thus, the intensity can be derived as $$\begin{gathered} R=r·r*=(|r1−|eiφ1+|A|eiφ*)·(|r1−|eiφ1+|A|eiφ*)* \\ =|r1−|2+|A|2+2|r1−·A|cos(φ1−φ*). \end{gathered}$$(3)

Apparently, the reflection intensity is highly related to the phase difference, φ1−φ*. Especially, when the phase difference is 0,±2π,… the constructive interference appears, resulting in reflection peaks on the spectra. And for ±π,±3π,…, it is the destructive interference and reflection dips.

After simulating the film stack mentioned above and many other Fano structures, it is found that there would be rapid changes of the phase left in the reflectance phase of continuum states. In Fig. 2, the reflective phase changes of MDM, MA, and MDMA are shown, respectively, using materials Ag for ‘M,’ LaTiO3 for ‘D,’ and GST for ‘A.’ For the MDM structure [Fig. 2(a)], the phase curve rises sharply at certain wavelengths (∼500nm, ∼970nm), reaching 0 and π in turn, so that there is a peak and a dip at corresponding positions in the spectra. Because of strong background light, the peak is not visible. Highly leaking films, such as MA [Fig. 2(b)], tend to have smooth transitions and can barely obtain two points satisfying the coherent interference in a short frequency range. However, when two types of structures are coupled with each other [Fig. 2(c)], phase surges that previously appeared only in MDM are preserved. In Fig. 2(d), the dashed lines and the solid lines represent optical properties of MA and the coupled Fano structure MDMA, respectively, with red representing the phase shift and blue representing the reflectance. Before coupling, the phase changes gently, and there are no asymmetric spectral line shapes, whereas after coupling, it fluctuates at around 500 and 1000 nm, causing two pairs of points satisfying the interference conditions (see the hollow stars in the dashed boxes), and Fano resonance line shapes arise. Remarkably, these patterns are universal no matter what materials are used.

It is also found that different asymmetric spectra are presented according to the energy contrasts of these two coupled states. To realize a high and isolated reflection peak that is needed for high-quality reflective structural colors, keys lie in constructing a low-energy-level continuum state. In Fig. 3, four structures are explored. The first one, Fig. 3(a), contains only one layer of nonabsorbing medium (use MgF2 as an example); therefore, the sideband reflection is extremely high, submerging the Fano resonance peak with just a dip left. In the second one, Fig. 3(b), the dielectric layer is replaced by an absorbing thin layer composed of absorptive materials, which can theoretically be Ge, a-Si, Ni, or GST. GST is used here. Moderate absorption makes it possible to obtain a dim background and then good colors. Furthermore, the antireflection (AR) unit is widely used to suppress the redundant reflection by alleviating the impedance mismatching of different materials. Thus, in Fig. 3(c), MAD structure is explored, with a layer of transparent dielectric MgF2 being deposited on GST material. It is true that another 15% of the energy is diminished, bringing a nice shape to the reflection peak. To reduce the background stray light further, a cavity-like structure is constructed here [Fig. 3(d)]. Materials with high refractive index and appropriate absorption, such as GST (4.0 at 600 nm), can be selected to cooperate with the metal layer. This traps the light in the cavity so that it can be effectively absorbed. As a result, the 8-nm GST absorptive thin film works even better than double the thickness value shown in Fig. 3(c). The reflection peak of the film stack has a narrow bandwidth and the weakest background light, below 8%. Beside the reflectance spectra are the simulated colors of four structures mentioned above: Figs. 3(a) to 3(d) from top to bottom.

The MDA structure was then used to construct the continuum state, forming a five-layer thin-film stack of Ag(100nm)/LaTiO3/Ag(14nm)/MgF2(42nm)/GST(7.5nm), and its film thickness was optimized. From the phase curve (left) in Fig. 4(a), it can be seen that a phase rise happens at ∼550nm (the blue dotted circles) on the reflectance phase curve of the whole film stack just as it happened in the Ag/LaTiO3/Ag structure. In addition, coupling with Ag/LaTiO3/Ag also strengthened the smooth phase transition of Ag/MgF2/GST in the red dashed circles. As a result, it reached 2π at ∼730nm, satisfying the destructive interference condition with an extra phase shift of π between the interface of air and GST. This helped suppress the sideband reflection [see the red dashed circles in Fig. 4(b)] and made it as low as 8% on average.

In Fig. 4(c), the adjustment of LaTiO3’s thickness was made, from 70 to 110 nm. There is a shift happening in the position of the abrupt phase change (π) of the discrete state Ag/LaTiO3/Ag. Thus, theoretically, the central wavelength of the reflectance peak in the Fano resonance spectra will vary with the thickness change of LaTiO3, leading to different colors. We adjusted the thickness of LaTiO3 with a regular gap; the results are shown in Fig. 5(a), where the color palette is calculated by varying the thickness of the dielectric LaTiO3 from 45 to 120 nm, when the gap is fixed at 5 nm and other layers are kept the same. Meanwhile, reflectance curves in Fig. 5(b) show the reflection peaks at different wavelengths from 400 to 800 nm by increasing the thickness of LaTiO3 from 45 to 125 nm with a gap of 10 nm. As the thickness increases, the background reflectance stays as low as 8% on average; the peak stays above 80% without obvious reduction bringing high color brightness, and the bandwidth increases slightly, but is still within 70 nm. Similar calculation is performed in Fig. 5(c) as well, but with a small thickness interval, 1 nm. And the colors are plotted in the chromaticity diagram where CIE 1931 observer and D65 light source are used. It covers 47.1% of the CIE color space. In comparison with other structures (F–P cavity 31.8%, the red triangles in the center), the sRGB gamut (34%, the big red triangle area), and the Adobe RGB gamut (45.2%, the blue triangle area), the value of FROCs designed by us is the largest. Furthermore, thickness adjustments of two layers (MgF2 and LaTiO3) even expand this figure to 56.7% [the red balls, named Fano (two layers)], 125% of the Adobe RGB gamut. Therefore, our scheme will play an important role in fields such as display, printing, and photography.

Experimentally, three representative colors, red, green, and blue, were fabricated by the ion-assisted electron evaporation method. The ion source is a Kaufmann high-energy ion source. To ensure the high density of the film and make the film material have stable optical constants, the screen voltages were 350 V (Ag) and 500 V (LaTiO3, MgF2, and GST), respectively, and the ion beam currents were all 120 mA. The BK7 glass with a diameter of 30 mm was chosen as the substrate, which was wiped clean with a mixture of alcohol and ethanol before it was placed into the electron beam evaporation chamber at a background vacuum of 3.0×10−4Pa. The thicknesses of each layer for three samples are listed in Table 1. Except for the LaTiO3 layer, which accounts for the color hue, nothing else is changed for better performance, which is almost impossible to achieve in any other multilayered structures. Before fabrication, factors, such as the depositing rates, the ion source power, and the substrate temperature, are optimized in advance to achieve better results. Eventually, the three primary colors of red, green, and blue with high brightness, high saturation, and wide color gamut were successfully prepared. As shown in Figs. 6(a)–6(c), the reflectance reaches up to 78%, 82%, and 80%, respectively, with a background of 10%, 8%, and 12% on average. Although in spectra the peak reflection of blue color deviates from the design for about 3%, and the background is enhanced at the long wavelengths for blue and green colors, there is little visual difference between pictures and the design colors. As for the deviations, the inaccurate thickness control of crystal sensors may take responsibility, especially when the Ag layer is only 14 nm and the GST counts 7.5 nm. In the future, this thickness monitoring problem of ultrathin-film layers could be solved by improving the precision of the control system.

In conclusion, basic principles of Fano resonance were further explored from the perspective of phase shift. Based on that, an optimized Fano resonance thin-film structure with high color saturation and high brightness in the full color gamut was successfully designed and fabricated. The reflection peak of the entire film stack has a peak value reaching up to 80%, a narrow bandwidth of ∼50nm, and a dim background, less than 8% on average. In addition, the carefully chosen materials GST, LaTiO3, Ag, and MgF2 make it the same for various colors with different center wavelengths. They all perform well in terms of color quality. As for the color diversity, layer thicknesses were changed to tune the color hue. Structural colors obtained covered 56.7% of the CIE color space, which is 125% of the Adobe RGB gamut. Therefore, so many advantages attach, including low manufacturing cost, high color quality, large gamut, and easy tuning colors; the scheme is firmly believed to broaden the application of structural colors in fields, such as decoration, display, printing, and textiles.