1. Introduction

Metamaterial absorber (MA) as an important branch of metamaterial-based devices, has been attracting great interest and making great progress in the past several years [1–14]. Landy et al. experimentally demonstrated the first MA in 2008, in which two resonators were printed on the top and bottom sides of a substrate [1]. Since then, MA has been extended to THz [3], infrared [4], and optical frequencies [5], which were based on metal-insulator-metal (MIM) architecture with zero transmissions [2]. The absorption bandwidth of MA is often narrow since resonance is utilized in the process of absorption. To realize a broadband absorption in microwave frequencies, a simple approach is to increase the loss of MA, such as loading lumped resistors [6,7] or employing resistive ohmic sheets [8]. The second approach is to utilize multi-resonance by incorporating multiple resonators within one unit cell [9]. The third approach is to utilize multilayered structure [10, 11], which is also adopted to expand the absorption bandwidth of THz MA [12], such as five-layered [13] and three-layered [14] THz MA.

For applications of absorbers in the infrared spectrum, the absorption bandwidth is one of the most important performance metrics. Some efforts have been made to expand the absorption band of infrared absorbers [4,15–17]. By combing two different resonators into one unit, dual-band absorption has been reported by Koechlin et al., which allows two distinct absorption peaks [4]. Soon after, the absorption bandwidth was further improved by using several resonators, including 1-D absorber with hybrid unit of four different slits [15] and 2-D absorber with hybrid unit of four different patches [16]. However, the absorption spectra are composed of discrete absorption peaks and the average absorption efficiency is not high enough [4,15,16]. Recently, Feng et al. proposed the dual-layered absorber based on the 2-D absorber [17], and the absorption bandwidth was greatly expanded (the simulated total absorption exceeds 80% from 8 to 12 um). Due to the advantages of broad bandwidth, perfect absorption, and ultrathin structure, MAs have potential applications in photodetectors [19], imaging [20–25] and micro-lens [26].

Inspired by these earlier works, here we demonstrate the design of an ultra-broadband gradient-metasurface-based absorber (GMBA) in infrared spectrum. The absorption of the single-layered GMBA exceeds 90% from 7.8 to 12.1 um, which is better than the performance of the dual-layered absorber reported by Feng et al. (absorption above 80% from 8 to 12 um) [17]. We further examine the performance of the dual-layered GMBA whose absorption exceeds 80% from 5.2 to 13.7 um. It is obvious that our structure shows more than twice the absorption bandwidth compared to the absorber [17], though both of them are dual-layered structure with nearly the same thickness. The presented design has several advantageous, such as being super thin and having an ultra-broadband absorption up to a relative wide angle. These features make it a good candidate for potential applications. It is noted that Azad et al. recently reported an optical broadband absorber, which has a super-cell containing sixteen resonators of different sizes and shapes [18].

2. Modeling and simulation

MA is usually composed of subwavelength structures based on MIM architecture [2]. By manipulating the magnetic resonance and the electric resonance simultaneously, the effective impedance of MA will match the free space impedance once the MA satisfies the condition $\sqrt{\mu (\omega )/\epsilon (\omega )}=Z_0$ [27]. As a result, the reflection is minimized, thus resulting in a perfect absorption of incident waves. Generally, the geometric configuration and the geometric parameters of a unit cell determine the resonance frequency of the MA structure [4]. Once the geometric configuration is selected, the geometric parameters become the unique factor in determining the resonance frequency. From this view we can place multiple resonators with different sizes in the two dimensional plane, which will result in multiple absorption peaks and expand absorption bandwidth. In our design, the GMBA is composed of four metallic pentagon patches of varying geometric parameters, as show in Fig. 1(c). One unit cell is divided into four equal portions and each resonator is located in the center of the corresponding portion. The period of the unit is P = 6.76 μm. The metal is selected as gold with conductivity of$\sigma =4.56\times {10}^{7}S/m$, and the insulator is selected as ZnS with the refractive index of 2.2 [17]. The thickness of ZnS dielectric layer is t = 0.69 μm. It is noted that the thickness of the gold is 0.1 μm throughout.

 

Fig. 1 (a) Schematic of the single resonator structure. (b) Simulated absorption spectra of the single resonator structure at the normal incidence. (c) Schematic of the single-layered GMBA. (d) Simulated absorption spectra of the single-layered GMBA.

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Absorptivity $A(\omega )$is usually utilized to characterize the absorber’s efficiency and is obtained from$A(\omega )=1-R(\omega )-T(\omega )$, where $R(\omega )$ and $T(\omega )$ are reflectivity and transmissivity as functions of frequency $\omega$, respectively. The transmissivity $T(\omega )$ is zero because the metal film is used as ground plane, which results in $A(\omega )=1-R(\omega )$. In order to clearly understand the physical mechanism of the GMBA, we first investigate the performance of the single resonator, as show in Fig. 1(a). As two metallic layers have strongly magnetic resonance under the incidence wave, we can tune the geometric parameters of the structure to get magnetic/electric resonance occur at the expected resonance wavelength. The resonator with four different sizes are examined, i.e. w₁ = 1.91 μm with L₁ = 0.83 μm, w₂ = 2.25 μm with L₂ = 0.88 μm, w₃ = 2.52 μm with L₃ = 1.23 μm, and w₄ = 2.76 μm with L₄ = 1.24 μm, respectively. Here, the parameters of w_i (i = 1, 2, 3, 4) are randomly selected. The parameters of L_i (i = 1, 2, 3, 4) are optimized values to ensure the absorption efficiency and bandwidth as good as possible. To examine the performance of the structure in Fig. 1(a), a full wave simulation was carried out based on the finite difference time domain (FDTD) method. In the simulation setup, the periodical boundary conditions were set along the x and y directions, and the open boundary condition was set along the z-direction. Figure 1(b) shows the absorption of the single resonator structure when the patch width varies from w₁ to w₄, with the change of chamfer from l₁ to l₄, respectively. Obviously, there are four distinct absorption bands with absorptivity as high as 99%. It indicates that the single resonator can be tuned to match to the free space with nearly perfect absorption at arbitrarily interested wavelength range. These discrete absorption bands mainly originate from the destructive interference of multi-reflection process between the metallic patches and the metallic background. If we can effectively connect the four absorption band, an ultra-broadband absorber can be obtained, which seems to be possible by assembling the four resonators into one unit cell.

In fact, we cannot get an optimal result if we directly assemble the four resonators in Fig. 1(b), because the coupling between the resonators cannot be neglected. For each single resonator, from Fig. 1(b) we know that the resonance wavelength is mainly dominated by the parameter w and the absorption bandwidth is mainly dominated by the parameter L. The larger L corresponds to the broader absorption bandwidth as well as the lower average absorptivity. When the four resonators are assembled into a subwavelength period, parameters optimization has to be carried out to achieve the aim that the total absorption exceeds 90% from 8 to 12 um. It is noted that w_i determines the position of the i-th absorption band, and L_i is responsible to smoothly connect adjacent bands, where i = 1, 2, 3, 4. On the basis of particle swarm optimization (PSO) method, we obtain the final optimal geometrical parameters, i.e. w₁ = 1.91 μm with L₁ = 0.8 μm, w₂ = 1.94 μm with L₂ = 0.85 μm, w₃ = 2.3 μm with L₃ = 1.2 μm, and w₄ = 2.76 μm with L₄ = 1.21 μm, respectively. The final optimized GMBA is shown in Fig. 1(c), and the simulated absorption spectrum is presented in the Fig. 1(d). It is obvious that the absorption goes beyond 90% from 7.8 to 12.1 μm for both TE and TM polarizations. The full bandwidth at width half-maximum (FWHM) achieves 50% with respect to the central frequency (7.54 μm ~12.54 μm). Compared with the absorber reported by Bouchon et al. (that absorbs 70% of the incident light on a 2.5 μm bandwidth at 8.5μm) [16], our structure shows much better performance in both efficiency and bandwidth.

To better understand the resonant mechanism and broadband absorption of the proposed GMBA, we investigated the magnetic field distributions at the different resonance wavelength, as shown in Fig. 2(a). Four resonances whose absorption is close to one are calculated at λ₁ = 7.94 μm, λ₂ = 8.6 μm, λ₃ = 9.68 μm, λ₄ = 11.43 μm, respectively. Obviously, each resonance is localized in a specific patch, where the smaller patch corresponds to the smaller wavelength. It is found that the power loss accumulates at resonances, where the energy is significantly reinforced and subsequently converted into thermal energy, thus leading to a perfect absorption. The magnetic field distributions further indicate that the perfect absorption of the GMBA is mainly attributed to the local electromagnetic coupling resonance mechanism. We also examined the influence on absorption with the change of chamfer size L, as shown in Figs. 2(b) and 2(c) for TE and TM polarizations, respectively. It is seen that the absorption property of the GMBA are sensitive to the parameter L. Specifically, the larger L corresponds to the broader absorption bandwidth as well as the lower average absorptivity. The absorber achieves the best performance with the optimal L.

 

Fig. 2 (a) Distributions of the magnetic field at the resonance wavelength of 7.94 μm, 8.6 μm, 9.68 μm, and 11.43 μm, respectively. (b) Absorption spectrum for TE polarization with different chamfer L. (c) Absorption spectrum for TM polarization with different L.

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In the previous discussion, all of the simulations were carried out at the normal incidence. It is necessary to examine the performance of the GMBA in the case of oblique incidence. `ure. 3(a) presents the absorption map as a function of the wavelength and of the angle of incidence θ with φ = 0°. It is found that the total absorption efficiency remains quasi-constant (>90%) up to relatively large angles (θ = 20°). When the incident angle continues to increase, the absorption begins to decrease with fluctuations. This is because the wave vector is no longer orthogonal to the metallic patches and thus a higher-order mode could appear, which leads to the component of the incident magnetic field drops rapidly to zero, and then cannot effectively induce a strong magnetic resonance. We define the angle φ between the incidence plane and the x-axis, as show in Fig. 1(a). The influence of the azimuthal angle on the absorption spectrum was also investigated, as shown in Fig. 3(b). It is seen that the absorption spectrum is a little sensitive to the azimuthal angle, which is attributed the asymmetric property of the structure [16]. Though the absorption efficiency decreases at some frequencies with the increase of azimuthal angle, the FWHM is nearly not changed and the average efficiency is still above 75%.

 

Fig. 3 (a) Absorption map as a function of the wavelength, and the angle of incidence for an azimuthal angle φ = 0°. (b) Absorption spectra under normal incidence with different azimuthal angles for TE and TM polarizations, respectively.

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3. Ultra-broadband dual-layered GMBA

It is well known that multilayered structure can be utilized to expand the absorption bandwidth of absorbers, such as microwave MAs [11] and THz MAs [13,14]. In infrared spectrum, dual-layered absorber has been reported by Feng et al. [17], which achieved twice the absorption bandwidth compared to the single-layered absorber [16]. The scheme of the designed dual-layered GMBA is demonstrated in Fig. 4(a), where four pairs of MIM subunit are placed in one square unit with a period of P = 9.2 μm. The dielectric spacing layers for the upper and lower are Al₂O₃ and ZnS, respectively. In the simulated wavelength range, the dielectric constant and the loss tangent of Al₂O₃ are 2.28 and 0.04, respectively [17]. It is noted that the upper and lower patches of each subunit have the same width w_i but different chamfer L_i1 (i = 1, 2, 3, 4). On the basis of PSO method, the final optimal geometrical parameters are obtained as following. The thickness of Al₂O₃ layer and ZnS layer are t₁ = 0.67 μm and t₂ = 0.59 μm, respectively. The width of patches are w₁ = 1.76 μm, w₂ = 2.21 μm, w₃ = 2.68 μm, and w₄ = 3.12 μm, respectively. The chamfer of the lower patches are L₁₁ = 0.82 μm, L₂₁ = 0.87 μm, L₃₁ = 1.16 μm, and L₄₁ = 1.22 μm, respectively. The chamfer of the upper patches are L₁₂ = 0.60 μm, L₂₂ = 1.02 μm, L₃₂ = 1.47 μm, and L₄₂ = 1.30 μm, respectively. The sample has a total thickness of 1.56 μm.

 

Fig. 4 (a) Schematic of the dual-layered GMBA. (d) Simulated absorption spectra of the dual-layered GMBA for TE (black) and TM (red) polarizations.

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Figure 4(b) shows the absorption spectra for the TE and TM polarizations at the normal incidence. It is clear that the absorptivity exceeds 80% throughout bandwidth for both TE (5.3~13.7 μm) and TM (5.17~13.73 μm) polarizations. The FWHM of TE and TM achieve 92.5% and 94.8% with respect to the central frequency, respectively. Compared to the dual-layered absorber [17], our structure achieves twice the absorption bandwidth with the same absorptivity. With these excellent properties, the proposed GMBA could be used as ultra-broadband thermal emitters [28, 29] and biochemical sensing [30].

4. Summary

In conclusion, an infrared absorber based on gradient metasurface has been designed and numerically verified. The simulated FWHM of single-layered and dual-layered GMBA are 50% (from 7.5 to 12.5 μm) and 95% (from 5.1 to 14.1 μm), respectively, much greater than those previously reported for infrared spectrum. The proposed GMBA has a super thin structure as well as an ultra-broadband absorption. With geometry scalability, it may operate at other frequency regimes. The ultra-broadband property makes it a good candidate for the design of a high-performance absorber used in thermal detectors, thermal emitters, as well as spectroscopic imaging, etc.