Tilted Wire Metamaterials Enabling Ultra-Broadband Absorption from Middle to Very Long Infrared Regimes

Abstract

Infrared metamaterial absorbers underpin many entrenched scientific and technical applications, including radiative cooling, energy harvesting, infrared detectors, and microbolometers. However, achieving both perfect and ultra-broadband absorption remains an unmet scientific challenge because the traditional metamaterial absorber strategy suffers from complex multi-sized resonators and multiple meta-element patterns. We demonstrate a simple ultra-broadband infrared metamaterial absorber consisting of tilted graphite wires and an Al reflector. The proposed tilted wires-based metamaterial (TWM) absorber exhibits absorption of above 0.95 across the middle to very long-wavelength infrared spectrum (3–30 µm). By increasing the aspect ratio, the bandwidth can be expanded and achieve near-perfect absorption in the 3–50 μm spectral range. The excellent infrared absorptance performance primarily originates from the ohmic loss induced by the electromagnetic coupling between neighboring tilted wires. Furthermore, we propose a typical three-layer equivalent model featuring a resonator/insulator/reflector configuration that requires more than 84 resonant cavities to obtain comparable infrared absorptance. Our high-performance TWM absorber could accelerate the development of next-generation infrared thermal emitters and devices and other technologies that require infrared absorption.

1. Introduction

Infrared (IR) absorbers have emerged as attracting great interest due to their great demand for various entrenched scientific and technical applications, such as radiative cooling [1,2], energy harvesting [3,4], IR detectors [5,6], and microbolometers [7,8]. Metamaterials comprising meta-element structures can flexibly manipulate electromagnetic wave properties, which has been demonstrated to be an efficient way to create perfect absorbers [9,10,11]. For example, graphene-based metamaterials, including multilayered graphene and graphene-Al₂O₃ or SiO₂ stacks, can realize needed absorption due to plasmonic resonance [12], adjustable chemical potential [13], and the easily modified effective refractive index [14,15]. The perfect absorption of metamaterials has made great progress based on diverse electromagnetic coupling resonance theories or modes, including the impedance matching theory [16,17,18], the epsilon-near-zero mode [19,20,21], Fabry–Pérot resonance [22,23,24], propagating surface plasmon resonance [25,26,27], localized surface plasmon resonance [25,28,29,30], and magnetic plasmon resonance [31,32,33]. However, IR metamaterial perfect absorbers only work at specific wavelengths due to their limited resonance features. To broaden the absorption bandwidth, two efficient methods have been proposed: coupling multi-sized meta-metallic resonators [34,35,36,37,38] and incorporating multiple meta-element patterns [25,39,40] in rationally designed unit cells. Despite these great achievements, there is still a significant unmet scientific challenge in achieving both high and ultra-broadband absorption due to the complicated structures of these metamaterials. Therefore, developing new structures and electromagnetic coupling mechanisms that avoid the complex design strategy of conventional IR metamaterial absorbers is highly anticipated to address the challenge.

In addition to rational structure design, embedding lossy materials in metamaterial structures provides an effective combination of intrinsic absorption and hybrid plasmon resonances, resulting in enhanced absorption and bandwidth in the target IR regime. For a typical metamaterial absorber with a metal/insulator/metal (MIM) configuration, lossy dielectric materials (e.g., Si₃N₄, Al₂O₃, ZnS, and SiO₂) [27,41] are selected as middle resonant cavities and lossy conductive materials are used as top resonators. The commonly used intrinsically lossy conductive materials are lossy metals (e.g., Cr, Ti, W, and Ni) [25,42] and transparent conductive oxides (e.g., Al-doped ZnO (AZO) and indium tin oxide (ITO)) [43,44,45]. Graphite also possesses lossy conductive properties and has been reported to function as a metamaterial resonator focusing on the THz and GHz regimes [46,47,48,49,50]. However, graphite-based metamaterial absorbers have rarely been explored for ultra-broadband absorption from the middle to very long IR regimes (3–50 μm). Wire metamaterials are also a broad class of artificial electromagnetic materials consisting of aligned metallic rods embedded in a dielectric matrix [51,52,53,54,55]. In contrast to the widely used MIM-based absorbers whose top resonator attaches to the insulator layer, wire resonators can directly grow on a substrate without insulator support. Furthermore, the orientation of the optical axis (tilted degree of wires) can be utilized as an additional degree of freedom to modulate the structural impedance for matching with free space [56,57,58]. These imply that utilizing graphite wires as resonators to form a simplified metamaterial has great potential for exciting strong electromagnetic coupling, leading to perfect absorption at the desired wavelengths.

Here, we propose an ultra-broadband metamaterial absorber with high absorptance from the middle to very long IR regions. The metamaterial exhibits a simple configuration consisting of tilted graphite wires and an Al reflector. Due to the ohmic loss induced by the electromagnetic coupling between neighboring tilted wires, the TWM absorber with an aspect ratio of 10 can absorb IR light of >0.95 in targeted IR wavelength ranges of 3–30 μm. An increase in the aspect ratio will further expand the bandwidth and enhance the absorptance. In contrast, an equivalent model with a conventional three-layer structure requires more than 84 resonant cavities to achieve a comparable IR absorptance. This work provides new possibilities for improving the performance of IR absorber-based materials.

2. Structural Design and Simulation Methods

The concept of the proposed ultra-broadband absorber consists of a square array of tilted graphite wires grounded by an Al reflector, as illustrated in Figure 1. We selected graphite for designing the resonators because of the lossy conductive property, which enables both intrinsic absorption and resonant electromagnetic coupling. We used Al as the back-reflector due to the excellent reflectivity in the IR spectral range. Other metals, such as silver and copper, can be used if they are thick enough to provide IR reflection and avoid penetration.

We performed the finite difference time-domain (FDTD) approach to calculate the optical performance for our proposed structure based on the FDTD solutions (V8.21.1882, Lumerical Solutions, Vancouver, BC, Canada) [59]. In the simulation, a plane wave with different wavelength ranges was employed in the z-axis backward direction and perpendicular to the Al reflector layer. In the x and y directions, periodic boundary conditions were used, and perfectly matching layer (PML) boundary conditions were set along the z-direction. The mesh sizes were set to the minimum value between one-sixth of the minimum wavelength and one-third of the minimum size of the structure, which is controlled by the script. The absorptivity (α) is determined by R + T + α = 1, where R and T represent the reflectivity and transmissivity, respectively.

Before optimizing the design, selecting the appropriate target bands is essential. The Earth’s atmosphere exhibits typical transparency windows in the wavelength range of 8–13 μm, which are utilized in various fields such as radiative cooling, IR detection technology, and IR imaging [6,60,61]. Additionally, the very long IR regime (14–30 μm) finds applications in interstellar target detection in space, as well as in tracking detection for missiles, satellites, and other aircraft [25]. Studies focusing on the wavelength ranges of 3–30 μm and 3–50 μm are particularly relevant to radiative thermal regulation, as ultra-broadband IR absorbers within these ranges demonstrate a larger net cooling power [62,63]. Furthermore, integrating an IR absorber (radiative cooler) with a thermoelectric generator can facilitate energy harvesting by generating electricity from darkness [4]. Consequently, we have selected the wavelength ranges of 8–13 μm, 3–30 μm, and 3–50 μm as our target bands for further investigation.

The geometrical parameters were optimized by the particle swarm optimization (PSO) algorithm [64] to maximize the average absorptivity aiming at wavelength regions of 8–13 μm, 3–30 μm, and 3–50 μm. We created optimization tasks using FDTD Solutions software’s built-in PSO algorithm. The average α is defined as figures of merit. The maximum generations, generation size, and tolerance are set to 50, 12, and 0, respectively. For the small aspect ratio (l/D) TWM, the ranges of the wire’s gap g, tilt angle θ, diameter D, and length l are set to 0–10 μm, 0–70°, 1–6 μm, and 0–10 μm, respectively. For the large aspect ratio TWM, the ranges of the wire’s gap g, tilt angle θ, diameter D, and length l are set to 0–20 μm, 0–70°, 0.2–10 μm, and 0–60 μm, respectively. We also ran a parameter sweep based on FDTD Solutions to verify the accuracy of the PSO results and investigate the effect of the geometry parameters on spectral performance. When sweeping the specific parameter values, other parameters maintain the optimal dimensions obtained by the PSO algorithm. During and after running the PSO algorithm and parameter sweep, no error messages should be displayed, and the “Auto shutoff” value should be less than 1 × 10⁻⁵.

3. Results and Discussion

For both Al and graphite materials, the real (n) and the imaginary (k) parts gradually increase with the increase in wavelength, as shown in Figure S1. Al shows typical metal behavior because the real part of dielectric permittivity (ϵ_real) is always less than zero (ϵ_real = n² − k² < 0). Although graphite is one of the well-known conductive materials, the n is slightly larger than the k across the infrared regions. In addition, there are no obvious peaks for k, which are different from the dielectric materials, for example, ceramic particles (e.g., Al₂O₃ [59]) and polymers (e.g., polyurethane [65]). The calculated results show that the Al film exhibits perfect reflectivity and zero absorptivity (Figure S2), which is consistent with those reported in the literature [66]. Thus, we confirm the reliability of the FDTD Solutions software’s simulation setup, including the light source, meshing, and boundary conditions. Unlike the perfect reflectivity exhibited by the Al film, the lossy conductive performance of graphite film provides both reflection and absorption in the IR regions (Figure S3). When the thickness of graphite film is larger than 10 μm, it shows a higher reflectivity (0.681) than absorptivity (0.319) in 3–50 μm. The absorptivity can be significantly improved if designed into TWM structures.

The optimized results show that the TWM absorber with a small aspect of 10 exhibits a high absorption of 0.952 over the ultra-broadband range from the middle to very long IR regimes (3–30 μm), as shown in Figure 2a and

Table 1. Optimal dimensions of the TWM absorber with the small aspect ratio (l/D) to maximize absorptivity using the PSO method.

Target Band (μm)	t (μm)	g (μm)	θ (°)	D (μm)	l (μm)	l/D	Average α
8–13	0	2.62	49.0	4.58	10	2.18	0.995
	0.3	2.06	42.6	5.71	9.9	1.74	0.995
3–30	0	2.66	47.6	5.18	9.9	1.91	0.904
	0.3	3.94	56.4	1	10	10.0	0.952
3–50	0	2.02	42.2	4.92	10	2.03	0.81
	0.3	3.29	50	2.06	10	3.27	0.89

. Notably, the TWM absorber with the small aspect can achieve near-unity broadband absorption in the 8–13 μm spectral range. Increasing the aspect ratio will significantly contribute to both the bandwidth and absorption (Figure 2a and Table S1). For example, a large aspect TWM absorber with D = 0.394 μm shows near-perfect absorption in 3–50 μm. Furthermore, the incorporation of an Al reflective layer is indispensable for achieving significant improvements in spectral absorption (Figure 2b,c). These benefits are attributed to the ability of the Al reflector to avoid IR wave transmission and provide more absorption opportunities for the wire resonators (Figures S4–S6).

Furthermore, we compared the performance of our TWM with the existing metamaterial absorbers to demonstrate its advantages, as shown in Figure 3 and Table S2. Remarkably, the proposed TWM absorber features both excellent absorptivity and bandwidth, exceeding most of the values achieved by broadband metamaterial absorbers in the IR regime. In addition, the TWM absorber features a simple structure and requires only two types of materials. In contrast, other absorbers typically employ multilayer, multi-sized resonators or a greater variety of materials to achieve broadband absorption (Table S2). The proposed tilted wires can be fabricated through standard lithographic protocols along with the angle-controllable reactive ion etching technique [67,68]. The detailed proof-of-concept fabrication processes and discussion are illustrated in Figures S7 and S8. Small aspect ratio wires are advantageous for fabrication [68,69,70]; however, large aspect ratio TWM absorbers more effectively demonstrate the IR response. Consequently, for the subsequent sections, we will study the impact of the dimensions on the IR performance and insight into electromagnetic coupling mechanisms using a large aspect ratio TWM absorber with an optimal α_{3–50 μm}.

We next explored the effect of the significant geometry parameters on the spectral performance of our TWM absorber. It is apparent that there exists a limited region possessing ultra-broadband near-perfect absorption (>0.95) for different gaps g, tilt angles θ, and diameter D as shown in Figure 4a,c,e, respectively. In contrast, we can obtain a larger and even unlimited open region when increasing the length l of the wires (Figure 4g). These large regions, surrounded by the contour of α = 0.95, provide additional alternative dimensions and a robust design for perfect absorbers. Furthermore, the average α shows a strong, nonlinear dependence on the wire’s gap g in terms of all the target spectral ranges, including 8–13 μm, 3–30 μm, and 3–50 μm (Figure 4b). The average α is low for small-gap wires, reaching a maximum at a pitch of 4.01 μm and then dropping at the increased gap. However, it shows a weaker dependence on other geometry parameters (Figure 4d,f,h). The results also show that the average spectral α at 8–13 μm (α_{8–13 μm}) is always larger than that of α_{3–30 μm} and α_{3–50 μm}, regardless of the increased dimensions. We also provide a comparison of the optimal results obtained by running a parameter sweep and the PSO methods, as shown in Tables S1 and S3. Despite slight variations in the parameters, the average absorptivity shows a negligible difference of less than 0.001. Therefore, we demonstrate that the maximum values of the average spectral α achieved by sweeping the geometry parameters are consistent and well within the optimal results obtained by the PSO algorithm, indicating the reliability of the PSO method. Furthermore, to investigate the nonlinear effect, we calculated the IR performance under varying incident power densities, as shown in Figure S9. Our results show that both the IR spectrum and average absorptivity remain constant as the incident light power density increases from 0.01 to 3000 W/m². Thus, it indicates the absence of apparent nonlinear effects in our proposed structure.

To reveal the absorption mechanism, we calculate the effective impedance of the proposed TWM absorber. The impedance of our structure can be acquired by the scattering parameter [17,71], expressed as

$$\begin{array}{c}Z=\pm \sqrt{{\displaystyle \frac{{\left(1+S_{11}\right)}^2-{S_{21}}^2}{{\left(1-S_{11}\right)}^2-{S_{21}}^2}}}\end{array}$$

(1)

where S₁₁ and S₂₁ are the S parameters and represent the scattering coefficients of normal incidence reflection and transmission, respectively. The behaviors of the incident electromagnetic waves reflected by the structure can be described as

$$\begin{array}{c}R(\lambda )={\displaystyle \frac{({{Z\left(\lambda \right)}^{\prime }-1)}^2+{\left({Z\left(\lambda \right)}^{″}\right)}^2}{({Z\left(\lambda \right)}^{\prime }+1{)}^2+{\left({Z\left(\lambda \right)}^{″}\right)}^2}}\end{array}$$

(2)

where ${Z\left(\lambda \right)}^{\prime }$ and ${Z\left(\lambda \right)}^{″}$ are the real and imaginary parts of the complex impedance ($Z(\mathsf{\lambda })={Z\left(\mathsf{\lambda }\right)}^{\prime }+{Z\left(\mathsf{\lambda }\right)}^{″}·i$) at a wavelength of λ.

From Equation (2), we can find that when ${Z\left(\lambda \right)}^{\prime }$ = 1 and ${Z\left(\lambda \right)}^{\prime \prime }=0$, the reflectivity R($\mathsf{\lambda }$) will equal 0, indicating that the impedance of the structure is perfectly matched with free space. Under this ideal condition, we can achieve unity absorbance if it is without electromagnetic wave transmission through the structure because α = 1 − R when T = 0. For our proposed TWM structure, ${Z\left(\lambda \right)}^{\prime }$ and ${Z\left(\lambda \right)}^{\prime \prime }$ approach 1 and 0, respectively, over an ultra-broadband wavelength range, which suggests that the input impedance matches well with free space (Figure 5a). This will provide electromagnetic coupling between the tilted wires in the targeted IR region. Therefore, these results prove that the TWM structure enables near-perfect absorbance due to the presence of the Al back-reflector preventing transmission. Furthermore, to investigate the physical mechanism of the variation in absorptivity with the tilt angle θ, we calculated the effective impedance of the TWM structure as a function of the tilt angle and wavelengths. The results show that altering the tilt angle significantly affects both the real part and the imaginary part of the impedance across the ultra-broadband IR regions (3–50 μm), as shown in Figure 5b,c. Specifically, when θ = 0, the real part and the imaginary part deviate substantially from 1 and 0, respectively. Conversely, when the tilt angle is increased to approximately 52.7°, the impedance of the proposed absorber closely matches that of free space (Figure 5a). As the tilt angle continues to increase, a slight impedance mismatch evolves. Notably, the variation in impedance is consistent with the IR spectral performance, as shown in Figure 4c,d. Therefore, the absorption characteristics vary with the tilt angle due to the tunable impedance matching between the proposed structure and free space.

To further understand the physical mechanism in the proposed ultra-broadband absorber, we calculated the distributions of the electromagnetic field, the current density, and the power loss for the TWM structures, as shown in Figure 6. We calculated them at a representative wavelength of 10.8 μm, where the proposed structure shows a peak absorption of approximately 1. Apparently, strong resonant electromagnetic coupling occurs between tilted neighboring wires and is mainly distributed on the top surface of the wires (Figure 6a). The direction of the induced current density vector mainly flows along the radial direction of the wires, and the intensity decreases from top to bottom (Figure 6b). Furthermore, the energy loss distribution coincides precisely with the location where the currents accumulate, indicating that the perfect absorption of the graphite-based TWM absorber originates from ohmic loss (Figure 6c). We also captured the time-domain dynamic distribution of the electric field ${\left|E\right|}^2$ to vividly perceive the electromagnetic wave coupling of our TWM absorber (Figure 6d). When IR light propagates from top to bottom, it is strongly confined around the surface of the wires and primarily dramatically dissipates at the upper part without transmitting and near-zero reflecting. Therefore, we can confirm that the ultra-broadband absorption of the TWM structure mainly arises from the strong electromagnetic coupling resonant induced by neighboring tilted graphite wires.

For a comparison, we proposed a typical three-layer equivalent model to clearly elucidate the advantages of our TWM structure. We decomposed the entire graphite wires into smaller elements with a quantity of m, each containing a square graphite resonator, air insulator, and Al reflector (Figure 7a). The equivalent model is analogous to a well-known MIM configuration with multi-sized insulator resonant cavities (the thickness is denoted as h_m − D/2) to achieve the same ultra-broadband absorption as the TWM structure. The simulated results show that the absorption spectrum of the equivalent model gradually increases with the increasing number of divided elements m (Figure 7b,c). Achieving excellent absorption performance (e.g., the average absorptivity > 0.97) at 3–50 μm requires more than 84 resonant cavities of different sizes, which indicates a more complicated structure than the TWM structure. Therefore, we can demonstrate that our proposed TWM structure possesses unprecedented properties, including a simple structure, high absorptivity, and ultra-broadband bandwidth.

4. Conclusions

In summary, we theoretically demonstrated an IR absorber using graphite-based tilted wire metamaterials. The proposed absorber exhibits excellent performance, such as simple structures, high absorptivity, and an extremely large bandwidth of 27 μm for the small aspect ratio and 47 μm for the large aspect ratio from middle to very long-wavelength IR ranges. This high absorption is confirmed by the impedance matching theory. Through insight into the physical mechanism, we find that ultra-broadband near-perfect absorptance mainly originates from the ohmic loss induced by the electromagnetic coupling between neighboring tilted wires. Furthermore, our TWM structure will significantly reduce the design parameters compared to the three-layer equivalent model like the MIM structure. We believe that the tilted wires metamaterial absorber may function as a general structure because there exists a broad range of lossy conductive materials (e.g., ITO, AZO, and doped silicon) that can be used as alternatives for realizing the advantage of CMOS compatibility and further expanding the application field. Moreover, our feasible design strategy for IR absorbers may open opportunities for the accelerated development of next-generation high-performance IR thermal emitters, and other technologies that require IR absorption.