Near-complete light absorption is of fundamental significance in many fields of science and technological applications including optical sensors, photovoltaics, and the inexhaustible renewable solar energy collection [1–7]. It is highly desirable for the applications to develop a kind of perfect broadband absorber in visible light that is ultrathin, polarization-insensitive, and highly absorptive for a large viewing angle. So far, a lot of strategies have been demonstrated to realize broadband optical absorption, including the planar multilayer configuration and nanostructure-based metamaterials [8–14]. For the latter, they always exhibit perfect optical properties for controlling the absorption. But most of them with complementary hole arrays or cylinder arrays are fabricated by complicated and expensive methods such as electron-beam lithography (EBL) and focused ion beam (FIB) milling [15–21]. These disadvantages significantly limit their extensive applications. For example, our group presented a kind of broadband absorber based on nanostructured germanium arrays fabricated by the complex EBL process, and the area was limited to only hundreds of microns, leaving a small space for the potential applications [16]. Moreover, some nanostructure metamaterial absorbers faced the severe problems of polarization dependence and viewing angle sensitivity due to anisotropic geometrical shapes [20]. On the contrary, some planar absorbers composed of multilayer film structures are easy to fabricate on a large wafer [22–27]. The lithography-free planar absorbers provide high-throughput manufacturing convenience and open a new opportunity for low-cost, high-performance optoelectronic devices. However, in order to get a higher absorption over a wider wavelength range, it usually needs plenty of layers composed of several different materials [22].

Here, the proposed absorber consisted of a four-layer structure with an alternating composition of lossy and lossless dielectric films that can achieve a nearly perfect absorption covering the entire visible light. Such a multilayer film system can have strong absorption as a result of a single broadband resonance in the highly lossy Fabry–Perot (F–P) cavity as well as the intrinsic loss property of Ge. In the range between 450 to 750 nm, the absorber exhibits an average absorbance of 97.4%. The high efficiency can be maintained well over ${\pm}{{50}}^\circ$ incident angles. In addition, it reveals a strong polarization-insensitive property due to the geometrical symmetry. Moreover, the planar feature makes it a lithography-free design, which is envisioned to be excellent options for large-scale and cost-effective production. Furthermore, the ease of experimental fabrication enables their implementation on flexible substrates, and the incident angular insensitivity could make the property of the flexible absorber membranes remain nearly unchanged when the membranes are bent, or twisted. To demonstrate these advantages associated with the new design, we covered the flexible membranes on a cartoon head model. Accordingly, its facial features are almost entirely cloaked after the coating. The multilayer-based broadband absorber operating in the visible spectra is of particular interest in many practical applications, including thermal photovoltaics, solar energy collectors, sensing and spectroscopy, camouflage coating, as well as other wearable devices.

As shown in Fig. 1(a), the proposed broadband absorber is an asymmetric F–P cavity with a ${{\rm{SiO}}_2}$ layer coating. The F–P cavity is composed of a lossless dielectric (${{\rm{SiO}}_2}$) core with a top partially transparent/reflective lossy dielectric (Ge) layer and a bottom lossy dielectric (Ge) with enough thickness. The top ${{\rm{SiO}}_2}$ layer is able to enhance light transmission owing to the refractive-index matching and protects the underneath Ge layer from oxidation. The top lossy Ge layer of several nanometers absorbs a small part of the incident light effectively as a result of intrinsic loss while allowing the other part to pass through, causing F–P resonance. The bottom layer of lossy Ge is thick enough to function as not only a reflecting mirror, but also an absorbing layer. Such a planar ${\rm{Ge}} - {{\rm{SiO}}_2} - {\rm{Ge}} - {{\rm{SiO}}_2}$ four-layer structure can thus achieve a broadband absorption with high efficiency owing to the combination of optically single broadband resonance in the highly lossy F–P cavity and the intrinsic loss of Ge.

 

Fig. 1. (a) Schematic of the broadband optical absorber based on an all-dielectric multilayer structure. (b) Experimental absorption plot of the multilayer structure with ${t_1} = {{300}}\;{\rm{nm}}$, ${t_2} = {{46}}\;{\rm{nm}}$, ${t_3} = {{6}}\;{\rm{nm}}$, and ${t_4} = {{65}}\;{\rm{nm}}$.

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In our case, the bottom and top Ge layers are deposited using the electron beam (e-beam) evaporation technique, and all the ${{\rm{SiO}}_2}$ layers are coated by the plasma-enhanced chemical vapor deposition (PECVD) furnace. The lithography-free nature of the multilayer structure makes it easy to fabricate and can be used for large-scale applications. Figure 1(b) shows the experimental absorption spectra of the multilayer structure fabricated on the flexible aluminum foil. The result demonstrates that the absorber could get a high absorbance, up to 98.8%, with an average absorbance of 97.4%. The absorption of the system can be calculated using the following formula: $A = 1 - R - T$, where $A$, $R$, and $T$ are the absorption, reflection, and transmission, respectively. Considering the bottom Ge layer is thick enough, the transmission of this structure is equal to zero. Therefore, the above-mentioned formula can be simplified to $A = 1 - R$.

After the analysis of influencing rules for each layer’s thickness on the absorption based on the transfer matrix method (TMM) [25,27], it can be inferred that the thicknesses of the top Ge layer and the middle ${{\rm{SiO}}_2}$ spacer are the major factors contributing to the optimization of absorbance. The top ${{\rm{SiO}}_2}$ layer as an antireflective film is also a small factor in the absorption. Here, the influence of structural parameters (${t_2}$, ${t_3}$) on the absorption is studied to optimize the absorptive performance, as shown in Figure 2. We fabricated the samples with different parameters on the silicon substrate, and obtained a palette of reflective colors by changing the thickness of ${t_2}$ and ${t_3}$ [Fig. 2(a)]. From the color appearance, it can be seen that the darker the color, the better the absorption.

 

Fig. 2. (a) The absorption color palette is revealed, with a square size of 1 cm in the array under the unpolarized white light illumination, as ${t_2}$ changes from 46 to 62 nm in 8 nm increments and ${t_3}$ changes from 2 to 6 nm in 1 nm increments, while keeping ${t_1}$, ${t_4}$ fixed at 300 nm and 65 nm, respectively. (b) AFM image on top layer of the sample with 46 nm ${{\rm{SiO}}_2}$ and 6 nm Ge. (c) Experimental  and (d) simulated  absorption spectra of the structure with ${t_2}$ ranging from 46 to 62 nm, while keeping ${t_3}$ at 6 nm, respectively. (e) Experimental absorption spectra of the structure with ${t_3}$ ranging from 2 to 6 nm, and keeping ${t_2}$ at 46 nm. (f) Experimental absorption spectra of the structure with and without ${{\rm{SiO}}_2}$ coating.

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The experimental results shown in Fig. 2(c) demonstrate that the absorption increases along with the increasing thickness of the middle ${{\rm{SiO}}_2}$ ${t_2}$. The bottom ${\rm{Ge}} - {{\rm{SiO}}_2} - {\rm{Ge}}$ layer acts to form an F–P cavity to trap the majority of the incoming light in the middle lossless ${{\rm{SiO}}_2}$ layer, which eventually decays in the neighboring lossy Ge layers. Clearly, the simulated absorption spectra calculated by the finite-difference time-domain (FDTD) method exhibit an appreciable consistency with the experimental results, as shown in Fig. 2(d). But there still exists a little difference due to the fabrication errors, such as the thickness and roughness. The red line in Fig. 2(d) shows that the simulated absorbance can reach to more than 99%, while the measured value of the fabricated sample is slightly decreased. In Fig. 2(b), the atomic force microscopy (AFM) image on top of the sample with 46 nm ${{\rm{SiO}}_2}$ and 6 nm Ge shows that the average roughness $Ra$ is 0.992 nm. Figure 2(e) shows the absorption spectra for the samples with ${t_3}$ varied from 2 to 6 nm while keeping ${t_2}$ at 46 nm. As ${t_3}$ increases, the absorbance increases significantly from 60% to above 90%. The top Ge layer helps to enhance the absorption when it is thin. If this layer is too thin, the reflected light from the bottom Ge can escape from the cavity and couple to the air, which results in a higher reflectance. If it gets too thick, then less incident light will be transmitted into the main cavity, bringing about less absorption. The top ${{\rm{SiO}}_2}$ layer acts as an antireflection coating layer that reduces the high contrast of the refractive index between the air and Ge, and its thickness is critical in providing an additional interference effect in the top ${\rm{Ge}} - {{\rm{SiO}}_2}$-air layers. As shown in Fig. 2(f), the absorption exerts a remarkable increase at shorter wavelengths after coating the top ${{\rm{SiO}}_2}$, and also enhances slightly at longer wavelengths. This result demonstrates that much more incident light can be coupled to the ${\rm{Ge}} - {{\rm{SiO}}_2} - {\rm{Ge}} - {{\rm{SiO}}_2}$ system with the help of the top cavity (${\rm{Ge}} - {{\rm{SiO}}_2} - {\rm{air}}$). Thus, the analyzed results above verify that all the thickness values for each layer in this structure contribute to the absorption.

Different from the normal F–P cavity, the proposed highly lossy F–P cavity could exhibit perfect absorption behavior, not only at a specific wavelength, but across the entire visible regime. The absorption is caused by a single broadband resonance in the highly lossy F–P cavity and the intrinsic loss property of Ge. In order to analyze the physical mechanism underlying the observed absorption, the distribution of the magnetic field at the $xz$-plane cross section calculated by the FDTD method is presented in Fig. 3. As shown in Fig. 3(a), the magnetic energy confined in the thin top Ge layer and thick bottom Ge layer is caused by the loss property of Ge, and the energy trapped in the ${{\rm{SiO}}_2}$ cavity is due to the strong F–P resonance. The little energy trapped in the top ${{\rm{SiO}}_2}$ antireflective layer illustrates that the top ${{\rm{SiO}}_2}$ layer could not only make much light enter the F–P cavity, but also enhance the resonance effect, increasing the absorption performance. Accordingly, for shorter wavelengths, the top cavity (${\rm{Ge}} - {{\rm{SiO}}_2} - {\rm{air}}$) plays a crucial role and for longer wavelengths, the bottom cavity (${\rm{Ge}} - {{\rm{SiO}}_2} - {\rm{Ge}}$) is predominantly absorbing. For clarity, we get the cross section showing the distribution of the magnetic field intensity at a certain wavelength [Fig. 3(b)], proving well the above analysis. These results confirm that the incident light is partially absorbed in the lossy Ge layer and partially coupled into the highly lossy F–P cavity, and a contribution in the overall absorption from the top ${{\rm{SiO}}_2}$ is also not negligible.

 

Fig. 3. (a) Distributions of the magnetic field intensity ($|H|^2$) for the structure with ${t_2} = {{46}}\;{\rm{nm}}$, ${t_3} = {{6}}\;{\rm{nm}}$ as a function of incident light wavelength. (b) Cross section ($xz$-plane) showing the distribution of the magnetic field intensity at 650 nm. The black dashed lines are the boundaries of the four layers.

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Here, the properties of the viewing angle effect were studied by the FDTD simulation. The simulation models were built based on the schematic diagram of the sample as shown in Fig. 1(a). The plane waves covering the wavelength of 450–750 nm were incident along the ${-}z$ direction. The broadband fixed angle source technique (BFAST) was used. Perfect matched layer (PML) boundary conditions were applied in the $z$ direction. The mesh size was set to 0.5 nm in all directions. The complex refractive index of the Ge model was based on the data measured by the spectroscopic ellipsometry (see Data File 1), and the other materials for simulation were based on the data from Palik in the material library of the software. As shown in Figs. 4(a) and 4(b), the absorber under p- and s-polarized light illumination presents a high angular tolerance up to ${\pm}{{50}}^\circ$. Although the overall absorption is a little lower with the increasing incident angle, it can still remain above 93%. In addition, the simulated results seem in excellent agreement with the experimental observations in Fig. 4(c). Thus, the proposed broadband absorber possesses a large absorption in a wide viewing angle.

 

Fig. 4. Contour map of simulated incident angle resolved absorption spectra at (a) p-polarization and (b) s-polarization for the structure with ${t_2} = {{46}}\;{\rm{nm}}$ and ${t_3} = {{6}}\;{\rm{nm}}$. (c) Recorded photographs of the corresponding absorption color palette taken under outdoor ambient light with an oblique incidence of 20°, 30°, and 40°.

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Due to the good substrate adaptation of the proposed absorber, we evaporate the multilayer film on the flexible aluminum foil substrate, and get the flexible broadband absorber. Owing to its simple fabrication technology, it can realize a large area and mass production. A photograph of a finally fabricated absorber sample on a 4-inch substrate is shown in Fig. 5(a). The result as shown in Fig. 5(b) demonstrates that the flexible sample continues to show a high absorptive performance after being bent due to its incident angle insensitivity. Figure  5(c) reveals that compared with the silicon substrate, the absorber fabricated on the aluminum foil substrate has a little higher absorption caused by the larger roughness (the average roughness $Ra$ is 44.8 nm).

 

Fig. 5. (a) Photograph of the absorber sample on a 4-in. (10.16 cm) circular flexible aluminum foil substrate. (b) The flexible absorber being bent. (c) Experimental absorption spectra of the absorber fabricated on the silicon and aluminum foil substrate.

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The flexible broadband absorbers operating in the visible spectra meet the demands for a wide range of applications, such as eliminating the stray light and camouflage coating. Here, the proposed absorber makes a three-dimensional (3D) object look like a two-dimensional (2D) black hole, so the details of the surface cannot be observed. As shown in Fig. 6(b), the facial features of the cartoon head model [shown in Fig. 6(a)] are almost hidden after being covered by the flexible absorber sample, which could hide the stereo information and achieve the stealth effect.

 

Fig. 6. Cartoon head model (a) before and (b) after being coated by the flexible absorber.

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In conclusion, a flexible perfect broadband absorber in visible light generated by the all-dielectric multilayer structure is proposed to realize a high-absorption, strong-polarization independence with a large viewing angle. Through the optimization design of the structural parameters, the absorber fabricated on the flexible aluminum foil substrate could get an average absorbance of 97.4% between 450 nm and 750 nm. The high-absorption performance remains nearly unchanged for both $p$- and $s\!$-polarized light with an incident angle up to ${\pm}{{50}}^\circ$. Moreover, with the advantage of simple all-dielectric multilayer configuration, the absorber can be fabricated in a large scale with the lithography-free, cost-effective manufacturing technology. Accordingly, a flexible absorber membrane with high absorption and a large viewing angle is well adhered on a cartoon head model with a complex surface profile, which makes the 3D object look like a 2D black hole and hides the facial features perfectly. Such a broadband, polarization-insensitive, large-viewing-angle absorber will easily find applications in solar cell, photodetection, and thermal emission. Additionally, this kind of structure can be further optimized for the application of perfect absorption in a wider band range or other bands.