1. Introduction

It has always been a technical difficulty to achieve high-efficient devices for manipulating THz radiations with natural materials for that natural materials present weak EM responses in the so called “terahertz gap” (0.1-10 THz) [1–4]. As is well known, the physical properties of conventional natural materials are essentially derived from the atoms or molecules and their arrangements. Apparently, it would be fantastic to design materials according to our own needs, and the concept of metamaterial appears. Since metamaterial is comprised of artificial sub-wavelength resonant building blocks, i.e., namely meta-atoms (or meta-molecules), its EM characteristics are mainly determined by the arrangements of meta-atoms. With exotic functionalities, not found in natural materials, metamaterial has attracted wide attention since it gets known to the whole world in the past decades [5, 6]. The electric and/or magnetic responses of the meta-atoms can be used to manipulate the properties of metamaterial. This provides a measure to match the metamaterial impedance to that of the free space, which can result in almost zero reflection. The resonant characteristics of metamaterial generate strong field enhancement and the incident EM energy will be dissipated by dielectric and/or Ohmic losses [7–9]. Based on this physical mechanism, Landy et al. constructed the first perfect MA working in the microwave regime in 2008 [7].

Since the property of metamaterial is determined by the ensemble of meta-atoms, it is convenient for people to design metamaterial absorbers (MAs) working at different frequency bands across the majority of the whole EM spectrum. Despite the MAs working in the microwave range [7, 9], the working frequencies of MAs have been expanded to THz [3, 10–15], infrared [16], visible frequencies [17–21] even to the near ultraviolet [22]. The MAs working at different frequencies have their unique applications among which the THz MAs have vital importance for the existence of the “terahertz gap”. The emergence of the THz metamaterials fills the gap between far infrared and microwave regions. Many of the THz MAs include the dielectric and metal materials. Recently, all-dielectric THz metasurface absorber has been proposed using the hybrid dielectric waveguide resonances [23].

Compared with the dual-band, triple-band and multi-band THz MAs [11, 24–33], the broadband THz MAs are more attractive in the realistic applications for their continuous high absorption in a broad wave band. In 2010, Ye et al. demonstrated a broadband THz MA based on the three-layer cross structure [34]. In 2011, Grant and collaborators proposed a broadband THz MA with stacked metal-dielectric layers. They also gave a broadband THz MA design which consisted of four coplanar cross-shaped resonators with different structural parameters [35]. Based on the metal-dielectric multilayered or double-layered composites, broadband THz MAs have also been proposed [36–41]. The design guideline of coplanar multi-resonators with different structural parameters is also widely used. For example, Cheng et al. designed a broadband THz MA using four coplanar square films [42]. Gong and collaborators proposed a broadband THz MA using four coplanar sectional structures [43]. In a word, the broadband THz absorptions mentioned above are realized by incorporating multi-resonators with different structural parameters either in the longitudinal [34–41] or transverse direction [35, 42, 43] of the MA unit cell.

Rich EM properties have been discovered on the fish-scale structure during the past decade [44–46]. The wire and meander pattern has been used to construct electrically reconfigurable metamaterial working in the near-infrared [47]. Recently, the closed fish-scale structures have been proposed to realize broadband absorption in the optical frequencies and reflective cross-polarization in the microwave range [20, 48].

In this paper, we design a broadband MA working at the THz frequencies with a metal-dielectric-metal (MDM) configuration. The top layer of the MA is a sub-wavelength connected rectangular fish-scale structure which is also called meander line [49]. The broadband absorption which shows independency of the incident and polarization angles is attributed to the mixtures of the electric and the magnetic resonances.

2. Structure design and simulation

The broadband MA working at the THz frequencies is a MDM sandwich as shown in Fig. 1(a). The structural parameters of the top layer are shown in Fig. 1(b). As seen, there are four groups of metal rectangular fish-scale structures (the yellow parts) with the same structural parameters but different arrangements on the top layer. A cross-shaped air gap with width of $g$ acts as the boundary of the four groups of rectangular fish-scale structures. All the air-gaps in the four groups of rectangular fish-scale structures have the same width of $g$ and length of $a-g$. The metal strips have the same width with the air-gaps. The bottom layer is continuous metal film which acts as the perfect reflector to block the transmission of EM wave. The connected rectangular fish-scale structure has four-folder symmetry (shown in Fig. 1 (b)).

 

Fig. 1 Schematic diagram of the (a) unit cell and (b) top view of the broadband THz MA with connected rectangular fish-scale structure.

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The frequency domain solver of CST Microwave Studio is applied to gain the scattering parameters of the THz MA. Open boundary condition is employed along the $z$ direction while the periodic boundary conditions are employed along the $x$ and $y$ direction. The absorption of the THz MA is expressed as $A(\omega )=1-R(\omega )=1-{\left|S_{11}(\omega )\right|}^2$, where $R(\omega )$ and $S_{11}(\omega )$ are the reflection and scattering parameter for reflection, respectively. The transmission is not considered in the calculation of absorption because the continuous metallic back of the THz MA blocks the transmission of the EM wave. When the impedance $z(\omega )=\sqrt{\mu (\omega )/\epsilon (\omega )}$ of the THz MA is matched to that of the free space ($z(\omega )=1$), the reflection $R(\omega )$ of the THz MA will obtain the minimum value [50]. Apparently, the THz MA will show good performance when its reflection $R(\omega )$ is nearly zero in a broad band. The optimal structural parameters are (in micrometers): $g=0.7,P=65,l=55,a=\frac{1}{2}(l-g),h=\frac{1}{2}l-(34+\frac{1}{2})g,t_d=25.$ The metal used in the THz MA is lossy gold whose conductivity and thickness are $\sigma =4.09\times {10}^7$ S/m and 1.2 micrometer, respectively. The dielectric is chosen to be polyimide with relative permittivity of 3.0 and loss tangent of 0.06 [51, 52].

3. Results and discussions

The absorption results of the THz MA with the polarization angle $\theta$ increasing from 0° to 90° (the step is set to be 15°) at normal incidence are shown in Fig. 2. As seen, a broadband absorption with an averaged absorption of higher than 85% can be found in the frequency range of about 0.85-1.95 THz. Especially, the averaged absorption is higher than 90% in the frequency range of about 1.2-1.9 THz. Due to the four-fold symmetric structure of the THz MA, the absorption is independent to the polarization states of the incident waves. As to the $y$-polarized (polarization angle is 90°) incidence, the maximum absorption is 99.5% (centered at 0.925 THz). The other two main absorption peaks are centered at 1.30 (95.2%) and 1.82 THz (97.4%), respectively. As shown in Fig. 2, all the absorption peaks are very close to the neighboring one which leads to the broadband absorption of the THz MA.

 

Fig. 2 Absorption characteristics of the polarization independent THz MA at normal incidence when the polarization angles vary from 0° to 90°.

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To understand the mechanism of the broadband absorption of the THz MA, we investigate the surface current distributions at 1.30 THz for the $y$-polarized incidence (shown in Fig. 3). As seen, the absorption peak centered at 1.30 THz is attributed to the mixture of the electric and the magnetic resonances. According to the surface current distributions (not shown here), the absorption peaks centered at 0.925 and 1.82 THz are also attributed to the mixtures of the electric and the magnetic resonances.

 

Fig. 3 Surface current distributions of the absorption peak centered at 1.30 THz for the $y$-polarized incidence.

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According to Ref [53], the mixture of the electric and the magnetic resonances can broaden the absorption band in the GHz regime. The absorption characteristics shown in Fig. 2 indicate that the mixtures of the electric and the magnetic resonances can also broaden the absorption band in the THz regime compared with the single mode of magnetic resonance [31].

Moreover, we give a further insight into the highly efficient broadband absorption property of the THz MA by calculating the magnetic field profiles for the $y$-polarized incidence (shown in Figs. 4(a) and 4(b)). The magnitude distributions of the magnetic fields at the main absorption peaks centered at 0.925 and 1.82 THz are used as examples to illustrate the results. Apparently, the magnetic fields are highly confined in the connected rectangular fish-scale structure at the absorption peaks centered at 0.925 and 1.82 THz, respectively.

 

Fig. 4 The magnitude distributions of the magnetic fields at the main absorption peaks centered at (a) 0.925 and (b) 1.82 THz, respectively, under the normal $y$-polarized incidence.

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The parameter sweeping is also a common measure to investigate the absorption characteristics of the MA [54]. We investigate the effect of the metal and dielectric thickness on the absorption of the THz MA. As shown in Fig. 5(a), the absorption band will have a slight blue-shift with the increase of the gold thickness under the normal $x$-polarized incidence. When the gold thickness is 0.6 µm (shown in Fig. 5(b)), the absorption of the THz MA is higher than 90% in the frequency range of about 1.16-1.85 THz. Compared with the absorption result when the gold thickness is 1.2 µm, the THz MA with gold thickness of 0.6 µm has a better performance in the high frequency part of the absorption band.

 

Fig. 5 (a) The effect of the metal thickness on the absorption of the THz MA. (b) Comparison of the absorption results between the THz MA with the gold thickness of 0.6 and 1.2µm, respectively, under the normal $x$-polarized incidence.

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The absorption band will have a red-shift with the increase of the dielectric thickness under the normal $x$-polarized incidence (shown in Fig. 6(a)). Despite the dielectric thickness value of 25 µm, this THz MA shows good performance when the dielectric thickness increases from 15 to 30 µm. This provides us a chance to shift the working band of the THz MA by adjusting the thickness of the dielectric layer while all the other structural parameters are fixed. As shown in Fig. 6(b), the absorption of the THz MA with dielectric thickness of 18 µm is higher than 90% from 1.31 to 2.06 THz. Apparently, the THz MA with dielectric thickness of 18 µm has a better performance in the high frequency part of the absorption band than that of the THz MA with dielectric thickness of 25 µm.

 

Fig. 6 (a) The effect of the dielectric thickness on the absorption of the THz MA. (b) Comparison of the absorption results between the THz MA with the dielectric thickness of 18 and 25µm, respectively, under the normal $x$-polarized incidence.

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Despite the normal incidence, the THz MA shows excellent performance for the oblique incidences. The absorptions of the THz MA for the transverse electric (TE) and the transverse magnetic (TM) waves are shown in Figs. 7(a)-7(d) when the incident angle increases from 0° to 80°. As can be seen, the THz MA maintains excellent performance in the angular range of about $\pm$70° for both TE and TM incidences.

 

Fig. 7 Absorption characteristics of the THz MA for (a) and (c) TE mode and (b) and (d) TM mode oblique incidences. In (a) and (c), the incident angle is scanned from 0° to 80° for TE and TM mode, respectively. (b) and (d) give the absorption results at incident angles of 0°, 30° and 60° for TE and TM mode, respectively.

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To understand the effect of the connected rectangular fish-scale structures, we simplify the structure of the THz MA by reducing the number of the elementary translational cells while all the structural parameters are invariant. When only the four boundary elementary translational cells of the four groups of rectangular fish-scale structures are reserved, the THz MA (shown in Fig. 1) develops into a MDM sandwich with four connected sub-squares at front (shown in Fig. 8(b)). As to this simplified MDM sandwich, there are two absorption peaks centered at 0.71 and 1.65 THz, respectively (shown in Fig. 8(a)). According to the surface current distributions (not shown here), the absorption peaks centered at 0.71 and 1.65 THz are aroused from the magnetic and electric resonances, respectively.

 

Fig. 8 (a) Comparison of absorption results between the broadband THz MA (shown in Fig. 1) and (b) the MDM sandwich with four connected sub-squares under the normal $x$-polarized incidence.

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Considering the comparison of absorption results between the broadband THz MA (red line in Fig. 8(a)) and the MDM sandwich with four connected sub-squares (black line in Fig. 8(a)), the dual-band absorption can be expanded into the broadband absorption through the use of the connected rectangular fish-scale structure. Apparently, the connected rectangular fish-scale structure provides the possibility/convenience of gaining the mixed modes of the electric and the magnetic resonances in the THz regime (shown in Fig. 3) compared with the MDM sandwich with four connected sub-squares.

4. Conclusions

We have proposed a broadband MA working at the THz frequencies based on the connected rectangular fish-scale structure. The averaged absorption of this MA with MDM configuration is higher than 85% in the frequency range of about 0.85-1.95 THz and the maximum absorption is 99.5% (centered at 0.925 THz). The C4 rotational symmetry of the structure (with four groups of rectangular fish-scales) enables the MA to be independent to the polarization states of incidences. This THz MA still has good performance with the increase of the incident angle for both TE and TM incidences even to 70° incidence. The broadband absorption property of this THz MA is aroused from the mixtures of the electric and the magnetic resonances. This finding opens a new route of broadband THz MA research. Furthermore, the proposed THz MA is easy to be fabricated with photolithography for its MDM configuration with only one structured layer. The MA design with polarization-incident angle independency is applicable to the THz absorbers and detectors.