1. Introduction

Metamaterials are a type of artificial subwavelength electromagnetic materials with numerous exotic properties that are absent in natural materials. Their electromagnetic responses are mainly determined by the constituent materials and microstructures of resonant units. By tailoring the structures of those resonant units, metamaterials can achieve free control of electromagnetic waves, breaking the limitations of natural materials that are difficult to modulate at the atomic or molecular level. The unique properties of metamaterials allow for many interesting applications, such as electromagnetic cloaking [1,2], metalens [3–7], photodetector [8,9], and sensing [10–13]. As a specific subtype, metamaterials can be utilized as perfect absorbers, resulting in near unity absorption over a small or broad frequency band. They can also overcome the thickness limitation of traditional quarter wavelength devices. Therefore, perfect metamaterial absorbers (PMAs) have garnered considerable interest in recent years. Since the first successful demonstration of a PMA in 2008 [14], various strategies have emerged, leading to rapid expansion of PMA research in visible light [15–17], infrared [18–21], and even terahertz frequencies [22–24]. Despite these advancements, the resonant properties of plasma excitation still limit the absorption bandwidth of PMAs, making it challenging to achieve a broadband response.

As a key research direction, long wavelength infrared (LWIR) PMAs garner significant attention and have been used in various photothermal applications, particularly those related to infrared imaging [25,26] and infrared sensing [27–29]. Numerous efforts have been made to broaden the absorption bandwidth and enhance the efficiency of LWIR PMAs through a variety of strategies (See Table S1, Supplement 1). The general methods to achieve broadband absorption mainly include metal-insulator multilayer stacks [30–32], pyramid hyperbolic metamaterial [33–35], and nanocomposites [36–39]. Among these methods, both metal-insulator multilayer stacks and pyramid hyperbolic metamaterial rely on a vertical multilayer structure, which can support multiple electromagnetic responses to achieve broadband absorption. However, a drawback of this configuration is the increase in device thickness and fabrication complexity. PMAs based on nanocomposites consist of both metal nanoparticles and a porous structure. Typically, these PMAs usually operate in the visible and near-infrared spectral regions due to the limitations of the plasma wavelength of the metal nanoparticles. PMAs employing coplanar multi-sized resonators are another effective means of achieving broadband absorption. By utilizing multi-sized crosses [40,41], rings [42,43], disks [44–46], squares [47,48], or composite resonator structures [49,50], multiple surface plasmon resonances (SPRs) with adjacent wavelengths can be excited, resulting in broadband absorption. However, the fabrication of these multi-sized resonators usually requires fabrication techniques such as electron beam lithography [50] and focused ion beam etching [20], which are inefficient and costly, severely limiting the mass production and the practical application of broadband PMAs. Therefore, there is a strong desire to achieve broadband PMAs with mass-producible, easily configurable, and omnidirectional absorption.

In this paper, we present the design and demonstration of a high-performance absorber based on coplanar four-sized Ti/ZnSe/Ti resonators. The absorber exhibits broadband absorption (8 µm∼14 µm) with high efficiency (∼96.7%), while being insensitive to polarization direction and angle of incidence (up to ± 60°). We employ particle swarm optimization to optimize the complex geometry parameters, and fabricate the optimized device using a combination of magnetron sputtering, conventional optical lithography, and ion beam etching techniques. To gain further insight into the working principle of the absorber, we analyze its impedance matching condition with free space and examine the electric/magnetic field distributions at resonant wavelengths. Additionally, this work explores the effects of the geometry parameters and constituent disk metals on the absorption characteristics of the device. The presented broadband PMA in this article possesses immense potential in thermal emitters, infrared detection, and imaging applications, thanks to its mass production capability, easy configurations, and polarization- and angle-insensitivity.

2. Results and discussion

Figure 1(a) shows the schematic diagram of the proposed absorber. Each unit cell is a typical metal-insulator-metal (MIM) configuration, consisting of four Ti disks with different diameters hovering on a continuous Ti film with a thin ZnSe film sandwiched between them. Here, D₁, D₂, D₃, and D₄ respectively represent the diameters of these four Ti disks. P denotes the period of the proposed absorber, and thicknesses of the top, middle, and bottom films are represented by t, h, and d, respectively. Ti is chosen for the metallic layers due to its high extinction coefficient in the LWIR range (8 µm∼14 µm), which facilitates the realization of high-performance optical absorber in this work. ZnSe is chosen for the cavity layer due to its high refractive index without any loss across the entire operational bandwidth.

 

Fig. 1. (a) Schematic diagram of the proposed absorber. Each unit cell consists of a patterned Ti film with four different diameters, a planar Ti thin film, and a thin ZnSe film sandwiched between them. Diameters of these four disks are respectively denoted by D₁, D₂, D₃, and D₄. P is the period, and thicknesses of the three films are represented by t, h, and d, respectively. Angle of incidence of the illumination light is represented by θ, and polarization direction of the incident light is indicated by an angle φ of the electric field (E) with respect to the x axis. φ=0° represents TM polarization, and φ=90° is TE polarization. I, R, and T respectively represent the incidence, reflection, and transmission. (b) Simulated (red solid line) and measured (green dotted line) absorption spectra of the proposed absorber under unpolarized normal incidence. The optimized geometric parameters for the simulation process are: P = 6.7 µm, D₁ = 1.05 µm, D₂ = 1.43 µm, D₃ = 1.73 µm, D₄ = 2.07 µm, t = 23 nm, h = 0.95 µm, and d = 100 nm. The fabricated geometric parameters for the measurement process are: P = 6.78 µm, D₁ = 1.01 µm, D₂ = 1.51 µm, D₃ = 1.82 µm, D₄ = 2.22 µm, t = 24 nm, h = 0.87 µm, and d = 97 nm. (c) Optical and (d) SEM images of the fabricated sample, verifying period of each unit, diameters of the four disks, and thicknesses of the three films.

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As the proposed device involves several geometry parameters, manually designing it for high absorption could be time-consuming and might end up with sub-optimal device structure. To accelerate the device design process, particle swarm optimization (PSO) [51,52], as one of the popular intelligent inverse design algorithms, is employed to obtain the geometry parameters of the proposed device. For this work, seven geometry parameters including P, D₁, D₂, D₃, D₄, t, and h need to be optimized during the PSO process to achieve high absorption over the entire operational bandwidth. The thickness of the bottom Ti film is set to be thicker than its penetration depth (e.g., d = 100 nm) so as to prevent light transmission (T = 0). A detailed design process can be found in Fig. S1 in Supplement 1.

After sufficient rounds of iteration, the optimized parameters of the proposed device are as follows: P = 6.7 µm, D₁= 1.05 µm, D₂= 1.43 µm, D₃= 1.73 µm, D₄= 2.07 µm, t = 23 nm, and h = 0.95 µm. The red solid line in Fig. 1(b) shows the simulated absorption spectrum under unpolarized normal incidence, which is performed using the commercial software COMSOL Multiphysics. During the simulation process, the refractive indexes of Ti and ZnSe are displayed in Fig. S2 in Supplement 1, which are derived from Ordal [53] and Querry [54]. The absorption spectra under unpolarized light incidence are calculated by averaging the results of TE and TM polarizations. The absorption spectrum illustrates five peaks at wavelengths of 8.25 µm, 9.95 µm, 11.05 µm, 12.34 µm, and 13.7 µm, with corresponding absorption efficiencies of 99.6%, 99.2%, 97%, 99.6%, and 96%, respectively. The designed absorber also demonstrates an average absorption rate of 96.7% in the spectral range from 8 µm to 14 µm.

The Ti/ZnSe/Ti multilayer stack is sequentially deposited on a 2-inch silicon substrate using a magnetron sputtering system. Conventional optical lithography and ion beam etching techniques are then used for the microfabrication of the four-sized disk patterns. Optical and SEM images of the fabricated sample are shown in Figs. 1(c) and 1(d), illustrating the geometry parameters, i.e., P = 6.78 µm, D₁= 1.01 µm, D₂= 1.51 µm, D₃= 1.82 µm, D₄= 2.22 µm, t = 24 nm, h = 870 nm, and d = 97 nm. The geometry parameters are measured by using the grayscale profile along the structural unit (Fig. S3 in Supplement 1). The green dotted line in Fig. 1(b) represents the experimental absorption spectrum of the fabricated sample, which is measured using Fourier-Transform Infrared (FTIR) spectroscopy under unpolarized normal incident light. An average absorptivity of 88.9% for unpolarized radiation is obtained in the range of 8 µm to 14 µm. The discrepancy between the simulation and measurement mainly arises from two aspects: firstly, the deviation of the refractive index of the experimentally prepared material from the theoretical model data; secondly, the error in the experimentally fabricated absorber structure size and film thickness compared to the design values. To better verify our claim regarding the discrepancy, we conduct the simulation using the measured geometric parameters of the fabricated sample and refractive index derived from Ordal [53] and Rakić [55] (Fig. S4 in Supplement 1). And the simulation result based on the refractive index from Rakić is closely coincidence to the experimental result. Taken together, these results provide compelling evidence of the PMA's efficacy at absorbing radiation in this range, highlighting its potential applications in various fields, including sensing and energy conversion.

The entire absorber can be regarded as a resonant cavity enclosed by magnetic walls that support cavity modes, which causes cavity modes-induced light absorption. The incident light rips into the absorber and excites the surface plasmas in the upper and lower metal-dielectric interface. The interference between the surface plasmas in the upper and lower metal-insulator interfaces leads to resonant modes within the dielectric cavity of the device [56,57]. Through reasonable geometric parameter design of the absorber, it is possible to prevent light transmission and simultaneously minimize reflection (i.e., T = 0, and R = 0). Consequently, the light absorption capacity can then be well enhanced since A = 1-R-T.

To gain further insight into the working principle of the proposed absorber, we analyze its impedance matching condition with free space. As mentioned earlier, the bottom Ti layer has been designed with a thickness that exceeds its skin depth to prevent light transmission. By achieving an effective impedance of the absorber that matches that of free space, reflection can be effectively minimized. According to the effective medium theory [14], the reflection of an absorber can be expressed as:

The real part of the relative impedance is near unity, and the imaginary part is close to zero in the wavelength range from 8 to 14 µm (Fig. 2). During the calculation, we employ the optimized geometry parameters to extract the effective impedance of the proposed absorber. This observation is consistent with our intent to match the impedance to free space across a broad wavelength range. As a result, absorption is significantly enhanced, as the reflection is effectively minimized according to Eq. (1).

 

Fig. 2. Extracted effective impedance of the proposed absorber. Geometry parameters used in the calculation process are also based on the optimized result (P = 6.7 µm, D₁ = 1.05 µm, D₂ = 1.43 µm, D₃ = 1.73 µm, D₄ = 2.07 µm, t = 23 nm, h = 0.95 µm, and d = 100 nm).

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To further demonstrate how the absorber achieves broadband absorption through the multiple resonances, we conduct calculations of the electric and magnetic field distributions at the five resonant wavelengths of the absorption spectrum. Figure 3(a) shows the electric field distributions on the top surface of the proposed absorber, while Fig. 3(b) displays the magnetic field distributions in the vertical direction. An enhanced electric field distribution is observed at the edge of Ti disks, attributed to the excitation of surface plasmon polaritons (Fig. 3(a)). For the first absorption peak at λ = 8.25 µm, the magnetic field is strongly confined to both the ZnSe spacer and the gap area between Ti disks. Whereas, for the remaining four absorption peaks at λ = 9.95 µm, 11.05 µm, 12.34 µm, and 13.7 µm, the magnetic fields are well confined within the ZnSe spacer beneath the Ti disks (Fig. 3(b)). As a result, the first absorption peak is attributed to the propagation surface plasmon resonance (PSPR) occurring between the continuous Ti film and ZnSe spacer, while the remaining four peaks are primarily controlled by the localized surface plasmon resonance (LSPR) supported by the periodic Ti disks. Furthermore, the absorption wavelength corresponding to LSPR is determined by the diameter of the Ti disk, where smaller-sized Ti disks correspond to absorption responses at shorter wavelengths. For example, the absorption peak at 9.95 µm occurs at the smallest Ti disk (D₁= 1.05 µm), while the absorption peak at 13.7 µm occurs at the largest Ti disk (D₄= 2.07 µm). As a whole, the electric and magnetic field distributions demonstrate that the broadband absorption of the absorber is primarily achieved through the synergistic absorption of both PSPR and the LSPRs, as discussed above.

 

Fig. 3. (a) Electric field distributions of the top-view of the absorber at five resonant wavelengths (λ = 8.25 µm, 9.95 µm, 11.05 µm, 12.34 µm, and 13.7 µm). The white dotted lines (i.e., a-a and b-b) represent two center cross-sections of the absorber. (b) Magnetic field distributions of the cross-sections at the above five resonant wavelengths. Upper panel: a-a cross-section; Lower panel: b-b cross-section. Here, a TM-polarized normal incidence is considered.

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Infrared devices usually operate within a large range of incident angles, including the polarization direction and the angle of incidence. This requires the absorbers to maintain high absorption across a wide range of angles. Figure 4(a) illustrates polarization direction-dependent absorption spectra, where the state of polarization varies from TM to TE polarization as $\varphi $ changes from ${0^\circ }$ to ${90^\circ }$. The absorption spectra of the absorber remain mostly unaffected by a shift in the polarization direction, indicating polarization insensitivity. The polarization-insensitive behavior is attributed to the highly symmetrical nature of the Ti disks, while the minor differences in absorption spectra under different polarization angles are caused by the asymmetrical patterns of the periodic cells.

 

Fig. 4. (a) The dependence of the absorber’s performance on the polarization angle. Here, the polarization direction varies from TM to TE polarization as $\varphi $ changes from ${0^\circ }$ to ${90^\circ }$. (b) Angularly-resolved absorption spectra under unpolarized light illumination. Here, angle of incidence varies from 0° to 60°. (c) Thermal images of the fabricated absorber taken at different angles of incidence (10°, 20°, 40°, and 60°). (d) Simulated average absorption spectra (the green solid line) and measured emissivity (the red dotted line) as a function of angle of incidence.

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To validate the angular performance of the proposed absorber, we also simulate its angle-resolved absorption spectra under unpolarized light illumination, as shown in Fig. 4(b). It is clear that the proposed absorber exhibits relatively high absorption for the entire opertional bandwidth as the angle of incidence increases from 0° to 60°. The simulated average absorption spectrum under different angles of incidence is plotted in Fig. 4(d) (the green solid line), exhibiting an average absorption higher than 80% for angle of incidence up to 60°. The angle-insensitive performance is due to the localized surface plasmon (electric dipole resonance) supported by this configuration. The electric and magnetic fields of the cross-sections at two electric dipole resonances (λ = 9.95 µm, 11.05 µm) are shown in Fig. S5 in Supplement 1. To further evaluate the angular insensitivity of the proposed absorber, we design a demonstrative test and experimentally probe this behavior through direct radiometric measurements of their directional thermal emission. The detailed setup and measurement process are described in Fig. S6 and Fig. S7 in Supplement 1. The pre-fabricated sample is placed upon a thermostatic hot plate (50°C), and infrared thermal images of the absorber are taken at different angles using an infrared thermal imager (Fig. 4(c)), only exhibiting a small change in the captured temperature. The emissivity of the absorber at different angles is calculated by adjusting the built-in emissivity parameters of the infrared thermal imager [59], as shown in the red dotted line in Fig. 4(d). The measured emissivity is higher than 0.8 (or 80%) for angle of incidence up to 60°, which is well consistent with the simulation.

In addition to the diameters of the Ti disks, which primarily affect the absorber’s resonant wavelength as aforementioned in this article, alterations in the constituent metals as well as other geometry parameters, including the period (P), thickness of the Ti disk (t), and height of the ZnSe spacer (h), can also affect the absorption characteristics. Figure 5(a), 5(b) and 5(c) systematically illustrate the effect of geometry parameters (P, t, h) on the absorption spectra of the device. The absorber’s absorption efficiency is responsive to variations in both P and h. The period of the top grating plays a crucial role in determining the coupling conditions of the PMA, which leads to a slight displacement of the first absorption peak (Fig. 5(a)). Similarly, increasing the thickness of the dielectric layer remarkably enhances the phase difference of the incident light, resulting in redshifts of the resonant wavelengths (Fig. 5(b)). Different from modulating the period or dielectric layer thickness, increasing the thickness of Ti disk mainly influences the dielectric constant of top metal layer, leading to the absorption peaks with a high-quality factor. As a result, the bandwidth of absorption peaks narrows and the overall absorption rate decreases (Fig. 5(c)). Figure 5(d) shows the simulated absorption spectra of the absorber incorporating Au, Cr and Ti disks, which demonstrates a dielectric constant ranking of Au > Cr > Ti [53,55,60]. Our simulation results suggest that metals with lower refractive index and higher loss properties (e.g., Ti) are more favorable for achieving broadband absorption and higher overall absorption efficiency compared to precious metals (e.g., Au). Altering the geometry parameters of the absorbers has a discernible effect on their absorption characteristics. Notably, even with modifications to these parameters, the absorbers maintain an impressively high absorption efficiency.

 

Fig. 5. The absorption spectra of the absorber with different (a) periods P, (b) dielectric layer thicknesses h, (c) top metal layer thickness t, and (d) different metal disk materials. The other geometry parameters are based on the optimized results using PSO method.

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3. Methods

Simulation: The wave optical module of the Comsol Multiphysics 5.6 is used to simulate spectra of the absorber. Perfectly matched layers are used to avoid non-physical reflections in the z-direction and periodic boundary conditions are used in the x- and y-axis. The overall structure is illuminated by plane wave propagating along the z-axis.

Fabrication: The Ti/ZnSe/Ti multilayer stack is sequentially deposited on a 2-inch silicon substrate by Multi-target Magnetic Control Sputtering System (Denton, Explorer-14). Ti and ZnSe are grown in an Ar atmosphere at 3.5 mTorr and 2 mTorr, respectively. The deposition rates are 1.1 Å/s for Ti and 1 nm/s for ZnSe. The top rounded resonators are fabricated on the top titanium layer by stepping lithography (NIKON-I7, Japan) and ion beam etching (LAM9600).

Characterization: The morphological features of the four-sized Ti/ZnSe/Ti metamaterial absorber are acquired using high-resolution SEM (JSM-7800F, JEOL, Japan). The unpolarized normal incident spectra of the fabricated absorber are measured using a Fourier-transform IR spectrometer (Thermo Scientific Nicolet 6700, USA) with a gold integrating sphere (Pike Technology, USA). Thermal images of the fabricated absorber at a range of angles of incidence are obtained by an IR camera (FOTRIC 285, FOTRIC, CN).

4. Conclusion

In summary, we have proposed and demonstrated a high-performance absorber in this work, based on coplanar four-sized resonators consisting of Ti/ZnSe/Ti films. Through an optimized process of the complicated geometric parameters using the PSO method, the proposed absorber exhibits an average high absorption efficiency (96.7% of the simulation and 88.9% of the measurement) across a broad bandwidth (8 µm∼14 µm) in the LWIR range. The broadband high absorption results from the impedance matching mechanism and the multiple surface plasmon resonances supported by this configuration. Furthermore, the absorber is polarization insensitive thanks to the highly symmetric feature of the circular pattern, and possesses an angular insensitive characteristic (up to ±60°) due to the electric dipole resonances excited in the structure. Additionally, we conduct investigations into the effects of the geometry parameters and constituent disk metals on the absorption characteristics of the device. The results indicate that metals with low refractive indices and highly lossy properties are more effective at achieving broadband absorption with high efficiency. In comparison to existing broadband absorbers with more complicated top resonator structures, the proposed coplanar device can be easily integrated into a standardized micro/nano manufacture process for cost-effective large-scale production, and offers a feasible solution for improving optical performance in thermal emitter, infrared detection, and imaging applications.