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Abstract
A triple-broadband infrared metamaterial absorber with polarization-independent and wide-angle absorption is proposed by a combination of three different configurations. The absorption of each band exceeds 80% in the three frequency ranges of 142–159 THz, 183–200 THz and 233–245 THz. The 3dB relative bandwidths are 14.5%, 13.1% and 9.9%, respectively. Based on the impedance matching theory, impedances of the absorber are calculated and match to those of the free space in the three absorption regions. To better understand the physical mechanism of the broadband absorption, electric field and surface current distributions of the combined structure are investigated. Multiband absorption mechanism is explained by using the wave-interference theory. Finally, absorption of the triple-broadband absorber at different geometric parameters and incident angles are also discussed for two polarizations. The proposed absorber can be a good candidate for the applications in thermal emission, sensing, photo-detection and solar energy harvesting.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As an important embranchment of metamaterial-based devices, metamaterial absorbers have attracted much attention due to their significant roles in thermal emission [1,2], sensing [3], imaging [4] and solar energy harvesting [5,6]. Metamaterial absorbers are generally designed as metal pattern-dielectric-metal ground sandwich structure where the metal ground prohibits the transmission of electromagnetic waves [7]. At the same time, the reflection can be reduced to zero when the impendence of the absorber matches to that of the free space [8,9]. Since Landy et al. [10] firstly demonstrated the microwave metamaterial absorber by using two metallic resonators separated by a substrate, metamaterial absorbers started its booming development and have been extended from microwave to visible band [11–21]. Among these, infrared metamaterial absorbers are especially attractive as they possess critical value for converting heat energy to radiation [22], thermal cooling [23], and thermal detectors [24].
To meet the need of multiple absorbing applications in the infrared band, dual-band [25–27] and triple-band [28, 29] absorbers with near perfect absorption have been obtained. In the design, the multiple band absorbers are achieved by arranging various sized subunits into a unit cell. As a result, several distinct resonant peaks appear due to the independence of resonances. However, bandwidths of the multiband infrared absorbers are very narrow and limited in the application of broadband absorption at the same time. Actually, wideband absorption can also be achieved by combining two or more resonators with different sizes in a unit cell [30, 31]. In which, the resonant peaks of each resonator couple together to form a wide band instead of forming peaks independence to each other. W. Ma et al. [30] demonstrated a wide-band absorber almost covering the full mid-infrared regime from 3 μm to 5 μm with absorbance higher than 50%. Two or four gold cross resonators with different sizes are multiplexed in the unit cell. M. Ghaderi et al. [31] proposed a broad absorber by combining four circular resonators with different radius in the unit cell. The absorbance was measured to be 98% with an absorbance of above 90% over the range of 3.5 μm to 4.1 μm. To our best knowledge, up to now, metamaterial absorber exhibiting both multiband and broadband absorbing characteristics is rarely reported in the infrared band.
In this work, we design a triple-broadband metamaterial absorber in the infrared band by combining three resonators with different sizes and shapes in the unit cell. Compared with the multiband or broadband absorbers mentioned above, the proposed absorber can exhibit both triple-band and broadband characteristics in addition to the polarization-independent and wide-angle absorption. The calculated impedances of the absorber match to these of the free space in the three absorption regions. To better understand the broadband absorption of the combined structure, individual responses of each configuration as well as electric field and surface current distributions of the combined structure are investigated, respectively. Multiband absorption mechanism is also explained by the wave-interference theory. Finally, absorption of the triple-broadband absorber at different geometric parameters and incident angles are also discussed for two polarizations. The proposed absorber can be a good candidate for the applications in thermal emission, sensing, photo-detection and solar energy harvesting.
2. Design and simulations
The schematic view of the 5 × 5 unit cells and unit cell of the proposed absorber are shown in Fig. 1(a) and (b), respectively. The unit cell consists of three types of gold patches and a gold ground plane separated by a dielectric spacer. The three gold patterns are one square patch and two different sizes of square patches by removing a small 45° rotating square in the center. The dielectric material is polymer with dielectric constant of εr = 3.4 and dielectric loss of tgδ = 0.02 [32]. The relative permittivity of gold can be obtained from the Drude mode [33–35]:
where the plasma frequency is ωp = 2π × 2175 × 1012 rad/s and the collision frequency is ωc = 2π × 6.5 × 1012 rad/s. Thickness of the square patches is t1 = 0.1 μm which is same as that of the bottom gold t3 = 0.1 μm, and the polymer thickness is optimized to be t2 = 1.85 μm. The period of unit cell P is 4 μm. The square patch is arranged in square lattice with the period distance of P/2 = 2 μm. The two hollow square patches locate at the center of the four square patches and are arranged in square lattice as well. The dimensions for other parameters are L1 = 1 μm, L2 = 0.4 μm, L3 = 0.4 μm, L4 = 0.2 μm, L5 = 0.3 μm.
Fig. 1 (a) 5 × 5 unit cell and (b) Unit cell of the metamaterial absorber. Parameters of the absorbers are P = 4 μm, L1 = 1 μm, L2 = 0.4 μm, L3 = 0.4 μm, L4 = 0.2 μm, L5 = 0.3 μm, t2 = 1.85 μm, and t3 = 0.1 μm.
In the simulation, commercial software (CST Microwave Studio) is used. The absorption A is obtained through the equation A = 1-|S21|2-|S11|2, where |S21| is the transmission and |S11| is the reflection [36]. The transmission |S21| is not considered in the calculation because the continuous gold ground is thick enough to block the transmission of the electromagnetic wave. Open boundary condition is employed along the z direction while the periodic boundary conditions are employed along the x and y directions. Electromagnetic wave incidents into the xy plane of the absorber with the angle θ and wave vector k. For the oblique incidence, the wave can be divided into the TE polarization where the electric field is parallel to the x-axis and the TM polarization where the electric field is parallel to the y-axis. The electric directions of the TE and TM polarizations are indicated in Fig. 1(b).
Figure 2(a) shows the absorption spectra of the triple-band metamaterial absorber at normal incidence. The dot and dot-dash line denote the reflection and transmission of the TE polarization. The transmission is zero due to the gold ground plane used at the bottom. The solid and the dash lines indicate the absorption of the TE and TM polarizations, respectively. It is seen that the absorption is polarization-independent and can improve practicability greatly. More interesting, the absorption of each band exceeds 80% in the three frequency ranges of 142-159 THz, 183-200 THz and 233-245 THz. The 3dB relative bandwidths are 14.5%, 13.1% and 9.9% respectively which can be obtained from equation Eq. (2):
where fc is the center frequency, f1 and f2 is the lower and upper frequency of 50% absorption, respectively. Therefore, a triple-broadband and a polarization-independent metamaterial absorber can be obtained in the infrared region.Fig. 2 (a) Absorption and (b) Real and imaginary parts of the relative impedance z for the proposed triple-band absorber.
The triple-broadband absorption can be explained by impedance matching theory [37–39]. In the impedance matching mechanism, the entire three-layered structure is considered as a thin slab made from a homogeneous medium with frequency dependent effective permittivity εeff and effective permeability μeff. In the perfect absorbing region, the effective permittivity and the effective permeability are same (εeff = μeff), so that the impedance Zeff (both the real part and the imaginary) matches to the impedance Z0 of the free space, that means the relative impedance z = Zeff /Z0 = 1. The real part of z is close to 1 while the imaginary part of z is 0 at the impedance frequency. Figure 2(b) shows the real part real(z) with solid line and imaginary part imag(z) with dash line for the relative impedance z of the triple-band absorber. It is very clear that real(z) is close to 1, and imag(z) is close to 0 only in the three absorption bands which meets the impedance theory basically.
To obtain a deeper insight into the broadband mechanism of the triple-band absorption, we investigate the individual responses of four types of configurations with the same period P = 4 μm. The geometric parameters of the three patches are the same with these in Fig. 1. Figure 3(a) presents the absorption with only four large hollow square patches, the distance between each patch is P/2. There are three resonances around the center frequency of 151 THz, 191 THz and 240 THz. However, the absorption of the first two bands are not flat with many dips appearing, which decreases its practicability greatly. The response of four small hollow square patches is presented in Fig. 3(b), the distance between each patch is also P/2. Three resonances take place around the three center frequencies while both the magnitude and width decrease compared with that in Fig. 3(a). For the four square patches with distance of P/2 in Fig. 3(c), the bandwidth decreases and the two absorption peaks at 151 THz and 191 THz become lower than the other two configurations, however the peak at 240 THz is larger than that of the small hollow square patches. To get better performance, we make these three patches in a symmetrical manner to form a combined unit cell in Fig. 3(d) which is the same structure as shown in Fig. 1. Apparently, the combination leads to an enhancement of absorption both in magnitude and bandwidth probably due to the integration and coupling of the three types of configurations.
Fig. 3 Absorption spectra of four types of configurations in unit cell. (a) only large hollow square patch, (b) only small hollow square patch, (c) only square patch, and (d) combined structure.
The electric field and surface current distributions of the combined absorber are given in Fig. 4(a)-4(f) for the center frequency of 151 THz, 191 THz and 240 THz, respectively. For the first resonance at 151 THz, the near-field response mainly focuses on the two hollow square patches shown in Fig. 4(a). The square patches seem to have little effect on the absorption at the frequency, which is consistent with the result shown in Fig. 3(c). For the surface current density at 151 THz in Fig. 4(d). It is seen that the current on the large hollow square patches mainly locates at the four vertexes of these resonators, which leads to the electric field hot spots shown in Fig. 4(a). As for the small hollow square patches, the current is much larger than that of others while the current is relatively weaker for the square patches. For the second and third resonance in Fig. 4(b) and (c), all patches play important roles at the resonance. The electric field hot spots mainly locate at vertexes of these resonators corresponding with the current distributions in Fig. 4(e) and Fig. 4(f). Therefore, the electric field and surface current distributions in Fig. 4 illustrate that the resonance of the combined unit cell can be considered as an integration of individual responses of the three configurations which contribute to the magnitude and width of the absorption.
Fig. 4 Electric field distribution of the absorber at the center frequency of (a) 151 THz, (b) 191 THz, and (c) 240 THz. Surface current density of the absorber at the center frequency of (d) 151 THz (e) 191 THz, and (f) 240 THz.
In Fig. 3, it is interesting that all the configurations have the triple-band absorption. So, the absorption of the same size structure without gold patches on the top is given in Fig. 5(a). It is seen that the dielectric-gold plane structure still has three absorption peaks at around 153 THz, 196 THz and 239 THz. This phenomenon can be explained by the wave-interference mechanism [40]. The resonant frequencies of 153 THz, 196 THz and 239 THz can translate into wavelengths λ1 = 1.96 μm, λ2 = 1.53 μm and λ3 = 1.26 μm, respectively. Within the dielectric, the wavelength λ1` = λ1/n = 1.06μm, λ2` = λ2/n = 0.83μm and λ3` = λ3/n = 0.68μm, where n = 1.844 is the refractive index of polymer. In the design, the polymer thickness t2 = 1.85 μm≈7λ1`/4≈9λ2`/4≈11λ3`/4, which is approach to the odd times of λ1`/4, λ2`/4 and λ3`/4, respectively. Consequently, minimal reflection can be obtained due to destructive interference of the incident and reflected wave. To confirm this, Fig. 5(b) shows the absorption of the dielectric-gold plane structure with polymer thickness t2 = 1 μm, 1.85 μm and t2 = 3 μm, respectively. It is seen that five absorption peaks appear at f1 = 148 THz, f2 = 175 THz, f3 = 202 THz, f4 = 229 THz and f5 = 256 THz for t2 = 3 μm while only one peak appears at f6 = 200 THz for t2 = 1 μm. Figure 5(c) presents the absorptions of the three absorbers with the combined three patches on the top layer for t2 = 1 μm, 1.85 μm and 3 μm. It is found that the wider and higher absorptions appear near the same resonant frequencies with the three structures without patches on the top. The wave-interference theory can also be used to explain this phenomena by calculating the wavelength of the resonant frequencies.
Fig. 5 Absorption spectra of the absorber (a) without square patches on the top for t2 = 1.85 μm, (b) without square patches on the top for t2 = 1 μm, 1.85 μm and 3 μm, and (c) with combined square patches on the top for t2 = 1 μm, 1.85 μm, and 3 μm.
Besides, the geometric parameters of the absorber affect the absorption. Figure 6(a), (b), (c) and (d) show the influence of the gold thickness on the top layer t1, sizes of the patches L1, L2, and L5 on the absorption of the triple-band absorbers through the color maps. In the calculation, all other parameters are the same with the structure in Fig. 1. It is clear that center frequencies of the three bands change little when the four parameters vary. Which confirms that the absorption frequencies are mainly determined by the dielectric thickness while the structure parameters mainly contribute to the magnitude and width of the absorption bands. In Fig. 6(a), we can see that increasing t1 from 0.05 μm to 0.30 μm makes the bandwidth and magnitude larger for the second and the third bands. While for the first band, the absorption first increases and then decreases when t1 is thicker than 0.10 μm. Figure 6(b) shows the color map of the absorption for L1 varying from 0.8 μm to 1.2 μm. The bandwidth and magnitude change little for the first and third bands while the bandwidth of the second band firstly increases and then decreases as L1 increases. In Fig. 6(c) and (d), changing the value of L2 will affect the first band and changing L5 has influence on all the three bands.
Fig. 6 Influence of the (a) gold thickness on the top layer t1, sizes of the patches (b) L1, (c) L2, and (d) L5 on the absorptions of the triple band absorbers through the color maps.
For practical applications, efficient absorber is required to absorb at different angles instead of only normal incidence. Figure 7 illustrates the absorbing performances of the triple-band absorber at incident angles θ varying from 0° to 45°, where θ is the angle between incident direction and the positive z-axis. The left and right sides of each map refer to the absorption of the TM and TE polarization, respectively. The absorption of the two polarizations have similar tendency as the angles increases. Figure 7(b), (c) and (d) show the influence of angle on the center frequency and bandwidth of the three bands. Where the dash line and solid lines denote the center frequency and bandwidth, the cycle and square symbols denote the TE and TM polarizations, respectively. It is seen that all the center frequency of the three band increase as the incidence angle increases except there is a little decrease at 9° for the first band of TE polarization. As for the bandwidth, variation of the center frequency for TE polarization is 11.62 THz, 20.23 THz and 15.47 THz, respectively. For TM polarization, variation of the center frequency is 10.53 THz, 18.45 THz and 17.46 THz, respectively. On the other hand, the absorption band of TM polarization is a litter wider than that of TE polarization in the three bands. The largest relative 3 dB bandwidth are 17.6%, 13.9% and 12.1% for the TM polarization. Furthermore, the absorption curves with incident angles beyond 45° is also investigated and the absorption characteristics are similar with that we have mentioned above. Therefore, broadband and wide-angle absorption can be obtained for the triple-band absorber.
Fig. 7 (a) Color map of the absorption spectra for the combined absorber with incident angle varying from 0 to 45°. The left and the right sides refer to the TM and TE polarization, respectively. Influence of incident angle on the center frequency and 3dB bandwidth in (b) the first absorption band, (c) the second absorption band, and (d) the third absorption band.
3. Conclusion
In conclusion, a triple-broadband infrared metamaterial absorber is proposed by the combination of three configurations in unit cell. For the normal incidence, the absorption of each band exceeds 80% in the three frequency ranges of 142-159 THz, 183-200 THz and 233-245 THz, the 3dB relative bandwidths are 14.5%, 13.1% and 9.9%, respectively. The broadband and multiband absorptions are explained by impedance matching theory and wave-interference theory. To better understand the coupling mechanism of the combined structure, electric field and surface current distribution of the combined structure are investigated at the three center frequencies of the absorption bands. Furthermore, the absorbing performances of the triple-band absorber at incident angles varying from 0° to 45° are studied. It is found that the center frequencies of the three bands change little below the incidence angle of 10° and begin to increase as angle increases both for the TE and TM polarization. The absorption band of TM polarization is a litter wider than these of TE polarization in the three bands. The proposed absorber can be a good candidate for the applications in thermal emission, sensing, photo-detection and solar energy harvesting.
Funding
National Natural Science Foundation of China (61107030); Fundamental Research Funds for the Central Universities of China; Opening Foundation of the State Key Laboratory of Millimeter Waves (K201703).
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