1. Introduction

Perfect absorbers made specially by metamaterials, which can be used in many fields of technology such as plasmonic sensors [1], solar cells [2], photodectors [3], thermal emitters [4] and thermal imaging [5], have attracted much attention. By minimizing the reflectance and eliminating the transmittance a perfect absorber is obtained, in principle. Most perfect absorbers are composed of two metallic layers separated by a dielectric spacer. The first layer is for the minimization of reflectance by impedance matching, and the second is for blocking the transmission, usually made of continuous metallic film. Many types of absorbers have been proposed, and most of them are based on the electric and/or the magnetic resonances [6–8]. In order to extend the range of absorption frequency some efforts have been put into the design of dual-band or multi-band absorbers [9–15]. However, most of these absorbers are based on the composition of two or more local electric and/or magnetic resonances, which make structures complicated, and short of flexibility. As discussed in Ref [16], the magnetic resonance is not the necessary condition for metamaterial perfect absorbers and the multiple reflections play a very important role. Furthermore, as discussed later, the multiple reflections are essential for the realization of dual-band absorption in our structure.

Extraordinary optical transmission (EOT) through a sub-wavelength single hole or a array of holes is also a very attractive research field, and have been widely studied. Xiao et al. [17] proposed a simple structure to enhance the transverse electric waves through sub-wavelength apertures. Here, we use the structure to design a tunable dual-band absorber based on the coupling of local electric resonance and Fabry-Perot (FP) cavity resonance, and demonstrate the roles of these two kinds of resonances in the absorber in detail. Although our structure is basically a combination of the EOT structure proposed by Xiao et al. [17] and the so-called Salisbury screen, it should be noted that the resultant dual-band absorption cannot be realized in the EOT structure without the Fabry-Perot (F-P)-type cavity resonance or by the cavity resonance alone. Remarkable advantage of the suggested absorber is that we can switch the single-band absorption peak to dual bands by changing the air gap between two metallic layers. It can be also modified to be a polarization-independent absorber.

2. Structural design and simulation

Dual-band absorber structure (DBAS) is made of two separated copper layers, which are deposited on a dielectric FR4 board with a thickness of 1.1 mm, a dielectric constant of ε = 4.2 and a loss tangent of 0.022, as shown in Fig. 1(a) . The thickness of copper layer is 0.03 mm, and the electric conductivity of copper is modeled as 5.8 × 10⁷ S/m. A periodic two-dimensional square array of sub-wavelength holes, which are incorporated with copper bars, is arranged in the front copper layer. Since the front copper-FR4 layers show the EOT effect, we call them the EOT structure (EOTS) for convenience. Incident electromagnetic wave is normal to the surface of copper plane, and the electric field is parallel to the long side of hole. The design of the EOT layer is inspired by the structure for EOT designed by Xiao et al. [17], and the FR4-rear copper layers are solid and play a role of mirror to prevent transmission, which are called the mirror layer. The periodicity of structure is 10 mm, the size of rectangular hole in the front copper layer is 3 × 9 mm², and the size of bar is 0.5 × 8 mm². The distance between the front FR4 substrate and continuous Cu layers, denoted by d, can be adjustable. The full-wave electromagnetic simulation has been performed by using CST Microwave Studio software. Since the rear copper layer totally blocks the electromagnetic-wave propagation, there is no transmission, and thus the absorption is calculated by A = 1 – R = 1 – |S₁₁|² where R is reflection and S₁₁ is S parameter for reflection.

 

Fig. 1 (a) Unit cell of dual-band absorber, (b) simulated absorption spectra of the dual-band absorber with d = 14 mm and single-band absorber with d = 3 mm, and (c) absorption as a function of d and frequency.

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3. Results and discussion

Figure 1(b) shows the absorption spectra of the structures with d = 3 and 14 mm. For d = 3 mm only one absorption peak exist, while in the case of d = 14 mm there are two bands with the absorption very close to unity at frequencies of 9.360 and 10.544 GHz.

To elucidate the physical origin of the dual-band absorption, we present the absorption spectra with different d’s in Fig. 1(c). One relatively broad absorption keeps staying at 10 GHz, and three significant absorption peaks appear one by one and show nearly linear red-shift as d is increased. Coupling effect comes to emerge where two main absorption peaks get close.

In order to analyze the contribution from different resonances on the absorption, we investigated three basic structures of DBAS. The first structure was constructed with the front copper layer which was deposited on FR4 substrate, and two-dimensional periodic array of rectangular holes was perforated in the copper layer, which is called rectangular-hole structure (RHS). The second structure is EOTS, as defined already in Section 2. The third, which is composed of RHS and the rear solid copper layer with FR4 substrate separated by d = 14 mm from the front one, is called cavity-resonance-absorber structure (CRAS), as shown in Fig. 2 . The electric field was parallel to the long side of hole and the configuration parameters of CRAS remained the same as those of DBAS. The spectra in Fig. 2 show that only a small portion of electromagnetic wave can pass though the sub-wavelength holes in RHS, as expected. By adding a bar in the hole the transmission was enhanced, as described in Ref. 17, and the maximum of transmission of EOTS turned out to be 0.47, which appears at 10.06 GHz. Even though a very small fraction of electromagnetic waves can be transmitted through RHS, a narrow absorption band appears at 9.76 GHz in case of CRAS, and the absorption reaches 0.96 which can be improved to be close to unity by adjusting the parameters of structure. The frequency of 9.76 GHz satisfies the resonance condition of our structure, d = λ × m/2 where λ is the resonance wavelength and m is integer number. This condition is different from the ordinary FP resonance, in which there are 180° phase shifts upon reflections at both interfaces, resulting in the resonance condition of d = λ × (m + ¼). Since the resonance frequencies of EOTS and CRAS are close to each other, the two absorption bands of dual-band absorber might originate from the coupling of the LC resonance of the front layer and the FP cavity resonance.

 

Fig. 2 Transmission spectra of RHS and EOTS,and absorption spectrum of CRAS. Transmission spectrum of RHS has been magnified by a factor of 10.

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The distributions of surface current at the resonance frequency on the front and the rear copper layers of EOTS, CRAS and DBAS are shown in Fig. 3 . In the case of EOTS, the surface current induced by LC resonance is localized at the center of unit cell. On the other hand, for the case of CRAS, the surface current induced by cavity resonance is rather uniformly distributed on the surface of copper layer, and the surface currents on both copper layers are in the same direction. To describe the coupling of cavity resonance and LC resonance in more detail, the surface current distribution of DBAS with d = 3 mm is also included in Fig. 3. According to the simulation result the absorption peak of DBAS with d = 3 mm appears at a frequency of 10.164 GHz, and the direction of surface currents in the bar area is opposite to those in the other areas. Most of the surface currents are distributed on the front copper layer, implying that the effect of cavity resonance is significantly weaker than that of LC resonance. Although the surface currents are mostly distributed on the first copper layer, it should be noted that, according to the power flow of DBAS at a resonance frequency of 10.164 GHz for d = 3 mm (not shown), most of the absorption evidently occurs at the FR4 substrate of the front layer, implying that the dielectric loss at the front FR4 is the main source of absorption. The surface current distribution of DBAS with d = 14 mm at a resonance frequency of 9.360 GHz is quite similar to that of DBAS with d = 3 mm, while, for the case of DBAS with d = 14 mm at another resonance frequency of 10.544 GHz, most of the surface currents are in the same direction except for the long-side edge area of hole, indicating that the cavity resonance is weaker than the LC resonance, and the current at the edge of hole is induced by the local LC resonance. In other words, the dual-band absorption can be explained by hybridization of the LC resonance and the F-P cavity resonance. The absorption of one, at the higher frequency, of dual band in Fig. 1(b), dominated by EOT, is higher than 0.99, which is significantly enhanced with respect to the transmission of 0.47 for pure EOT (see the dashed line in Fig. 2). The dominance of EOT in the high-energy peak can be deduced by the following two facts; 1) the resonance frequency of the high-energy peak is quite higher than that of CRAS, and 2) the surface currents on the central bar and the edges of hole are much stronger than that of the rest of the layer compared to the case of the low-energy peak. The peak also becomes narrow, enhancing the Q-factor from 16.88 to 49. The enhancements of both absorption and Q-factor are ascribed to the coupling between LC resonance and FP-type cavity resonance.

 

Fig. 3 (a) Distribution of surface currents on the front copper and the rear copper layers of EOTS, CRAS, DBAS with d = 3 mm and DBAS with d = 14 mm. (b) Schematic energy-level diagram for two absorption peaks of DBAS with d = 14 mm. The red arrows indicate the arrangement of the surface currents in the central bar and the edge of the hole.

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The EOT of the first layer can be explained by the LC-circuit model given by Xiao et al. [17]. Although EOT is crucial for the transmission of incident wave, its transmittance of 0.47 is not enough for perfect absorption because the transmission should be close to unity in the first layer. The transmittance close to unity can be achieved by the coupling between the LC resonance and the FP cavity resonance. The resultant resonance frequencies are not the same as those of EOTS and CRAS. The frequency shifts can be explained by the hybridization model, which is similar to that for molecular orbitals. A schematic energy-level diagram is presented in Fig. 3(b). For both absorption peaks of DBAS the surface currents of the EOT layer and the continuous layer are in the same direction except for that in the central area, while the surface current in the central bar is opposite to that of the edge of hole. For the high-energy peak the surface current in the edge area of hole is opposite to that of the rest of the layer, which is denoted as the anti-parallel arrangement of red arrows in Fig. 3(b), while they are the same for the low-energy peak, which is denoted as the parallel arrangement of red arrows in Fig. 3(b). These low- and high-energy peaks correspond to the bonding and the anti-bonding orbitals, respectively, in the hybridization model of molecular orbitals. To understand the energy-level diagram we will discuss them one by one.

First, we have to explain why the resonance frequency of DBAS with d = 3 mm (10.164 GHz) is higher than that of EOTS (10.06 GHz). For EOTS the resonance frequency can be given as

where L₃ is the inductance of continuous layer and C’ is the capacitance of capacitor made of the front and the continuous layers. The “-“ sign in front of L₃ is due to the fact that the direction of surface current in the continuous layer is the same as that in the front layer. Since $C^{\prime }>>C$, $\frac{CC\text{'}}{C+2C\text{'}}\approx \frac{C}{2}$. Therefore,

and thus f_DBAS, _{3 mm} > f_EOTS. Similarly, the high-energy peak should have the resonance frequency identical to Eq. (3) with different L₂, i.e.,

where L’₂ is the inductance of the edge of the hole, which is smaller than L₂ because of the anti-parallel arrangement of the surface currents. Therefore, f_{DBAS, 3 mm} < f_high.

It should be noted that the distribution of surface currents of the low-energy peak is very similar to that of CRAS. Therefore, we might safely argue that the cavity resonance is dominant for the low-energy peak and the resonance frequencies of the low-energy peak and CRAS should be close to each other. Since the inductances are almost the same as those of CRAS, while the capacitance is larger than that of CRAS, owing to the insertion of the central bar, the resonance frequency of the low-energy peak is lower than that of CRAS, i.e. f_low < f_CRAS, as observed in experiment.

Figure 4(a) shows the photo of fabricated structure, and the comparison of experimental and simulational results for the single-band absorber with d = 3.1 mm and dual-band absorber with d = 13.1 mm, as shown in Figs. 4(b) and 4(c), respectively. For the case of d = 3.1 mm, the experimental and the simulation results agree with each other very well, however, for the dual-band case two results do not match perfectly. The discrepancy might come from the fact that the two copper layers are not absolutely parallel in the experiment.

 

Fig. 4 (a) Photo of the fabricated structure. Experimental and simulated absorption spectra with d = (b) 3.1 and (c) 13.1 mm.

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4. Extension of applications

Since these two resonances are derived from the EOT effect and the half-wavelength cavity resonance, the incident angle also can switch the number of absorption bands. Figure 5 shows single-band and dual-band absorption at incident angleθ = 0 and 45°, respectively. Whenθ = 0, both EOT and FP-type cavity resonance play the role and, thus, the dual-band absorption results in. On the other hand, whenθ = 45°, the distance between two metallic layers is effectively times lengthened and the FP-type cavity resonance is impossible, resulting in a single absorption at 9.87 GHz.

 

Fig. 5 Absorption spectra of DBAS at incident angle θ = 0 and θ = 45°.

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In order to extend the range of applications, we also designed a polarization-insensitive DBAS [structure D in Fig. 6(a) ]. Three basic structures (structure A, B and C), relevant to structure D, are also shown in Fig. 6(b). Structure A, B, C and D correspond to RHS, EOT, CRAS and DBAS, respectively. As in Fig. 6(b), the absorption spectra are nearly identical to the perpective spectra of Figs. 1(b) and 2. Figure 6(c) presents the absorption spectra by varying polarization angle. It is clearly manifested no polarization dependence for structure D, corresponding to DBAS, as expected because of the symmetry of structure. The other three structures (A, B and C) also reveal the polarization independence.

 

Fig. 6 (a) Unit cells of structure A, B, C and D. Related parameters are set to be d = 14 mm, w = 0.5 mm, r = 3.6 mm and periodicity as 22 mm. (b) Transmission spectra of various structures. (c) Absorption spectra of structure D according to polarization angle.

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5. Summary

We presented a tunable dual-band perfect absorber based on the coupling between LC resonance, utilizing EOT, and FP-type cavity resonance. By combining EOT and FP-type resonance, not only the EOT absorption peak but also another absorption peak originating from the FP-type cavity resonance appear, resulting in dual-band absorption. The coupling effect makes the EOT-induced absorption peak become narrower. We also modified slightly and optimized the structure to obtain even polarization-independent dual-band absorbers.