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Metamaterial-based absorbers utilize the intrinsic loss, with the aid of appropriate structure design, to achieve near unity absorption at a certain frequency. The frequency of the reported absorbers is usually fixed and operates over a limited bandwidth, which greatly hampers their practical applications. Active or dynamic control over their resonance frequency is urgently necessary. Herein, we theoretically present a novel frequency tunable terahertz metamaterial absorber formed by a square metallic patch and a ground plane separated by a strontium titanate dielectric layer. Up to 80.2% frequency tuning is obtained by changing the temperature of the absorber, and there is very little variation in the strength of the absorption. The frequency shift is attributed to the temperature-dependent refractive index of the dielectric layer. Furthermore, the ratio between the lattice period and the resonance wavelength is close to 1/36 at 0.111 THz, which is smaller than the previously reported results. The proposed absorber has potential applications in detection, sensors, and selective thermal emitters.
© 2015 Optical Society of America
1. Introduction
Metamaterials, with a subwavelength-scale unit cell, have attracted significant attention because of their exotic properties that are unavailable in nature, such as invisibility cloaking [1], perfect lensing [2] and negative index of refraction [3]. Split-ring resonators [4,5], fishnet structures [6], cut-wire pairs [7], and other stereostructures [8] have been proposed for landmark predictions of metamaterial theory. Since most proposed metamaterials are metallic resonant structures and rely on strong resonances, the absorption losses are inevitable. The existence of the losses degrades their performance. Different ways to reduce the losses have been studied, including the use of low loss materials [9], the optimization of the design [10] and the use of gain materials to compensate losses [11]. Instead of trying to reduce the absorption losses, recently, ideas have been proposed to build resonant absorbers with metamaterials. For an artificial light absorber, however, the absorption loss becomes useful and could be significantly enhanced by proper design of the structure.
The first perfect metamaterial absorber, having the measured absorptivity of about 88%, composed of a metallic split ring and a cut wire separated by a dielectric layer was demonstrated by Landy et al. [12]. Since then, metamaterial-based perfect absorbers have received considerable attention, and a great number of absorbers have been proposed [13–16]. Unfortunately, all these efforts share the common shortcoming of narrow absorption bandwidth (typically no more than 10% of the center frequency), which greatly hampers their practical applications. An effective method to broaden the absorption bandwidth is to make the metamaterial units resonate at several neighboring frequencies. Following this design strategy, broadband or multi-band absorbers have been demonstrated in a wide frequency region ranging from microwave to optics [17–26, 31–34]. For example, Liu et al. [17, 18], Viet al. [19], and Zhang et al. [20] presented broadband absorbers based on multiple subunit elements in a coplanar structure. Luo et al. [23], Wen et al. [24], Cui et al. [25], and Ding et al. [26] demonstrated wideband absorbers by stacking multiple different-sized metallic patterns.
Although the multi-band or broadband absorptivity behaviors are very desirable, the resonance frequency and absorption strength of the reported absorbers are usually fixed, which greatly hampers their practical applications [27–30]. Particularly, confining and steering electromagnetic waves at dimensions much smaller than the wavelength are of great importance for miniaturization of optical-integrated devices and improvement of the spatial resolution in optical imaging. Unfortunately, the lattice constant (or the period) of the reported absorbers is only 1/2 ∼ 1/5 of the resonance wavelength. Therefore, working on a compact and frequency tunable absorber is very important and helpful for the metamaterial community.
Herein, we present a frequency tunable and deep-subwavelength scale terahertz metamaterial absorber formed by a square metallic patch and a strontium titanate dielectric layer on top of a ground plane. The proposed structure not only provides a compact unit cell but also apparently increases the tuning range, which is needed for the practical application. Specifically, the unit-cell size of absorber can be down to 1/36 (at 0.111 THz) with respect to the resonance wavelength, which is much smaller than previously reported absorbers. Most importantly, up to 80.2% resonance frequency tuning can be obtained without significant variation of the absorption strength. The shift of the resonance frequency is attributed to the temperature-dependent refractive index of the dielectric layer, and the compact unit cell originates from the large real part of the dielectric constant. The proposed absorbers with its superior performance pave a path toward applications with different operating frequencies requirements, such as tunable selective thermal emitters, sensors, and bolometers.
2. Structures design and results discussion
The unit cell of the proposed absorber is illustrated in Fig. 1; it consists of a patterned square metallic patch and a thin strontium titanate (STO) dielectric layer on top of a metallic ground plane. The frequency dependent complex relative permittivity of STO can be given by [35,36]:
where the ε∝ = 9.6 is the high-frequency bulk permittivity, f is a temperature independent oscillator strength, and here f = 2.6×106cm−2, w is the angular frequency of the incident terahertz wave. The w0 and γ are the temperature dependent soft mode frequency and damping factor, respectively. The soft mode frequency w0 can be fitted by: The soft mode damping γ then can be fitted by an empirical linear dependence: where the T is the temperature (K).
Fig. 1 Cross section (a) and top view (b) of the proposed temperature tunable terahertz metamaterial absorber.
Figures 2(a) and 2(b) show the dependence of the dielectric permittivity on the change of the temperature T. It can be seen from Fig. 2(a) that the real part (Re(ε)) of the STO gradually increases with the decrease of the temperature T. Particularly, at each certain temperature, the increase in Re(ε) with the increase of the frequency is very small (or the dispersion of the STO is very weak). The Re(ε) extremely sensitive to the change of the temperature T immediately suggests the potential in tunable terahertz metamaterials and meta-devices. Besides, the large real part of the permittivity helps to design a deep-subwavelength unit cell. The Re(ε) can be further changed (increased or decreased) by proper temperature, which is not discussed in this manuscript. In contrast to the change of the Re(ε), the loss tangent of the STO (i.e., the loss: tan δ), which is less than 0.03 in the frequency of interest, largely does not change with the temperature T (see Fig. 2(b)). The without significant variation of the absorption peak originates from the slight change of the loss: tan δ (see below Fig. 5(a)).
Fig. 2 Temperature dependence of the permittivity (Re(ε)) and the loss tangent (tan δ) of the STO dielectric layer in the frequency of interest.
We now numerically analyze the absorption performance of the absorber. The coupling between the STO and the metallic part of the absorber is investigated through finite-difference time-domain (FDTD) simulations, where the periodic structures are illuminated by a normally incident plane wave with the electric field parallel to the x-axis. Perfectly matched layers are applied along the z direction and periodic boundary conditions in the x and y directions. The repeat period is P = Px = Py = 75 μm, and the patch length is l = lx = ly = 40 μm. The thickness of the dielectric layer is t = 15 μm, and the thickness of the metal (Au) is 0.4 μm with a frequency independent conductivity of σ = 4.09×107Sm−1. The mesh size in metal and dielectric is Δx = Δy = 0.2 μm and Δz = 0.05 μm. The absorption, A, is obtained from A = 1−T−R, where T and R are the transmission and reflection coefficients, respectively. Since the bottom layer is a continuous metallic layer (2 μm) that has a thickness much greater than the skin depth of the incident beam, the transmittance should be zero. Consequently, the absorption can be simplified to A = 1−R. The absorptivity may achieve unity when the reflection is close to zero.
Figure 3(a) shows the calculated absorption spectra of the proposed absorber for a certain temperature (here we choose the room temperature (T = 300 K) as an example). It can be seen from Fig. 3(a) that the proposed absorber has a resonance absorption peak, located at a frequency of 0.171 THz, with an absorptivity of 98.64%. The absorption bandwidth, defined as the full width at half maximum (FWHM), is 0.01 THz, and the quality factor Q (which is defined as: Q = f/FWHM, where the f is the frequency of the absorption peak) of resonance absorption peak is 17.1. Additionally, the off-resonance absorption is very small. These results indicate a frequency selectivity of the absorber due to the narrow absorption bandwidth. Particularly, the ratio between the lattice period and resonance wavelength (in μm) is close to 1/23.4, which is much smaller than previously reported results. Furthermore, the calculated results for different polarizations are shown in Fig. 3(a). As shown in the figure, the absorption is polarization insensitive with respect to the incident electromagnetic wave. This is attributed to the high degree of symmetry of the structure.
Fig. 3 (a) dependence of the absorption spectra on the polarization angles of the incident wave for the proposed tunable absorber at temperature T = 300 K; (b), (c) and (d) show the distributions of the electric (|E| and real (Ez), in the center plane of the patterned structure) and magnetic (|Hy|, in the plane of y = 0) fields for resonance at 0.171 THz. Inset of the Fig. 3(a) shows the calculated absorption spectra for different material properties.
We next investigate the origin of the loss to understand the contributions of each part of the metamaterial absorber. Inset of Fig. 3(a) shows the dependence of the absorption spectra on two different loss conditions (loss-free and lossy) of the dielectric layer. It can be seen that about 30% of the electromagnetic energy is dissipated in the dielectric layer, and about 70% of the energy is dissipated in the metallic layer (i.e., through ohmic losses) for the proposed absorber, which is differs from based on conventional dielectric materials metamaterial absorber [12] that the dielectric losses are about an order of magnitude higher than the ohmic ones. The large absorption in metal maybe originates from the shape of the top structure, the ratio of the patch size to the unit cell area, and the tan δ of the dielectric material. However, the loss-free and lossy resonance frequencies of the dielectric are maintaining the same resonance frequencies, and such an absorption mechanism has been reported in single-band or dual-band absorbers [12–15].
To better understand the physical origin of the proposed absorber, we give the calculated electric (|E| and real (Ez), in the center plane of the patterned structure) and magnetic (|Hy|, in the plane of y = 0) fields distribution corresponding to the absorption maximum (0.171 THz at T = 300 K) in Figs. 3(b)–3(d). As shown in Fig. 3(b), it is obvious that the electric field (|E|) is mainly focused on both sides of the metallic patch. The great enhancement of the electric field (|E|) in the patch indicates that the larger charge accumulates at the edges of the metallic array. Thus, the charge is mainly focused on both sides of the patch [38, 39]. As shown in Fig. 3(c), it is obvious that the opposite charges accumulate at both sides of the metallic patch (along the direction of the electric field). In fact, the opposite charges accumulate at both sides of the metallic patch indicate the excitation of the electric dipole resonance in the metallic array. This electric dipole is strongly coupled with the bottom metallic layer, and an anti-parallel surface current on the top and bottom metallic layers can be obtained. As a result, a magnetic polariton is formed, which induces a strong magnetic resonance (see the magnetic field (|Hy|) in Fig. 3(d)). The coupling strength of the electric dipole and the magnetic response is mainly determined by the dielectric layer thickness. By tuning its thickness, we can obtain an optimal value t = 15 μm, at which the electric and magnetic responses make the proposed structure impedance matched the free space, and a perfect absorption is obtained, as shown in Fig. 3(a).
Furthermore, according to the LC circuit model, the frequency of the absorber is given by [21, 40]:
where l is the metallic patch length, L and C are the inductance and capacitance, respectively, εr is the dielectric constant of the dielectric layer, and in this manuscript the εr is equal to the Re(ε). From this equation, we can acknowledge that the absorber frequency is inversely proportional to the value of . On the one hand, if we fixed the dielectric constant εr, the absorber frequency should be only inversely proportional to the patch length. Figure 4(a) shows the dependence of the absorption spectra on the length change of the absorber. As shown in Fig. 4(a), it is obvious that the absorber frequency gradually increases with the decrease of the length l, while the change in the absorption strength is negligible. The linear dependence of the resonance frequency on the length l is demonstrated in Fig. 4(b), as predicted by Eq. (4). These results show that the absorber frequency could be easily tuned by varying different lengths to meet different application needs. However, the tuning of the frequency by changing the patch length suffers from one crucial drawback, namely that it is unfeasible for a fixed structure to modify its geometric parameters. In other words, this is a passive method to achieve the tuning of the resonance frequency. On the other hand, the absorber frequency is only inversely proportional to the dielectric constant of the dielectric layer if we fixed the length l. This property gives us the opportunity to tune the absorber frequency by changing the dielectric constant εr. As mentioned in Fig. 2(a), the dielectric constant of the absorber can be dynamically tuned by changing the temperature T. Thus, the absorber frequency can be actively tuned by only changing the dielectric constant of the absorber.Fig. 4 (a) Dependence of the absorption spectra for different values of the metallic patch length l for temperature T = 300 K. (b) shows the resonance frequency as a function of the metallic patch length l.
Fig. 5 (a) Dependence of the absorption spectra of the proposed absorber on different temperatures; (b) A comparison between the resonance frequency fm and the inverse of the refractive index indicating fm ∼ 1/n. The values of n have been taken from (a) at the corresponding metamaterial resonance frequencies.
Figure 5(a) shows the calculated absorption spectra at several different temperatures T. At all these temperatures, the absorber exhibits perfect absorption (greater than 98.5%) due to the coupling of the electric and magnetic resonances. The frequency of the absorber experiences a gradual red shift from 0.20 THz at 400 K to 0.111 THz at 150 K. The total frequency shift is 89 GHz, which is about 52.0% of the resonance frequency at room temperature (0.171 THz at 300 K). Particularly, up to 80.2% frequency tuning is obtained from 0.111 THz to 0.20 THz, which is much larger than previously reported results. The without significant variation of the absorption strength is attributed to the slight change of the loss: tan δ (see Fig. 2(b)). The tuning of the frequency is attributed to the temperature dependent permittivity Re(ε) (or the refractive index n, because the n2 is equal to ε), which is shown in Fig. 2(a) and reveals an increasing permittivity Re(ε) (or n) with decreasing temperature T. According to the Eq. (4), if we fixed the length l, we can deduce that the absorber frequency is not sensitive to the length of the metallic patch, and is a linear function of the , i.e., the , over a large range of Re(ε). This is verified by the plots shown in Fig. 5(b), where excellent agreement is achieved in the temperature dependence of the frequency and the inverse of refractive index taken at the corresponding resonance frequencies. Moreover, the ratio between the lattice period and wavelength (in μm) for the proposed absorber is close to 1/36, 1/29.9, 1/26, 1/23.4, 1/21.5 and 1/20 at T = 150, 200, 250, 300, 350 and 400 K, respectively. These results are all much smaller than previously reported results.
Although our approach is presented using the square patch structure, it is a genetic method and can also apply to other type structure designs. Here we employ the metallic ring and cross structures as two typical examples. The unit cell of the metallic ring structure is shown in Fig. 6(a), the optimal parameters are followed: P = Px = Py = 75 μm, the diameter of the metallic ring is D = 40 μm. The conductivity of the Au, the thickness and dielectric constant of the dielectric are the same in the square patch structure. Figure 6(b) shows the calculated absorption spectra of the proposed metallic ring absorber at different temperatures. It is obvious that the absorber frequency gradually increases with the increase of the temperature, which is in accordance with the results presented in Fig. 5(a). The total frequency shift is 101 GHz, which is about 52.1% of the resonance frequency at room temperature (0.194 THz at 300 K). Particularly, up to 80.2% frequency tuning is obtained from 0.126 THz at 150 K to 0.227 THz at 400 K. Furthermore, Figure 6(c) shows the excellent agreement in the temperature dependence of the frequency and the inverse of the refractive index. Therefore, the metallic ring structure is suitable to design the frequency tunable absorber.
Fig. 6 (a) and (d) show the unit cell of the proposed frequency tunable metallic ring and cross absorbers, respectively; (b) and (e) show the calculated absorption spectra of the proposed frequency tunable metallic ring and cross absorbers at different temperatures, respectively; (c) and (f) show the comparison between the resonance frequency fm and the inverse of the refractive index for the proposed metallic ring and cross absorbers, respectively.
Figure 6(d) shows the unit cell of the metallic cross absorber. The optimal parameters are followed in micrometers: P = Px = Py = 75, l = lx = ly = 50, w = 4, the dielectric thickness t = 17, and the conductivity and thickness of the Au, the dielectric constant of the dielectric layer are the same in the Fig. 1. Figure 6(e) shows the calculated absorption spectra of the proposed metallic cross absorber at several different temperatures. It can be seen from Fig. 6(e) that the proposed absorber has a resonance absorption peak located at a frequency of 0.208 THz with an absorptivity of 99.85% at temperature T = 400 K. As the temperature is decreased, its resonance frequency successively shifts to 0.194, 0.178, 0.161, 0.141 and 0.116 THz for T = 350, 300, 250, 200 and 150 K, respectively, and finally a 79.3% frequency tunability is obtained. The shift of the spectra toward lower frequencies is explained by the increase in the effective permittivity of the dielectric layer (see Fig. 2(a)). Therefore, the metallic cross structure is appropriate to design the frequency tunable absorber. Besides, the unit-cell size of the absorber can be down to 1/34.5, 1/28.4, 1/24.8, 1/22.5, 1/20.6 and 1/19.2 with respect to the resonance wavelength at T = 150, 200, 250, 300, 350 and 400 K, respectively. Moreover, the polarization insensitive absorption characteristic is valid for the metallic ring and cross structures due to the high degree of symmetry of the resonance structure (not shown here).
3. Conclusion
In conclusion, we demonstrate a frequency tunable and compact terahertz metamaterial absorber formed by a square metallic patch and a metallic ground plane separated by a temperature dependent strontium titanate (STO) dielectric layer. The absorber frequency can be controlled effectively by varying the temperature, and finally a 80.2% (ranging from 0.111 THz at 150 K to 0.20 THz at 400 K) frequency tunability is obtained, without significant variation of the strength of the absorption. The tuning mechanism is attributed to the temperature dependent refractive index of the dielectric layer. Moreover, the unit cell size for the perfect absorption resonance peak can be down to 1/36 (at 0.111 THz) with respect to the resonance wavelength, which is much smaller than the previously reported results. The deep-subwavelength unit cell originates from the large real part of the permittivity of the STO. Furthermore, the proposed concept is applicable to other types of the absorber structure and the frequency tunable absorbers have potential applications in detection, imaging and stealth technology.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61176116, 11074069), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120161130003), and the 2013 Graduate Science and Technology Innovation Program of Hunan province (Grant No. 521298927).
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