Design of a Far-Infrared Broadband Metamaterial Absorber with High Absorption and Ultra-Broadband

Abstract

We designed a metamaterial far-infrared absorber based on an MDM (metal–dielectric–metal) structure. We made a hollow crossed Ti microstructure at the top of the absorber. It is known that the coupling effect of equipartitional exciton resonance and intrinsic absorption at the surface of the depleting material has a strong influence on the absorber. Based on this, we investigated the absorption characteristics of the absorber using the Finite Difference in Time Domain (FDTD) theory. The results show that the absorber absorbed more than 90% of the light within a bandwidth of 12.01 μm. The absorber has an average absorption of 94.08% in the longwave infrared (LWIR) to ultra-longwave infrared (UWIR) bands (10.90–22.91 μm). The polarization insensitivity of the designed absorber is demonstrated by analyzing the absorption spectra of the absorber at different polarization angles. By adjusting the relevant geometric parameters, the absorption spectrum can be independently adjusted. Furthermore, the absorber exhibits good incidence angle insensitivity in both transverse electric (TE) and transverse magnetic (TM) modes. The absorbers are simple and easy to configure for applications such as optical cloaking, infrared heat emitters, and photodetectors. These advantages will greatly benefit the application of absorbers in practice.

1. Introduction

Electromagnetic metamaterials are manmade materials consisting of sub-wavelength artificial cells [1,2,3,4]. They have a different cellular structure than natural materials and can be impedance-matched to free space [5]. The design of metamaterials is very flexible. We can change their structural and geometric parameters to provide them with many physical properties that are difficult to obtain in nature [6,7,8]. Thus, by artificially altering and optimizing the structure of metamaterials, they can be made to exhibit a wide variety of peculiar electromagnetic properties on a macroscopic scale [9]. These properties make electromagnetic metamaterials very promising for many applications, such as imaging [10], sensing [11,12,13], and optical manipulation [14,15]. It is because of their rich electromagnetic properties that they have also been referred to as left-handed materials [16], photonic crystals [17], and hypersurfaces [15]. The study of metamaterial absorbers has received more and more attention since Landy et al. experimentally found that metamaterial absorbers have a perfect absorption peak in the microwave band [18]. Their spectral absorption properties are well characterized in the terahertz [19,20,21], microwave [22,23], near-infrared [24,25], and visible wavelength bands [26,27,28], and they have great application potential in solar energy collection [29,30,31], heat emitters [32], gas detection [33,34], and other fields. Typical metamaterial absorbers consist of two metallic layers and a dielectric layer, usually comprising a three-layer structure [35]. Due to their structural properties, they are called metal–insulator–metal (MIM) structures. With the expansion of electromagnetic metamaterials research, MIM absorbers stand out because of their resonance properties and have received much attention. Prior to this, there have been many reports on metal–metal (MM) absorbers. However, MM absorbers are mostly narrowband absorbers, and the broadband absorption problem needs to be solved. The emergence of MIM absorbers can solve this problem. In 2019, Ling Li et al. designed a periodic array MIM structure consisting of single-size Ti patches and interlayer (Ti/SiO₂/Ti) planes [36]. It has an average absorbance of 96.7% over the wavelength range of 8–13 μm. In 2020, Yu Zhou et al. designed an MIM absorber with a Ti–Ge–Ti structure which was able to achieve an average absorption of 87.9% in the range of 8–14 μm [37]. In 2021, Zheng Qin et al. proposed an absorber consisting of an array of Ti–Si–Ti cut lines [38]. It has an average absorption of 94% in the 7.5–13.25 μm wavelength range and is insensitive to polarization and the angle of incidence. From previous studies, we can find that metal nanostructures on the surface of metamaterials can broaden their absorption spectra. However, the absorption bandwidth of these absorbers is still limited. Therefore, it is essential to design absorbers with a wider absorption bandwidth.

In this work, our team designed a long-wave infrared broadband absorber based on a metal–dielectric–metal (MDM) structure [39]. It is easy to configure and has a novel structure. It is topped by a hollow crossed Ti microstructure. The hollow shape of the microstructure is orthorhombic. Ti was chosen as a microstructural material because it can more easily achieve perfect absorption compared to other metals commonly used in metamaterials [40,41]. The intermediate layers of the absorber are the dielectric layers Si, Si₃N₄, and SiO₂. It uses Ti as a reflector on the bottom. This structure can realize the perfect coupling of the surface plasmon resonance and the intrinsic absorption of the material, thus improving the absorption efficiency of the absorber. Meanwhile, Si in the dielectric layer is a lossless material with a small imaginary part of the dielectric constant. It can effectively extend the absorption bandwidth in combination with lossy dielectric layers. Si₃N₄ has a high loss effect on electromagnetic waves. It has unique physical and chemical properties. This enhances the absorber’s absorption properties in the long-wave infrared band. Through the design of its surface microstructure and the tuning of other structural parameters, an absorption of more than 90% in the long-wave infrared (LWIR) to ultra-long-wave infrared (UWIR) bands (10.90–22.91 μm) was realized. It has an average absorbance of 94.08% and an absorption bandwidth of 12.01 μm. In a word, we designed a simple and unique absorber structure with polarization insensitivity. This structure has good absorption in the LWIR to UWIR bands. We thus designed absorbers for applications such as light detection, optical stealth, and solar energy harvesting.

2. Structural Design and Parameterization

We propose and investigate an absorber design that realizes high absorbance and a broad band from long infrared to ultra-long infrared wavelengths. To achieve this goal, we tuned the dielectric layer composition of field metamaterial perfect absorbers (MAPs). On this basis, an absorber based on the metal–dielectric–metal (MDM) structure was designed. We designed the absorber structure as shown in Figure 1. The structure of each cell of the absorber is shown in Figure 1b,c. Each cell consisted of five layers of material, and we used a hollow crossed Ti microstructure for the top of the absorber. The absorber’s dielectric layer included a lossless material planar layer and two lossy planar layers. In contrast to other absorber materials containing lossy materials (including SiO₂ [24] and Si₃N₄), we used a composite dielectric layer consisting of both lossy and lossless materials. Figure 2 illustrates the real and imaginary parts of the dielectric constant of the absorber material. The real and imaginary parts of the dielectric constant are related to the refraction and loss of light, respectively. Si₃N₄ has a larger imaginary part of the dielectric constant in the first half of the target band, while SiO₂ has a larger imaginary part of the dielectric constant in the second half of the target band. The larger real part of the dielectric constant of Si increases the propagation distance of the electromagnetic wave in the lossy material. When an electromagnetic wave is incident into the absorber, most of the band is absorbed. This allows our absorber to achieve high broadband absorption. The refractive indices and other parameters of Si₃N₄ in the dielectric layer are from Kischkat [42], and the refractive indices and related parameters of Ti, Si, and SiO₂ are from Pailk [43]. In addition, we fitted the material parameters. We used FDTD (Lumerical FDTD Solutions) for simulation. In the simulation, we set the mesh precision to 3 and set the mesh type to automatic non-uniform mesh. We set up the mesh in the microstructure and the rest separately. The microstructure part of the grid had a dx of 0.1 microns, a dy of 0.1 microns, and a dz of 0.0025 microns. The dx of the mesh in the rest of the structure was 0.1 microns, the dy was 0.1 microns and the dz was 0.01 microns. We set the periodic boundary conditions (periodic) in the X and Y directions and the ideal matched layer boundary condition (PML) in the Z direction to prevent the dispersion of the material simulation. We obtained the transmittance and reflectance of the absorber by setting up monitors. In this case, the reflectivity monitor was located 1.6 microns directly above the surface of the absorber and the transmittance monitor was located 0.8 microns directly below the lowermost layer of the absorber. After several simulations of the structural parameters, the optimized parameters were obtained.

The results of the designed absorber are still satisfactory, balancing the high absorption rate and broadband absorption. The top of the absorber is a hollow crossed titanium microstructure, and the hollow shape of the microstructure is orthorhombic. The cross-structure has a length of b = 1400 nm, a width of a = 680 nm, and a thickness of h5 = 23 nm. The length of the hollow side of the orthorhombic structure is w = 820 nm and is the same thickness as the nanosquare. In the unitary structure, the period of the absorber is P = 2.8 μm, and the thicknesses of the intermediate SiO₂, Si₃N₄, and Si dielectrics are h2 = 510 nm, h3 = 300 nm, and h4 = 390 nm, in that order. The thickness of the substrate Ti is h1 = 200 nm, which is the default value. We know that its thickness is much greater than the skinning depth of Ti. So, it can be assumed that the electromagnetic wave is completely absorbed by the Ti substrate at this point. In other words, the use of this thickness of Ti substrate prevents electromagnetic waves from passing through the absorber. The effect of these variations in structural parameters on absorber performance will be studied in more detail later.

3. Calculations and Discussion

In this section, we will specifically analyze the effects due to the structural parameters of the absorber. Figure 3a shows the absorption, reflection and transmission curves of the designed Ti–Si–Si₃N₄–SiO₂–Ti five-layer absorber. As shown in this figure, the absorber we designed has the dual characteristics of a wide absorption bandwidth and a high absorption rate. The absorber has an absorption bandwidth of 12.01 μm above 90% absorption. It has an absorption band of 10.90–22.91 μm, and has an average absorption of up to 94.08%. The absorber has four different resonance wavelengths of 11.69 μm, 14.95 μm, 20.14 μm, and 22.28 μm. These corresponded to absorbances of 94.35%, 97.40%, 98.18% and 92.60%, respectively. Polarization characteristics are an important measure of how good an absorber is. They can have a direct impact on whether the absorber can be put into actual production. The absorption spectra of the absorber under different polarization modes (polarization angle 0–90°) are shown in Figure 3b. From this figure, we can see that the absorption spectrum of the absorber does not change when the polarization angle is varied. The absorption spectrum varies only with wavelength [44,45]. Therefore, we design our absorbers to be polarization-independent.

A comparison of the absorption data of our designed absorber with other absorbers is given in

Table 1. Comparison of the band range of absorption of different structures with the average absorption over the wavelength range.

Reference	Band Range with Absorption	Average Absorption in the Band Range
[46]	2.98–4.84 μm	More than 90%
[47]	900–1825 nm	More than 50%
[48]	8–12 μm	More than 90%
[36]	8–13 μm	96.7%
[38]	7.5–13.25 μm	94%
[35]	8–12 μm	95%
[6]	8.98–16.21 μm	94.1%
Proposed absorber	10.90–22.91 μm	94.08%

[6,35,36,38,46,47,48]. From the data in this table, it is clear that the absorption bandwidth of our designed absorber far exceeds that of the previously proposed absorber. Moreover, our absorber has a higher average absorption rate than most absorbers. This indicates that our design is far superior to previous absorbers. Therefore, our absorber has more potential in areas such as solar energy collection and infrared detection.

In this work, we use the finite difference method with a three-dimensional time domain to optimize the structural characteristics of the absorber [49,50,51]. For numerical calculations, we choose a planar light source of 10–25 μm as the incident light of the absorber. This light source is incident vertically on the absorber along the z-axis. We consider the total absorption rate of the designed absorber to be [52,53,54]

$$A\left(\lambda \right)=1-R\left(\lambda \right)-T\left(\lambda \right)$$

(1)

where A(λ) is the wavelength, R(λ) is the absorber reflectance, and T(λ) is the absorber transmittance. In addition, due to the thicker design of the bottom Ti layer, its depth is greater than the penetration depth of the target incident light. It is used to prevent the incident light from passing through the absorber to achieve complete absorption. So, the transmittance T(λ) = 0. At this time, the absorption rate can be expressed as [35,55,56]

$$A(\lambda )=1-R(\lambda )=1-{\left|\frac{Z-1}{Z+1}\right|}^2=1-{\left|\frac{\sqrt{\mu }-\sqrt{\epsilon }}{\sqrt{\mu }+\sqrt{\epsilon }}\right|}^2$$

(2)

where μ and ε are the dielectric constant and effective permeability of the absorber, respectively. Z is the equivalent impedance of the absorber. When μ = ε, A(λ) can take the maximum value of 1. This indicates that at this point in time, the absorber achieves complete absorption, and we all know that perfect absorption can be obtained when the impedance of the absorber matches the impedance of the free space. So, electrical resonance is as important as magnetic resonance. After calculation, the equivalent impedance of the absorber is found to be [57,58]

$$Z=\frac{\sqrt{(1+{{\displaystyle S}}_{11}{)}^2-{{\displaystyle \left({{\displaystyle S}}_{21}\right)}}^2}}{\sqrt{(1-{{\displaystyle S}}_{11}{)}^2-{{\displaystyle \left({{\displaystyle S}}_{21}\right)}}^2}}=\sqrt{\frac{\mu }{\epsilon }}$$

(3)

where S₁₁ and S₂₁ are scattering coefficients with respect to the incident and reflected waves. We can use these two parameters to calculate the equivalent impedance, where $R(\lambda )={\left|{{\displaystyle S}}_{11}\right|}^2$, $T(\lambda )={\left|{{\displaystyle S}}_{21}\right|}^2$. We can achieve matched resonance by tuning the dielectric constant of the metamaterial to obtain high absorbance and broadband absorption.

We calculated the relative impedance, effective permittivity, and effective magnetic permeability curves of the absorber, and the results are shown in Figure 4.

Table 2. The relative impedance, effective permittivity and effective permeability at the peak wavelength of the absorber.

Wavelength (μm)	11.69	14.95	20.14	22.28
Re(Z_eff)	0.62	0.76	0.88	0.87
Im(Z_eff)	−0.06 i	−0.15 i	−0.22 i	−0.51 i
Re(ε_eff)	3.25	1.43	0.32	−3.02
Im(ε_eff)	9.30 i	9.49 i	11.21 i	10.60 i
Re(μ_eff)	1.95	2.99	4.62	7.99
Im(μ_eff)	3.29 i	4.94 i	7.95 i	7.95 i

“i” is an imaginary unit.

shows the values of relative impedance, effective permittivity, and effective permeability at the four absorption peaks. It is well known that when the relative impedance is 1 + 0i, it matches perfectly with the free space, resulting in perfect absorption. According to Figure 4, the position of the absorption peaks from the simulation highly coincides with the position of the absorption peaks calculated from the relative impedance curve. According to the calculation, only the relative impedance at 20.14 µm is closest to the perfect match condition. This verifies that the absorption is highest at 20.14 µm. The remaining three absorption peaks have a slightly lower impedance match and therefore lower absorption rates. Based on Equations (2) and (3), it can be seen that the impedance matching is also related to the effective dielectric constant and effective permeability. Here, we use the values given in Equation (3) and Table 2 to verify the relative impedance values at the absorption peaks. We find that the relative impedance values derived from the simulations are equal to the relative impedance values calculated using Equation (3). Moreover, we calculated the absorption at the absorption peak using the relative impedance value (Equation (2)). It is equal to the simulated absorption. This indicates that the effective permeability and effective permittivity are approximately matched at this point, bringing the relative impedance close to the ideal matching condition. This explains why our absorber shows four absorption peaks. Therefore, we can achieve a match by adjusting the dielectric constant and permeability of the absorber to achieve efficient absorption.

In order to study and analyze the physical mechanisms of the absorber, we examine the electric and magnetic field distributions at four resonant wavelengths. As seen in Figure 5a–h, the absorption bandwidth of the absorber is affected by the mixed resonance of the top hollow crossed titanium microstructure resonant cavity. The electric field exists mainly in the air slots at the edges of the cross-titanium microstructure hollow core and on both sides. Plasma excitations are generated from the edges of an orthogonal hollow and propagate in the X direction. In order to better analyze the absorption mechanism, the magnetic field distribution at the resonant wavelength is given in Figure 5i–l. From this figure, we can see two different resonance modes. Figure 5i shows that at the first absorption peak, the PSP (propagating surface plasmon) and the LSP (localized surface plasmon) modes jointly affect the absorption [59,60,61]. However, the PSP mode dominates the absorption. As shown in Figure 5j, the LSP mode of the second absorption peak is enhanced compared to that with the first absorption peak, but is still dominated by the PSP mode [62]. As the wavelength increases, the LSP mode gradually dominates the PSP mode, and it becomes dominant at the 20.14 μm and 22.28 μm wavelengths, as shown in Figure 5k,l. We therefore concluded that changes in the LSP mode affect the PSP mode. The interaction of the LSP and PSP modes increased the absorption rate from 92.60% to 98.18%.

To better demonstrate the excellence of our absorber design, we designed three different shapes based on the original top microstructure shape for comparison. The absorption spectra under these four structural shapes are shown in Figure 6a, and the corresponding top layer diagrams of the absorbers for these four structures are given in Figure 6b. Individual nanocubes have the same length and width. The hollow thickness of each of these microstructures is the same as that of the nanocube. As we can see from this figure, the absorption curves of case 1 and case 2 are only slightly different. This suggests that plasma resonance occurs mainly on both sides of the hollow crossed Ti microstructure. The only difference between the case 3 and case 1 structures is that case 3 consists of a hollow structure, but their absorption curves are very different. From Figure 6a, it is obvious that the absorption effect of case 3 is much worse than that of case 1. This suggests that the presence of a central hollow structure tends to reduce the absorption performance when there is only a single titanium nanoblock. However, a hollow structure in the middle of a cross structure consisting of two nanosquares leads to higher absorption effects. This demonstrates the uniqueness of the microstructural shapes that we chose. In addition, we chose an axisymmetric structure shape with polarization insensitivity. This initiative greatly improves the plasma resonance at the absorber surface [63]. From Figure 6a, it can be seen that the peak absorption for case 4 was 94.35%, 97.40%, 98.18%, and 92.60%. It has a higher average absorption rate that can reach up to 94.08%. During the evolution from case 1 to case 4, the effect of absorption changes. In summary, we believe that the generation of surface plasmon resonance is inextricably linked to the geometrical parameters of the microstructures [64]. This reflects the uniqueness of our designed microstructured MDM absorber, and it absorbs better than the other microstructured MDM absorbers in the LWIR to UWIR bands.

In this work, by adding lossy materials to the dielectric layer, we increase the absorptivity of the absorber and broaden the absorption bandwidth. As is known, plasma resonance is related to the structure of the absorber. Therefore, we change the structural parameters of the absorber to realize the complementary resonant absorption of LSP and PSP [65]. This can flexibly adjust the pattern of advantage absorption. Based on this, we further investigated the effect of these parameters on the absorption performance. Figure 7a–c show that the thickness of the dielectric layer has an effect on the absorption effect. When the thickness of the dielectric layer is increased, the resonance wavelength is red-shifted. In this case, the positions of the absorption peaks that dominate both the PSP mode and the LSP mode are red-shifted [66]. When we reduced the thickness of the dielectric layer, a different situation was observed. From Figure 7a, it can be seen that a decrease in the thickness of the dielectric layer leads to a blue shift in the resonance wavelengths. At the same time, we also find in Figure 7c that the reduction in the thickness of the dielectric layer leads to a blue shift in the resonance wavelength. However, Figure 7b indicates a different scenario. It is seen from this figure that the first resonance wavelength is red-shifted and the rest of the resonance wavelengths are blue-shifted when the thickness of Si₃N₄ decreases. We believe that this situation is related to the fact that Si₃N₄ has high losses at these wavelengths. The shift of the resonant wavelength in the rest of the cases can be explained by interference theory [67,68], where an increase in thickness increases the phase difference. This causes the resonant wavelength to increase. Conversely, a decrease in thickness decreases the resonant wavelength. Figure 7d shows the absorption profile of the absorber as the thickness of the surface microstructure varies. It can be seen that the absorptivity is insensitive to changes in the thickness of the microstructure. The optimal thickness is between 13 and 33 nm.

We analyze the influence of the period of the absorber. Figure 8a shows that continuous absorption with more than 90% absorption cannot be achieved when the absorber period is P = 1800 nm or P = 2300 nm. The absorption bandwidth is narrower when the period is P = 3300 nm or P = 3800 nm. We therefore chose the optimal period, P = 2800 nm. We also explored the effect of the top microstructure parameters on the absorber. In Figure 8b, we find that the absorber does not achieve continuous absorption when the width of the nanocube is a = 0.48 µm or a = 0.88 µm. From Figure 8c, we find that the absorption bandwidth of the absorber is too narrow for a nanocube length b = 1.2 µm. At b = 1.6 µm, the absorber cannot achieve continuous absorption. In Figure 8d, we find that the absorption bandwidth of the absorber is too narrow at the edge length of the orthogonal hollow w = 0.62 µm. At w = 1.02 µm, the absorption profile does not change much compared to our chosen parameters. However, it cannot realize continuous absorption. Therefore, we did not choose it. In summary, the structural parameters we chose are excellent. Our results also show that the structural parameters of the structural absorber affect the plasma resonance. Therefore, we adjusted the structural parameters of the absorber to make the absorption satisfactory.

In this section, we will explore whether the absorption performance of the designed absorber is insensitive to the angle of incidence. We performed a parameter scan in transverse electric (TE) and transverse magnetic (TM) modes with a 5° step for the angle of incidence from 0 to 50° (keeping the electric/magnetic field parallel to the x/y axis). At this point, electromagnetic waves are incident into the absorber from above the absorber. The results are shown in Figure 9. We analyzed the results and found that in TE mode, when the incidence angle is in the range of 0–20°, it exhibits angle-independent absorption. The average absorption increases when the angle of incidence exceeds 30°. Angle-independent absorption is also observed when the angle of incidence is between 0° and 25° in the TM mode. The average absorption decreases when the angle of incidence exceeds 30°. In summary, the absorber we designed has a better insensitivity to the incidence angle. This is of great importance in practical applications [69,70,71].

Finally, we changed the material of the absorber surface microstructure to verify its universality. The results are shown in Figure 10. Au is a precious metal that has a high Q factor. Cr, Ni, and Ti are all metals with high melting points and high dielectric constants in the imaginary part. Due to their high losses, they have high absorption in the broadband range [72,73,74,75]. When we used Cr as the microstructure material, it had three absorption peaks, as shown in Figure 10. Its average absorption was more than 75%. However, we did not choose it because it could not achieve a continuous absorption of more than 90%. When we used Cu and Ni as the top layer materials, respectively, we found that their absorption curves were only slightly different. We know that Cu and Ni can be infinitely solid-solved with each other. They have similar crystal structures [76]. These properties result in small differences in their absorption curves. However, their average absorption when used as microstructure materials is too low for us to choose them. In the graph, we can see that the absorption of Au is below 90%, meaning that it is not suitable as a surface material. In summary, we find that refractory metals are significantly more effective as absorber surface materials than precious metal materials. Taken together, we chose Ti as the surface material of the absorber. It can balance high absorptivity and broadband absorption.

4. Conclusions

In summary, we have designed a broadband metamaterial absorber based on an MDM structure with a material composed of Ti, Si, Si₃N₄, and SiO₂. The top of the absorber is a hollow crossed Ti microstructure. We have performed numerical simulations of the absorber using the three-dimensional time-domain finite-difference method. The results show that the broadband absorption of the surface absorber in the far-infrared band from 10.90 to 22.91 μm exceeds 90%. The average absorption rate reaches 94.08% in the continuous absorption band (more than 90% absorption). In addition, we investigated the relationship between the absorber’s absorption performance and the structural parameters of the absorber, using the structural parameters of the absorber as variables. Based on this, we obtained the optimal structural parameters. In addition, we explained the mechanism by which the absorber realizes broadband absorption. We also verified that the absorber is polarization-independent and insensitive to the angle of incidence by simulating the absorption spectra. Finally, we changed the absorber surface structure material and quantitatively verified the superiority of refractory metals as microscopic materials over precious metals by simulating absorption curves. The absorber we designed has a simple structure and excellent absorption performance. It has great potential for solar energy harvesting, photodetection, and so on.