1. Introduction

Metamaterials (MMs) also namely meta-atoms (or meta-molecules) are artificial materials or structures consisting of patterned periodically sub-wavelength unit-cells to gain exotic physical properties unavailable in nature [1,2]. In recent years, the rapid developments of MMs have paved a new platform for designing novel sub-wavelength scale electromagnetic (EM) or optical devices [5–8], such as modulators [3], filters [4], antenna [5] etc. The perfect metamaterial absorber (MMA) concept was firstly proposed by Landy et al. [9], which could excite electric and magnetic resonances simultaneously to realize the impedance match well with free space, thus yielding near unity absorption. Due to its potential application in sensing, detecting and imaging, MMA is becoming a burgeoning branch of MMs devices. After this, different sets of designs have been proposed and investigated intensively, which have considerably enriched the research area of MMAs from microwave to optical frequency [10–23]. MMAs worked in terahertz (THz) region have been attracted considerable attentions since a strong absorbing material unavailable readily in nature in this frequency range. Recent years, the theoretical analysis, design and experiment realizations of high performance MMAs have been reported in THz region by many groups [12–15,24–36]. However, most of the previous THz MMAs have common drawbacks of absorption bandwidth, which usually work at limited frequency ranges and may not be suit many practical applications.

In general, three strategies have been used for extending the bandwidth of the THz MMAs. The first one is to form a coplanar structure by combing multiple sub-units structures with different sizes into a large unit-cell [14–16]. The second one is utilizing multiple vertically stacked metal-dielectric layers into a new unit-cell [13,19,24–26]. The last one is based on doped silicon or graphene or other composite structures [24–32]. However, the first approach will make the unit-cell of MMAs too large, which will result in increasing angular dependence in practices due to the many interactions between the sub-units. In addition, the extension of bandwidth is limited due to the limited number of sub-units in a coplanar structure. The broadband and even ultra-broadband stronger absorption could be realized by the second and third methods. However, these two approaches are usually constrained by fabrication complexity and cost [33,34]. Therefore, the simple design and realization of THz high performance MMAs are still the significant issue in the MMs fields.

In effect, high-order resonances of MMs are vital, but often overlooked in the design of MMAs. It is very useful to design a multi-band or broadband MMA by combining the fundamental and high-order resonance modes in a single patterned metallic structure. In this paper, we present a new type design of a dual and broadband THz MMA based on the high-order resonances response using a compact single resonator structure. The unit-cell of the MMA consists of a closed meander wire structure and a continuous gold film separated by polydimethylsiloxane (PDMS) substrate. Both simulation and theoretical calculation results exhibit that the absorbance of over 90% around 1.19 THz and 1.64-2.47 THz can be realized. The further simulations show that the designed MMA can operate well at a wide range of polarization and incident angles for both TE and TM waves. Compared with the previous reported THz MMAs [10–17,24–36], the main novelties of our proposed structure including: Firstly, it has a compact unit-cell structure and novel resonance mechanism. Secondly, the MMA can achieve a dual and broadband high level absorption performance in a single resonator structure. Thirdly, the designed MMA is polarization-insensitive and wide-angel for both TE and TM waves. Thus, our design has some potential applications in communications, sensing and imaging at THz frequencies.

2. Structure design and simulations

We employ a compact design scheme for the unit-cell structure of the THz MMA, as shown in Fig. 1. Over past few years, many exotic EM properties based on meander and its various structures have been investigated intensively [36–41]. The meander wire structure has been used to design various devices, such as absorber [36,41], circular polarizer [37,39], and polarization convertor [40]. Thus, it is also inspired that the meander wire structure can be used to construct the compact and high-performance MMA in THz region. Figures 1(a,b) show the front and perspective view of the unit-cell structure, which is composed of a metallic closed four-fold meander wire structure array above a continuous gold film separated by a dielectric substrate. The top and bottom layers of the proposed MMA can form a Fabry-Pérot-like resonance cavity, leading to a multiple interference effect in multi-reflection [43–46]. The PDMS with the permittivity of 2.35(1 + i0.03) was selected as a middle dielectric substrate due to its favorable EM properties in THz region. The gold was used as the front and back metallic layers, and material parameters can be explained by surface impedance model with Drude parameters, which has been confirmed by experiment in previous reference [42]. In fact, in our interested frequency range of 1-3 THz, the metal gold also can be regarded as approximate perfect electric conductor, and the conductivity is 4.09 × 10⁷ S/m [12,43].

 

Fig. 1 Schematic of the designed THz MMA: (a, b) front and perspective view of the unit-cell structure. The unit-cell is composed of a metallic closed four-fold meander structure above a continuous gold film separated by a dielectric substrate.

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The optimized geometrical parameters of the unit-cell structures are given as: p_x = p_y = 55 μm, l = 52 μm, w = 1.5 μm, g = 1.1 μm, t_s = 15 μm. The unit-cell structure of the MMA is periodic along the x- and y- axes with periods of 55 μm to avoid diffraction under normal incidence for frequencies up to 5.45 THz. In our interested frequency range (1-3 THz), the metallic layers were made of a gold film with thickness of 0.4 μm, which is much larger than the typical skin depth in terahertz regime (to avoid transmission through the ground plane metallic film). To realize perfect absorption of the proposed MMA in a broadband THz frequency range, the impedance of which should be matched to that of free space. By adjusting carefully the thickness of the dielectric substrate and size of the metallic meander wire structure of the MMA, whose impedance could be matched to free space at resonances, and stronger absorption bandwidth could be extended effectively.

To verify its efficiency of our design, the full wave simulations were carried out by employing the frequency domain solver based on finite integration technology (FIT) in CST Microwave Studio. The open boundary condition is applied along the z-axis direction while the periodic boundary conditions in the x- and y-axis directions are employed for the transverse boundaries to replicate an infinite array of the MMA. When the THz wave is normal incidence to our MMA, no transmission can be examined as it is blocked off by the continuous gold film. Thus, only the reflectance$R\text{(}\omega \text{)}$ of the designed MMA needs to be measured, and the absorbance$A\text{(}\omega \text{)}$can be written as$A\text{(}\omega \text{)}\text{=}\text{1}\text{-}R\text{(}\omega \text{)}$.

3. Results and discussions

Figure 2(a) shows the simulated reflectance and absorbance of the proposed MMA, dual and broadband stronger absorption can be observed clearly. The reflectance is below 10%, and the corresponding absorbance is greater than 90% around 1.19 THz and 1.65-2.49 THz. In addition, the absorbance is up to 99.9% at 1.87 THz, 2.17 THz and 2.35 THz, respectively. The corresponding electric thickness of the MMA is less than λ/8 at 2.49 THz. Thus, our designed MMA possess a relative thinner thickness compared with the operation wavelength (<λ/8, at 2.49 THz). According to the S-parameter retrieved method [10,15], the relative wave impedance ($\tilde{z}(\omega )$) was calculated from the simulated reflection coefficients, as shown in Fig. 2(b). The real part of relative impedance is near unity ($\mathrm{Re}(\tilde{z})\approx 1$), and the imaginary part is near zero ($\mathrm{Im}(\tilde{z})\approx 0$) at resonance absorption frequencies, so the reflection is nearly zero. These results indicate that the relative impedance of the proposed MMA can be tuned to approximately impedance-match to free space at interested frequency range.

 

Fig. 2 (a) Shows the absorbance and reflectance spectra of the proposed THz MMA, (b) shows the corresponding relative wave impedance; which indicate a dual and broadband high level absorption and impedance-matched properties.

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In our design, the meander wire structure can be treated as a series of metal wire or patch with side length linearly increasing in cascade. The resonance is analogous with metal cut-wire or patch in principle, such as electric and magnetic dipole resonance response [10–12]. The resonance mechanisms creating by the meander wire structure also can be analyzed quantitatively by the equivalent LC circuit theory. The equivalent capacitor and inductance can be expressed approximately as$C\text{=}a{\epsilon }_0{\epsilon }_{d}lw/t_s$and$L\text{=}b{\mu }_{0}l{t}_s/w$, where ε₀ and μ₀ is the permittivity and permeability of free space, l and w is the side length and wire width of metal meander structure, ε_d and t_s is the permittivity and thickness of middle dielectric layer, and a, b are numerical factors, respectively [13,15]. So, the resonance frequency can be predicated approximately by$f_{\text{m}}\text{=}1/2\pi \sqrt{LC}\sim 1/l$. Obviously, the resonance absorption frequency is inversely proportional to the side length of the meander wire structure. By adjusting the gap (g) and wire width (w) of the meander wire structure and the thickness (t_s) of dielectric layer, the several absorption peaks can close to format broadband MMA when making the distance of neighbor resonance peak |f_{i + 1}-f_i|<Δf_i [14]. The absorption peak is corresponding to the nature of the different resonances modes, which will be illustrated by analyzing the distributions of the electric fields and surface currents of the unit-cell structure. It can be conjectured that the high level absorption of the proposed dual and broadband MMA is mainly attributed to the mixture modes of electric and magnetic resonance responses of the meander wire structure.

To better understand the absorption mechanism of the proposed MMA, as shown in Figs. 3 and 4, we present the distributions of electric field (E_z) and surface current of the unit-cell structure at stronger absorption frequencies of 1.19 THz, 1.87 THz, 2.17 THz, and 2.35 THz. It is clearly that the z-component (E_z) of the electric field is mainly concentrated on the wire edges, gap edges, and corners of the meander wire structure.

 

Fig. 3 (a-d) Show the electric filed (E_z) distributions of the unit-cell structure of the proposed MMA at different resonant frequencies under the normal x-polarized wave incidence: (a) f₁ = 1.19 THz, (b) f₂ = 1.87 THz, (c) f₃ = 2.17 THz, and (d) f₄ = 2.35 THz, respectively.

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Fig. 4 Distributions of surface current the (a1-d1) front and (a2-d2) back layer of the unit-cell structure of the proposed MMA at different resonant frequencies under the normal x-polarized wave incidence: (a1-a2) f₁ = 1.19 THz, (b1-b2) f₂ = 1.87 THz, (c1-c2) f₃ = 2.17 THz, and (d1-d2) f₄ = 2.35 THz, respectively. The solid arrow indicates current flow direction.

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The red region is corresponding to the excited positive charges and blue region are the negative charges are as shown in Fig. 3(a-d). The charges oscillation driven by incident electric field is supplying electric resonance response. The accumulation region of charges format multiple wire shapes with negative and positive charges, respectively, revealing the higher-orders electric dipoles excitations with frequency increasing. At the lowest frequency (f₁ = 1.19 THz) as shown in the Fig. 3(a), only two different wire shapes with negative and positive charges can be observed in the meander wire structure, indicating excitation of dipole resonance. The electric dipolar resonances are due to excitations of the localized surface plasmon (LSP) caused by the opposite charges accumulated at the edges of the meander wire structure. At other frequencies (f₂ = 1.87 THz, f₃ = 2.17 THz and f₄ = 2.35 THz) as shown in Fig. 3(b-d), the electric field distributions revealing similar quadrupolar, hexapolar and octupolar resonances. These higher-order dipole resonances are correspond to natural of the excitations of LSPs and spoof surface plasmon polaritons (SPPs) [35,47–51]. Thus, the incident THz energy is confinement at metal-dielectric interfaces of the MMAs due to the excitations of the spoof SPPs and LSPs [47–51].

Essentially, the higher-order resonance modes occur at the higher frequencies is due to the fact that the dimension of the meander wire structure is larger than a multiple of a half-wavelength of the resonance modes [16,35,47–52]. As shown in Fig. 4(a1-d1) and (a2-d2), the most surface currents on the meander wire structure are anti-parallel to that on metallic background along with oscillation electric field due to the accumulation of the opposite charges. These different anti-parallel currents can form several equivalent current loops supplying magnetic resonance response. We conjecture that the electric and magnetic response with higher-orders could be overlap by adjusting the geometrical parameters of the unit-cell structure of the proposed MMA. At the meantime, the impedance matches well to free space, thus the perfect absorption occurs. Thus, the dual and broadband strong absorption is due to the overlapping and mixtures of the different resonance modes in a single resonator structure of the MMA.

We study the influences of different polarization and incident angles on the absorption performance of the proposed MMA for both TE and TM waves, as shown in Fig. 5. Obviously, as shown in Figs. 5(a,b), the absorbance with different polarization angles is unchanging for both the TE and TM modes due to its four-fold (C₄) rotational symmetry of the unit-cell structure. For oblique incidence, the case is different for TE and TM modes as shown in Figs. 5(c,d). For the TE mode, the dual and broadband absorption performance can be maintained up to 55° as shown in Fig. 5(c). Beyond 55°, the performance will be degraded gradually since the magnetic flux of the incident wave becoming less and less with the increase of incidence angle. For the case of TM mode as shown in Fig. 5(d), the stronger absorption performance of the lower frequency is nearly unchanged since the magnetic flux between the meander wire structure and bottom metal film is nearly unchanged at all incidence angles. However, the stronger absorption performance of the second broadband frequency can only be maintained up to 65°. It is because that the magnetic flux keeps unchangeable for TM mode, but the electric component of incident EM wave will decrease with the incident angle increasing, so the mutual resonance effect decrease. These results indicate that the proposed MMA can keep the absorption stability with different polarization angles and wide incident angles in practical application.

 

Fig. 5 (a,b) and (c,d) show the simulated absorbance for different polarization and incident angles with different modes: (a,c) TE mode, (b,d) TM mode. The polarization angle is varied by a step of 5°from 0° to 90°, and the incident is varied in 5° steps from 0° to 90°.

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To further reveal the physical insight of the high level absorption of the MMA, quantitative analysis method is employed. It is initially thought that the perfect absorption of the MMA is originated from the stronger local EM resonance and impedance matching between the MMA and the free space. In fact, according to interference theory, the MMA can be regarded as a Fabry-Pérot-like resonance cavity, which can induce multiple interference effect in multi-reflection for the incident EM waves, finally resulting in the high level absorption [43–46]. The superposition of the multiple reflections then destructively interferes with the direct reflection from the air-spacer interface with meander wire resonators [44].

Here, we also adopt the interference theory to quantitatively analyze the absorption mechanism of the MMA. As shown in Fig. 6(a), the multiple reflection interference model of the MMA is composed of two interfaces, where top metal meander wire structure and ground plane are treated as two non-thickness surfaces. This interference model can be considered as an uncoupled system where the near-field coupling between the top layer and the ground plane can be neglected. The top metal layer works as the surface which can partially reflect/transmit the incident EM wave. Subsequently, the transmitted waves continue to travel in the dielectric spacer until they encounter the ground plane with a complex propagation phase$\beta =-\sqrt{{\epsilon }_r}{k}_0{t}_s$, where k₀ is the free space wave number. The reflection coefficient will be −1 after propagation waves completely reflected to the dielectric spacer.

 

Fig. 6 (a) Shows the multiple reflection resonance cavity model of the proposed THz MMA based on Fabry-Pérot interference theory, (b,c) show the simulated magnitude and phase of the complex reflection and transmission coefficients at interface, respectively.

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The partial reflection and transmission waves arrive at the air-spacer interface again from reverse direction after additonal propagation phase β in dielectric spacer. The ${\stackrel{\leftharpoonup }{r}}_{12}=r_{12}\cdot e^{{\phi }_{12}}$is reflection coefficient of the top metal layer from air to air, the${\stackrel{\rightharpoonup }{t}}_{12}=t_{12}\cdot e^{{\varphi }_{12}}$is transmission coefficient of the top metal layer from air to substrate, the ${\stackrel{\leftharpoonup }{t}}_{21}=t_{21}\cdot e^{{\varphi }_{21}}$is transmission coefficient of the top metal layer from substrate to air, and the ${\stackrel{\rightharpoonup }{r}}_{21}=r_{21}\cdot e^{{\phi }_{21}}$ is reflection coefficient of the top metal layer from substrate to substrate. The directly reflected wave and the following multiple emergent waves effectively traps the wave in the sandwiched structure MMA, resulting in the high absorption [53]. Then the overall reflection is superposition of the above multiple reflections. The overall reflection coefficient of metal structure layer from air back to air can be written as [44]:

Thus, the reflectance is calculated by use of Eq. (1). Then, the calculated absorbance can be obtained by equation$A=1-|r{|}^2$. The magnitude and phase of transmission and reflection coefficients at two interfaces are obtained by numerical simulation are shown in Figs. 6(b,c).The corresponding calculation and simulation absorbance is depicted in Fig. 7. It can be observed that the theoretical calculation results are in a good agreement with the numerical simulation ones for the lower frequency range (1-2.3THz). However, there are some minor discrepancies in the higher frequency range of about 2.3-3THz due to the higher-order multipolar resonance.

 

Fig. 7 Shows the numerical results of absorbance spectra of the designed MMA, which are from the simulation based on FIT and calculation based on Fabry-Pérot interference theory.

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Taking a further step, we also study the influence of geometric parameters of the unit-cell structure on the absorption properties of the proposed MMA. Based on analysis of the above equivalent LC circuit theory, the effect of geometric parameters on the absorption of the MMA could be easily understood. According to the above analysis, the absorption properties of the MMA mainly depend on the side length l and the thickness t_s of the dielectric layer.

Firstly, the unit-cell structure of the MMA with different side length l (l = 48 μm, 50 μm, 52 μm, and 54 μm) were simulated when the other geometric parameters are fixed unchanged, as shown in Fig. 8(a). Based on multiple reflections interference model, we also calculated the absorbance with different l according to the Eq. (1). It can be seen that the calculation results based on interference theory are agreement well with numerical simulation ones with different l. Both calculation and simulation results indicate that the absorption level are nearly unchanged, while the operation frequency has an obvious red-shift with the increase of l. The linear dependence of the resonance absorption frequency on l of the meander wire structure is consistent well with the predication of the above mentioned LC circuit theory. This provides a chance to shift the operation frequency range of the proposed MMA by adjusting the l of meander wire structure while all the other parameters are fixed.

 

Fig. 8 (a,b) Shows the absorbance spectra of the proposed MMA with different wire length (l): (a) simulation and (b) calculation results. The wire length (l) of the meander wire structure is 48 μm, 50 μm, 52 μm, and 54 μm, respectively.

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Furthermore, we discuss the influence of dielectric layer thickness t_s (t_s = 12 μm, 14 μm, 16 μm, and 18 μm) on the absorption, and Figs. 9(a,b) show the calculated and simulated absorbance when the other geometric parameters are unchanged. It also can be seen that the calculation results are agreement well with numerical simulation ones with different t_s. From the Figs. 9 (a,b), the resonance absorption frequencies have a minor red-shift with the increase of the t_s from 12 μm to 18 μm. In this case, the thing is different to the change of l, and the resonance absorption frequencies are nearly not sensitive to the change of t_s. This agrees well with our previous predication and analyses of the equivalent LC circuit theory. In addition, the absorption level of the lower frequency is increased while the ones of the higher frequency range are decreased gradually with the increase of t_s.

 

Fig. 9 (a,b) Show the absorbance spectra of the proposed MMA with different dielectric substrate thickness (t_s): (a) simulation and (b) calculation results. The substrate thickness (t_s) is 12 μm, 14 μm, 16 μm, and 18 μm, respectively.

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From above numerical calculation and analysis, the absorption level and frequencies are sensitive to the geometrical parameters of the unit-cell structure of the MMA. Thus, we could adjust the absorption properties by changing these geometrical parameters.

4. Conclusions

In summary, a novel dual and broadband MMA based on a four-fold closed meander wire structure in THz region is proposed and investigated numerically and theoretically. Distinct advantages of our design on the previous MMAs are shown in terms of the combination of compact meander wire structure design, excellent absorption performance, and polarization-insensitive and wide incident angle. Simulations confirm that the absorbance is more than 90% around 1.19 THz and 1.65-2.49 THz, which is agreement well with the calculation based on the interfere theory. The electric field and surface current distributions of the unit-cell structure reveal that the high level absorption originates from electric and magnetic resonance response with higher-orders. Further simulations indicate that the MMA is independent to polarization angles due to the C₄ rotational symmetry of the unit-cell structure. The MMA also has a good performance with increase of the incident angle even to 65° for both TE and TM waves. Furthermore, the absorption properties of MMA can be adjusted by varying the geometric parameters of the unit-cell structure, which gives a considerable freedom to change the operation frequencies and absorption level to meet different application needs. The efficient design of the dual and broadband THz MMA may find some potential applications in imaging, communications, sensors, stealth, and so on.