1. Introduction

Metamaterial absorbers (MMAs), an important aspect of terahertz technology, has attracted enormous attention for its promising intriguing applications in nondestructive detection, sensing and imaging, and solar harvesting [1–4]. Plenty of structures of MMAs has been proposed in the past several years since the first MMAs was demonstrated by Landy [5]. However, the absorption spectra of many proposed absorbers are narrow in bandwidth which limits their practical application in the electromagnetism regime [6]. To achieve broadband absorption, various approaches have been investigated from microwave, terahertz to optical frequencies [7–11]. A common strategy is to utilize multi-resonances by embracing multiple resonators with small differences in geometry sizes within one unit cell [12–14], and the continuously small different resonance frequencies will be merged to form a broadband absorption. Another branch of effective broadband structures is to overlay the multi-layered pattern with different geometry parameters separated by dielectric with different thickness [15,16]. Besides, the lossy material including lumped resistor-loaded absorber and magnetic material-based absorber also have broadband absorption characteristic [17,18]. However, once the structure is fabricated, the absorption spectra of the absorber is fixed. From the viewpoint of practical applications, tunable absorbers are highly desired in switch, photodetector, absorption filter and so on [19–21]. Therefore, designing a dynamically tunable absorber is essential.

To implement tunable property in the absorber, several methods have been reported [22,23]. One popular way nowadays is to adopt new tunable materials such as graphene [24–27]. Various structures based on graphene have been proposed to make the absorber tunable. For example, a tunable absorber with periodically sinusoidally-patterned graphene layer is proposed and peak absorption of the absorber can be tuned from 14% to 100% by controlling the chemical potential from 0 to 0.8 eV [28]. However, the special-shaped graphene layer is often difficult in fabrication and realization, and then a dielectric-loaded graphene plasmon structure using nonstructured graphene is reported [13]. Nonetheless, the tunable modes in these absorbers are based on electric control and often only the amplitude of absorption can be effectively tuned. There also exist some other ways to achieve tunable property, as mentioned in [22] by Schalch and Duan, a tunable air spacer which can change continuously is adopted as the dielectric layer, so the absorption spectrum is dependent on the spacer thickness. Although there are some researches about the thermally tunable metamaterials, most are focused on modulators or converters, less about the thermally tunable perfect absorbers [29–32].

In this paper, we introduce a thermally tunable perfect absorber in the terahertz regime, whose central frequency can be effectively tuned. In our design, the frequency tunable property is achieved by adoption of active material-strontium titanate (STO) through temperature changes. Full-wave numerical simulation results show that a near unity absorption is obtained in the absorber with a 120 GHz bandwidth above 90% absorption when the temperature is set as 400K. And the central frequency can be tuned from 2.48 to 1.71 THz when the temperature varies from 400 to 200K while keeping 99% peak absorption.

2. Design and simulation

The designed thermally tunable absorber based on the strontium titanate (STO) active material in the THz regime is presented in Fig. 1, which is a sandwich structure composed of a metallic elliptical pattern and back ground spaced by the dielectric layer of STO material. As shown in Fig. 1, the terahertz wave vector is perpendicular to the pattern face, and the electric field direction is along the $P_x$ axis. The corresponding geometry dimensions of the unit cell are illustrated in Fig. 1(a), where the radius of the metallic elliptical pattern on the top layer is $R=25$$\mu m$, and the period$P_x=P_y=98$$\mu m$. Both the top pattern and background plane are made of gold material with a conductivity$\sigma =4.56\times {10}^7$$S/m$, and the thickness is $m=n=200$$nm$. The gold pattern and background is separated by a strontium titanate dielectric spacer with a thickness $H=2$$\mu m$. Strontium titanate is a kind of thermal active material, whose frequency dependent complex relative permittivity can be expressed as [32,33]:

 

Fig. 1 Proposed tunable terahertz absorber with a classical sandwiched structure consisted of metallic top layer and ground plane, spaced by STO material film. (a) Schematic presentation of the geometrical parameters in the unit cell. (b) Top view of the unit cell. (c) Schematic of the absorber. The corresponding geometry parameters are set as (unit:$\mu m$):$P_x=P_y=98$,$R=25$,$H=2$, $m=n=0.2$.

Download Full Size | PDF

In the modeling and simulation, we employ frequency domain solver of CST software and the frequency range is set as 1.5 to 3.0 THz. In the boundary condition setting, both the x-axes and y-axes as periodic boundary are set as unit cell and the two sides of z-axes are Floquet ports. According to the effective medium theory, absorption of the absorber can simplified and calculated by the equation $A(\omega )=1-{\left|S_{11}(\omega )\right|}^2-{\left|S_{21}(\omega )\right|}^2$, where $S_{11}(\omega )$ and $S_{21}(\omega )$ are reflection coefficient and transmission coefficient, respectively. Furthermore, the $S_{21}(\omega )$equals to zero here due to the electromagnetic shielding by the gold background plane whose thickness ($n=200$$nm$) is much larger than the skin depth of incident wave. And the $S_{11}(\omega )$ can be theoretically restricted as zero through impedance matching between free space and metamaterials, so near-unity absorption is achieved.

3. Results and discussion

A full-wave simulation based on finite integration algorithm of CST has been performed to study the absorption spectra of the absorber. Firstly, the parameters of the structure are optimized and the absorption spectra with the primary temperature $T=400\text{K}$ is presented in Fig. 2. As we can see, a broad bandwidth of absorption with a near-unity peak absorption is obtained in the absorber. The peak absorption is located at$f=2.48$THz with a 99.9% absorption and the bandwidth of 90% terahertz absorption is 120 GHz from 2.42 to 2.54 THz.

 

Fig. 2 Absorption spectra of the absorber under normal incidence with the primary temperature 400K in the TE mode.

Download Full Size | PDF

Primarily, we investigate the thermally tunable property of the absorber in detail, which is one of the most important features in the absorber. Firstly, we calculate the temperature-dependent permittivity of STO material. As shown in Fig. 3(a), the real part of permittivity of STO material under different temperatures between 200K to 400K are given and described by the curves with diverse colors. We can see that the real part of permittivity changes obviously with lower temperature levels, as the value increases from 223 to 509 when the temperature varies from 400K to 200K. And the value keeps increasing slowly across the whole study frequencies where the increasing rate rise at lower temperature levels. In the Fig. 3(c), we give the real part of permittivity changing with temperatures at the resonance frequency of 2.48 THz to know the STO material more intuitively. From the curves represented in Fig. 3(b), we can know that the losses angle tangent of STO material increase with both the temperature and frequencies of incident waves, and the increasing rate is greater when the temperature is lower.

 

Fig. 3 The permittivity of STO material at different frequencies (1.5 to 3 THz) and temperatures (from 400 to 200K), (a) Real part of the permittivity, (b)The losses tanδ, (c) Real part of the permittivity changing with temperature at the resonance frequency of 2.48 THz.

Download Full Size | PDF

With the study above, we further investigated the thermally tunable property of the absorber by changing the temperature. From the Fig. 4, we can see that the central frequency shows an obvious red shift when the temperature decreases from 400K to 200K with a step-width of 50K, where the central frequency changes from 2.48 THz (corresponding to 400K, represented by the cyan curve) to 1.71 THz (corresponding to 200K, represented by the black curve). The tuning range of the central frequency reaches 0.77 THz in the absorber, and the peak absorption always remains more than 99%. Moreover, the absorber’s bandwidth of 90% terahertz absorption keeps stable with a partially narrowing down. which changes from 120 GHz to 60 GHz. It is worth noting that the structure is simple and ultrathin (only about$\lambda /60$), which enable the ease of fabrication and application.

 

Fig. 4 Absorption spectra of the absorber with different temperature 200K, 250K, 300K, 350K, and 400K under normal incidence.

Download Full Size | PDF

To better understand the tunable absorption mechanism of the absorber, we study the electric field distribution corresponding to the peak absorption frequency 2.48 THz with the temperature 400K. As shown in Fig. 5(a), we can see that the strong electric field is mainly focused on the up and down side of the circle pattern, which indicate large charges are accumulated at the edge of the metallic pattern. For the TM mode, from the Fig. 5(b), we can see that the field distribution is the same when the unit cell is rotated by 90${}^{\circ }$. Then, we get the field distribution from the normal incidence (${\text{E}}_z$) from Fig. 5(c), and opposite charges are observed in the up and down parts of the golden pattern which agrees well with the description of electric dipole resonances.

 

Fig. 5 Electric field distribution of the proposed absorber at the resonance frequency 2.48 THz. (a) For the TE mode in the x-y plane. (b) For the TM mode in the x-y plane. (c) normal incidence of incidence wave, along the ${\text{E}}_z$direction.

Download Full Size | PDF

Next, we continue to investigate the surface current distribution of the proposed structure on the front pattern layer and the back ground layer. As shown in Fig. 6(a), the surface current on the back ground layer mainly flow from the bottom to the top along the corresponding edge of the top pattern. Meanwhile, when it comes to the surface current on the top pattern layer shown in Fig. 6(b), we can see the main current direction is opposite with the back ground layer. As a result, a virtual circle current is formed by the anti-parallel current from the top and back ground layer, which is the same as the description of magnetic polaritons [34]. As a result, we can conclude that the high absorption in the structure is based on the electric dipole resonances and magnetic polaritons, where the electric field and magnetic field of the incident terahertz wave are absorbed independently.

 

Fig. 6 Surface current distribution at the peak absorption frequency point 2.48 THz with the temperature 400K. (a) Current on the back ground layer. (b) Current on the top layer.

Download Full Size | PDF

Furtherly, when it comes to the frequency tunable mechanism, we provide the electric field distribution of the peak absorption frequency points with different temperatures between 400K to 200K. As shown in Fig. 7, the electric distribution at 2.48, 2.33, 2.13, 1.94, 1.71 THz are given one by one from left to right pictures, responding to the temperature of 400, 350, 300, 250, 200K, respectively. We can see that all the field distributions are much similar with slightly different field strength, which is the same as the distribution of dipole resonance revealed above. It can be concluded that the main absorption resonance in the absorber is not changed with the temperature, and the central frequency occurring an obvious red shift from 2.48 to 1.71 THz can be attributed to the change of effective electrical size in the unit cell, where the effective electrical size of gold pattern increases due to the great permittivity increment of STO dielectric layer when the temperature varies from 400 to 200K.

 

Fig. 7 Electric field distribution at different frequency points of 2.48, 2.33, 2.13, 1.94, 1.71 THz, when the temperature is set as 400, 350, 300, 250, 200 K, respectively.

Download Full Size | PDF

The effect of oblique incidence for both the TE and TM modes on the absorption in the absorber is also studied, as shown in Fig. 8. In the calculation, the absorption spectrum is given with the incident angles varying from 0 to 80${}^{\circ }$with a step-width of 5${}^{\circ }$when the temperature is set as 400K. We can see that the peak absorption decreases gradually with the oblique angles increasing for the both modes, but the peak absorption remains above 90% up to 60${}^{\circ }$of the incidence angles for the TE mode and 55${}^{\circ }$for the TM mode. And we can also see around 60% absorption at some frequencies points near the central frequency 2.48 THz, which is formed by other resonances resulted by the oblique incidences. The central frequency occurs a slight blue shift for the TM mode while remains almost unchanged for the TE mode.

 

Fig. 8 Absorption contour map of the absorber as a function of incidence angle and frequency under oblique incidence angels from 0° to 80° with a step width 10°. (a) TE mode. (b) TM mode.

Download Full Size | PDF

4. Conclusion

In this paper, we proposed a thermally tunable absorber with near-unity absorption in the terahertz regime. By introducing the special active material strontium titanate (STO) as the dielectric layer in the traditional sandwiched-structured metamaterial absorber, the central frequency of the absorber can be effectively tuned by changing the temperature. According to the full-wave numerical simulation, the results show that a 99.9% absorption is obtained at 2.48 THz under normal incidence when the temperature is set as 400 K, and the absorber’s 90% terahertz absorption is 120 GHz. Besides, the central frequency of the absorber can be tuned from 2.48 to 1.71 THz gradually by adjusting the temperature from 400K to 200K, and the peak absorption always remains near-unity. Additionally, we performed the electric field distribution and surface current distribution to better understand the absorption and thermally tunable mechanism in the structure. Furthermore, some valuable properties are also found in the proposed absorber, such as polarization-independence and ultrathin thickness, which are resulted by symmetry design of the unit cell and high dielectric coefficient in the STO material. The proposed structure can be scalable to the infrared and visible frequencies, and can be applied in imaging, detection and tunable sensors.