1. Introduction

Terahertz metamaterial absorbers (TMAs) have attracted increasing interests with the rapid development of terahertz (THz) technologies [1,2]. They are capable of completely absorbing THz electromagnetic radiation in a narrow spectrum which is adjustable by fashioning their configurations and dimensions. TMAs become realizable thanks to the emerging metamaterial techniques allowing for the creation of artificial materials with engineered electromagnetic properties [3]. To date, various TMA designs have been presented in diverse subwavelength metastructures [4–6], and currently with special focus on the tunable, multiband and broadband perfect absorption functionalities [7–10]. Particularly, tunable TMA can enable the dynamical shift of absorption spectrum. Multiband resonance in TMA can induce frequency-selective absorption at the THz spectra of interest. Near-unity absorbance is highly required for efficient absorption detection. Thereby development of dynamically tunable multiband perfect TMA designs becomes a keystone objective due to the high demand from biomolecular spectra-selective THz imaging and sensing [11,12].

Generally, to achieve multiband TMAs, the effective method is on single layer by combining different geometries of subwavelength plasmonic resonators [13,14]. Another approach is by stacking multi-layer metastructures with different geometries separated by dielectric layers [6,15]. Recently, other important methods based on graphene subwavelength gratings to produce multiband perfect absorption have been presented. By shaping periodic graphene nanoribbons into in-plane bended gratings, two absorption peaks can be created [16]. By using single-layer graphene-based rectangular gratings, triple- and four-band perfect absorptions can be achieved [17]. To actively control TMA devices, the feasible mechanisms have been suggested involving mechanical, electrical and optical tuning methods. Consequently, a few schemes of controllable TMAs have been demonstrated with microelectromechanical systems (MEMS) [18–20], graphene [21–25] and semiconductor-based metamaterials [26,27]. However, there are still some challenges regarding the dynamically tunable perfect absorption performance [11].

MEMS-tunable metamaterial absorbers can mechanically control the THz frequency tuning, but they exhibit strong dependence on incidence angle and have difficulties to integrate for multiband tuning operation [19,20]. Graphene metamaterials show good controllability of THz absorption spectra by electrically tuning the Femi level (i.e., chemical potential) of graphene, but the reduction of peak absorbance is caused inevitably due to the changes in graphene chemical potential, and more seriously in the multiband tuning schemes [14,21,22]. Such problem of absorbance deterioration occurs also in semiconductor-tunable TMA devices with optically-controlled free carrier mobility [26,27]. As one knows, the degeneration of absorbance during the spectra tuning is undesirable in advanced THz optical systems for high-quality detecting and imaging [12,28].

In contrast to the tuning methods mentioned above, liquid crystal (LC) materials, owing to the property of voltage-controlled refractive index change, have been suggested to manipulate the spectra response of bulk THz devices used for phase shifter and modulator [29–32]. Recently, several prominent works have explored monoband metamaterial absorbers for LC-based THz modulation via the spectral shifting regime [7,33–37]. The first demonstration of LC-tunable absorber in the THz regime was reported by Padilla et al. in 2013 [34]. By incorporation of active LC into the metastructure unit cell, a 30% absorption modulation was achieved at 2.62 THz, with a frequency shift of 4.6%. In 2014, they further presented the ability of TMA functionalized with LC to work as a spatial light modulator [35]. An modulation factor of 70% at 3.67 THz was obtained with an frequency shift of 6.5%. Then, another LC tunable THz absorber by exploiting the critical coupling between periodically arranged resonators and external fields was proposed by Isić et al. in 2015 [36]. A reflectance modulation depth above 23 dB was predicted, as well as a spectral shifting of 15%. Most recently, an electrically-controlled TMA consisting of complementary split ring resonators integrated with LC was performed by Kim et al. [37]. A spectrum shift of about 0.005 THz was observed at the operating frequency of 0.567 THz, with the peak absorbance of 90%. Note that the obtainable amounts of spectral shift were restricted by the birefringence of LC materials used. In the LC-tuning operations, the degeneration of peak absorbance was somewhat less serious in comparison with other tuning methods [21–27]. The previous works suggest the potential of LC-based schemes for tunable TMA design. However, multiband LC-tunable perfect TMA devices have been not reported yet.

In the paper, we present a compact triple-band tunable perfect terahertz absorber at sub-wavelength scale of thickness, which is composed of a planar metallic disk resonator array above a conductive ground plane separated with LC material. The THz absorption spectra are calculated to demonstrate the performance of both multiband spectral tuning and near-unity absorbance with wide angle of incidence and weak polarization dependence. Three resonance frequencies of the perfect TMA exhibit continuous linear-tunability as the refractive index of LC changes. Remarkably, at the triple resonance bands, each peak absorbance can maintain at a near-unity level (>99%) in the whole tuning operation; meanwhile, the peak absorbance can remain more than 90% over a wide range of incident angles. The dramatic performance improvement is associated with the strong coupling between the confined fields in the gap plasmonic resonant cavity and the LC material. Our work suggests that the LC tunable absorber scheme has the potential to overcome the basic difficulty to perform simultaneously multiband spectral tuning and near-unity absorbance with wide angle of incidence and weak polarization dependence.

2. Design and simulation

The structure of the proposed LC tunable multiband TMA is shown in Fig. 1. It is composed of a planar metallic disk resonator array above a conductive ground plane separated with LC material. The metallic resonator array consists of gold circular and elliptical disks, where r denotes the radius of circular disk, a and b represent the major and minor axis semidiameters of elliptical disk, respectively. In each lattice, the circular disk lies in the center and is surrounded with four elliptical disks, which is periodic in two dimensions. Into the gap between the superstrate of metallic disk array and the conductive ground plane is LC material infiltrated completely, with two dielectric spacers covered with THz transparent electrodes. The electrodes can be prepared with the commercial indium tin oxide (ITO) or newly invented super polymer films with high electrical conductivity and THz transparency [31,38]. By applying electrostatic fields via the pair of electrodes, the refractive index of LC material can be controlled to achieve multiband spectral tuning of TMA.

 

Fig. 1 Schematic of the LC tunable TMA structure. (left) cross section (not to scale); (middle) bird's eye view of the whole structure; (right) the unit cell of the metamaterial.

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In design, changes to the disk resonator dimensions allow for specification of effective resonant permittivity and permeability that can provide impedance matching to minimize the reflection [39]. The presence of the conductive ground plane assures negligible transmission. The change to LC-infiltrated gap can result in large absorption and sensitive tuning due to the strong coupling interaction of gap plasmonic resonator with LC material [40]. The pair of planar electrodes supply a uniform electrostatic field to the LC, which can maximize the obtainable tunability of TMA in both far-field and near-field [7]. The method of creating multiband resonance by combining different geometries of resonators has been discussed in Refs [2,13]. Accordingly, the geometries of the metallic disk array and the gap size can be optimized to achieve multiband tunable perfect absorption at THz frequencies of interest.

In the work, we concentrate on triple-band tunable perfect absorption performance near the 1-2 THz region. As shown in Fig. 1, the geometric parameters are summarized. For the superstrate of metallic disk array, a = 55 μm, b = 25 μm, r = 36 μm, the period p = 130 μm and the thickness t = 0.2 μm. The metallic disks are chosen to be gold. The gold permittivity can be calculated by Drude model which works well at THz frequencies. The Drude formula is ${}_{\epsilon \text{Au}}(\omega )=1-{\omega }_p^2/\left({\omega }^2+i{\gamma }_c\omega \right)$ with the plasma ω_p = 1.37 × 10¹⁶ rad/s and collision frequency γ_c = 4.05 × 10¹³ rad/s taken from Ref [41]. The ground plane layer is described by the perfect electric conductor boundary condition [6]. The dielectric spacer has the thickness of s = 1 μm, with free space impedance matching. The LC-infiltrated cell size is d = 3.3 μm. The LC mixture used here has favorable properties of very high birefringence (Δn ∼ 0.4, flattened in 0.5 − 2.5 THz), low loss (α_o< 1.3×10^-3 μm^-1, α_e< 2.2×10^-3 μm^-1, maximized at 2 THz) and low dichroism at THz frequencies, whose parameters can be found in Ref [42]. (Table 2 and Fig. 3 therein). Due to the high birefringence combined with low absorption and low dichroism, the LC mixture is particularly well suited for thin, switchable and cost-efficient THz components. The model calculations have been implemented by finite element method to solve the Maxwell equations in the frequency domain. The relative tolerance is set to 1×10^-3 in numerical calculations, which is known to be adequately accurate while the meshing is refined until reaching the convergence of scattering coefficients. The reflection R(ω) = |S₁₁|² and the absorption A(ω) = 1 − R(ω) can be obtained from the S-parameters realized in a commercial solver of COMSOL multiphysics.

3. Results and discussion

Figure 2 shows the THz absorption spectra of LC-based TMA under normal incidence excitation, with the LC ordinary refractive index ${\tilde{n}}_o\left(\lambda \right)=n_o\left(\lambda \right)+i\lambda {\alpha }_o\left(\lambda \right)/4\pi$ [42]. The incident THz beam is polarized along the x-axis. Triple-band perfect absorber can be achieved when the disk resonator array distributes as arranged in Fig. 1.

 

Fig. 2 The THz absorption spectra for periodically-patterned disk metamaterials composed of (a) only elliptical disks with the major axis parallel to x-axis, (b) only circular disks, (c) only elliptical disks with the minor axis parallel to x-axis, and (d) hybrid circular-elliptical disks meta-molecules shown in Fig. 1. In the panels (a), (b) and (c), the color inserts illustrate the electric field distributions under the resonant excitation of 1.05, 1.51 and 1.95 THz, respectively. In the panel (d), three dashed lines represent the intrinsic resonance response corresponding to the subfigures (a), (b) and (c), and the solid line shows the triple-band perfect absorption of the proposed structure.

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The simulation results in Fig. 2(a) show that, the dipolar plasmon resonance can be excited in the array of only elliptical disks with the major axis parallel to the x-axis. The peak absorbance of 99.5% at 1.05 THz performs nearly perfect absorption. Another dipolar plasmon resonance produced by only circular disks in the array can be obtained at 1.51 THz with the peak absorption of 99.0%, as shown in Fig. 2(b). The third dipolar plasmon resonance can be observed in Fig. 2(c) when the minor axis of elliptical disks is parallel to the x-axis. It occurs at 1.95 THz with the peak absorbance of 96.5%.

Further with remaining the incident polarization along x-axis, we can simulate the hybrid resonance absorption of the integral structure. It can be seen from Fig. 2(d) that the absorption spectra of the integral TMA display the characteristics of triple resonance perfect absorption. The peak absorbances at the triple bands are, respectively, 99.9% at ƒ₁ = 1.05 THz, 99.7% at ƒ₂ = 1.47 THz and 99.7% at ƒ₃ = 1.90 THz. Note that the peak absorbance values of the integral structure are all improved near 100% in comparison with the intrinsic resonance of the individual patterns. The plasmonic intercoupling effect of the disk resonators is believed responsible for the absorption improvement [43].

It is worth noticing that the incident polarization dependence on the geometrical structure of TMA has been eliminated through carefully arranging the circular and elliptical disks array in a two-dimensional symmetry. In simulation, the LC mixture is modeled as a homogeneous anisotropic medium. By taking into account the low dichroism and ultrathin LC thickness (around λ/100 ~ λ/50) in the design, as discussed in Refs [34–36], it is believed reasonable to present the LC-infiltrated cell by an equivalent isotropic dielectric having a high electrically-induced birefringence. This indicates that the absorption of LC-infiltrated TMA is weakly dependent on the incident polarization direction. It has been confirmed by simulations with the incident polarizations along x- and y-axis, which exhibit no obvious changes in absorption spectra under normal incidence.

Figure 3 shows the triple-band absorption dependence on the LC thickness. As changing the LC thickness, the peak absorbance at ƒ₁, ƒ₂ and ƒ₃ resonance modes is evaluated respectively. For each absorption mode, there is an available range of LC thickness in which the peak absorbance beyond a level of 99% can be steadily achievable and the maximum absorbance can reach over 99.9%. The shadow region in Fig. 3 indicates the range of optimum LC thickness for the triple-band perfect absorption. It is found that the peak absorbances at the triple modes can simultaneously ensure more than 99% in a relatively wide range of 2.6-3.6 μm thickness showing an acceptable technical tolerance.

 

Fig. 3 The peak absorbance dependence on the LC thickness for the triple resonant modes. The shadow region indicates the range of optimum LC thickness for near-unity perfect absorption simultaneously at the triple modes.

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To get insight into the underlying mechanism in the LC-infiltrated TMA structure, Fig. 4 illustrates the electric and magnetic field distributions at the three resonant frequencies. The excited fields on the planar disk resonator array were simulated in Figs. 4(a)–4(c), respectively at ƒ₁, ƒ₂ and ƒ₃ absorbing modes. The fields concentrate mostly on the vertex of metallic disks along the x-axis under the polarized excitation. No electric multipolar resonant modes are observed. This indicates that the perfect absorption at the triple bands is associated with the significant electric dipolar resonance.

 

Fig. 4 The electric field distribution on the superstrate of gold disk array (x-y plane), corresponding to three resonance frequencies at (a) 1.05 THz, (b) 1.47 THz and (c) 1.90 THz; The local amplifications marked by dashed frames in the panels (a), (b) and (c) are displayed, respectively, in the panels (d), (e) and (f); The panels (g), (h) and (i) illustrate the magnetic field distributions at the p₁, p₂ and p₃ cross-section planes, respectively under the resonant excitation of 1.05, 1.47 and 1.90 THz. The dashed line pairs indicate the position of LC layers.

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Particularly, the local distribution of concentrated fields are enlarged in Figs. 4(d)–4(f) to manifest the gap plasmonic coupling between two neighboring disk resonators. It is clearly found that the intercoupling effect is negligible on the absorption of ƒ₁ band, but makes contribution to the absorption of ƒ₂, ƒ₃ bands. Accordingly, it becomes understandable for the slight red-shifting of frequency and the absorbance improvement observed at the ƒ₂ and ƒ₃ absorbing modes in the integral TMA.

Accompanied by the electric dipolar resonance, the magnetic dipolar resonance can take place in the gap plasmonic cavity between the planar metallic disk array and the conductive ground plane. The electric dipoles induced on the disk array can make strong couplings with their own images which oscillate in anti-phase on the conductive ground plane [43]. This leads to the formation of magnetic polaritons. The magnetic polaritons can induce strong magnetic response in the LC-infiltrated gap and contribute to the triple-band perfect absorption. Here, the magnetic field distributions (|H|) in the cross-sections were simulated respectively under the excitation of ƒ₁, ƒ₂ and ƒ₃ modes. The fields at the p₁, p₂ and p₃ cut planes are visualized in Fig. 4(g)–4(i). The enhanced magnetic fields are confined in the closed space between the metallic disk array layer and the ground plane. Such high overlap in space between the enhanced fields and LC material enables the maximized light-matter interaction [40]. Thereby it is suggested that the triple-band perfect absorber can be effectively tuned in frequency by the refractive index of LC.

The complex refractive index $\tilde{n}\left(\lambda \right)$ of LC material relates basically to the orientation of LC molecules, which can be controlled by applying external voltage [29]. This provides a electrically-tuning approach in practice. Figure 5(a) shows the THz absorption spectra of the LC-infiltrated TMA at the refractive indices of ${\tilde{n}}_o\left(\lambda \right)$ (ordinary polarization) and ${\tilde{n}}_e\left(\lambda \right)$ (extraordinary polarization). Note that the dispersion of refractive index and absorption coefficient has been taken into account in all simulations [42]. It can be seen that as switching the LC molecules between the ordinary polarization (${\tilde{n}}_o$) and the extraordinary (${\tilde{n}}_e$), one can induce a frequency shift in the triple resonant response of the order of more than 100% in terms of bandwidth, as well as the amount of spectral tuning (Δƒ/ƒ) reaching 10% for each band. Moreover, the peak absorbance at each band remains beyond 99% in the operation. Note that recently a hybrid tunable THz metadevice with high birefringence LC as tuning element has performed a spectral shift of the order of 7−8% in terms of bandwidth and about two orders of magnitude change in the absorption, showing its potential for THz spatial modulator [44].

 

Fig. 5 The THz absorption spectra at the refractive indices of LC mixture ${\tilde{n}}_o$ (red curve) and ${\tilde{n}}_e$ (blue curve), (b) The simulated absorption efficiencies as a function of the operating frequency and refractive index of LC material.

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Due to the ability of continuous change in LC refractive index [42], the dynamical tuning operation is practicable in the LC-based TMA device. Figure 5(b) shows the simulated spectral absorbance as a function of THz frequency and the refractive index of LC. The three red strips in Fig. 5(b) indicate the triple resonant absorption bands. When changing the refractive index from ${\tilde{n}}_o$ to ${\tilde{n}}_e$, the triple resonant bands exhibit the continuous linear-tunability in frequency, and remarkably, maintain perfect absorption at a near-unity level (>99%) during the whole LC-tuning process. In contrast to the absorbance deterioration during the frequency shift by graphene or semiconductor tuning methods [21–27], the improvement of tunable multiband perfect absorption performance is attributed to the unique LC-coupling scheme introduced in the TMA structure.

Additionally, the THz absorption spectra as a function of the operating frequency and incidence angle are discussed at the ordinary (${\tilde{n}}_o$) and extraordinary (${\tilde{n}}_e$) refractive indices, respectively, as shown in Figs. 6(a) and 6(b). The incident THz beam keeps s-polarization. In Figs. 6(a) and 6(b), the three narrow strips (red-highlighted) indicate the triple resonant bands of angle-dependent perfect absorption. One can see that the proposed TMA can work over a wide range of incident angles for both cases of ${\tilde{n}}_o$ and ${\tilde{n}}_e$. No obvious change in frequency response occurs for the triple resonant absorption bands. Furthermore, by taking into account the whole dynamic LC-tuning process, the spectral absorbance as a function of LC refractive index and incidence angle are evaluated in Figs. 6(c)–6(e), respectively at the ƒ₁, ƒ₂ and ƒ₃ resonance modes. The areas below the dotted boundaries indicate the peak absorbance at a more than 90% level. The results give the effective working angles under oblique incidence. It is found that the peak absorbance at each resonance mode can steadily remain more than 90% over a wide range of incident angles throughout the whole tuning from ${\tilde{n}}_o$ to ${\tilde{n}}_e$, specifically up to ± 50° at the ƒ₁, ƒ₂ absorbing bands and beyond ± 20° at the ƒ₃ band.

 

Fig. 6 For the s-polarized incident beam, (a) and (b) are two-dimensional absorption spectra as a function of the operating frequency and angle of incidence, respectively at the LC refractive index of and ${\tilde{n}}_o$and ${\tilde{n}}_e$(c), (d) and (e) are the spectral absorbance as a function of LC refractive index and angle of incidence, respectively at the three resonant modes of ƒ₁, ƒ₂ and ƒ₃.

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When the incident THz beam is switched to be p-polarized, the angle-dependent perfect absorption under oblique incidence can be presented by the simulations of Fig. 7. Figures 7(a) and 7(b) show the THz spectral absorption as a function of the operating frequency and incident angle, respectively at the LC refractive index of ${\tilde{n}}_o$ and ${\tilde{n}}_e$. Evidently, the wide working angle of incidence can be still achievable at the triple absorption bands. The resonant absorption frequencies do not make notable changes with the incident angle. During the whole dynamic LC-tuning process from ${\tilde{n}}_o$ to ${\tilde{n}}_e$, as shown in Figs. 7(c)–7(e), more than 90% of peak absorbance can be ensured over a wide range of incident angles for each resonant mode. The results give the working angles up to ± 50° at ƒ₁, ƒ₂ modes and beyond ± 20° at ƒ₃ mode. In comparison with the results for the s-polarized incidence, the similar performance for the p-polarization indicates that the wide-angle perfect absorption has a weak polarization dependence in the LC-tunable TMA structure under oblique incidence.

 

Fig. 7 For the p-polarized incident beam, (a) and (b) are two-dimensional absorption spectra as a function of the operating frequency and angle of incidence, respectively at the LC refractive index of ${\tilde{n}}_o$ and ${\tilde{n}}_e$; (c), (d) and (e) are the spectral absorbance as a function of LC refractive index and angle of incidence, respectively at the three resonant modes of ƒ₁, ƒ₂ and ƒ₃.

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4. Conclusion

In conclusion, we have presented a LC-tunable multiband perfect terahertz absorber at subwavelength scale of thickness, which comprises a planar metallic disk resonator array above a conductive ground plane separated with LC material. The calculations of THz absorption spectra demonstrate triple near-unity absorption bands located at ƒ₁ = 1.05 THz, ƒ₂ = 1.47 THz, and ƒ₃ = 1.90 THz, respectively. Three resonance frequencies of the perfect absorber exhibit continuous linear-tunability with the change of the refractive index of LC material. And remarkably, the peak absorptions at the triple resonant bands can maintain at a near-unity level (>99%). Meanwhile, the peak absorbance at each band can remain more than 90% over a wide range of incident angles, specifically up to ± 50° at the ƒ₁ and ƒ₂ absorbing bands and beyond ± 20° at the ƒ₃ band in the whole dynamic tuning operation. Compared with the previous devices in which the absorbance deterioration occurs during the frequency tuning [21–27], our work suggests that the LC-based tunable absorber scheme has the potential to overcome the basic difficulty to perform simultaneously multi-band spectral tuning and near-unity absorbance with wide angle of incidence and weak polarization dependence. The proposed LC-tunable multiband perfect TMA design is promising for biomolecular spectra-selective THz detecting, imaging and sensing.