1. Introduction

Terahertz (THz) radiation provides many useful applications for spectroscopy, biomedical imaging, security, food quality control and communication [1–2]. Since the very field of the THz science and technology is relatively young, new devices and materials are on demand. Metamaterials with peculiar electromagnetic properties have attracted considerable interest to terahertz devices in the last decade [3]. Recently, the Metamaterial absorber is an important application to metamaterials in microwave and terahertz [4], which typically consists of two metallic layers spaced apart by virtue of a dielectric spacer. The top metal layer is geometrically patterned in order to strongly couple to the incidence electric field. By pairing the top layer with a metal ground plane, a mechanism with impedance-match to that of free space may be created. Landy et al [5] firstly reported the concept of the perfect metamaterial absorbers and demonstrated the absorption of 88% in experiments. Since then, many metamaterials absorbers have been proposed and demonstrated towards narrow-band [6, 7], wide-band [8-10], dual-band or multi-band [11-16] and polarization independence structures [17-20].

However, if operation frequencies of traditional metamaterial absorbers are fixed, it is inconvenient to change after fabrication, if the impedance of one or more of the constituent layers of the absorber can be varied in response to an applied electrical or optical control signal, then it is possible to realize an active, or adaptive absorbing structure. One approach to achieve a variable impedance is to incorporate pin diodes into the absorber structure. A. Tennant et al. [21] described an active absorber using pin diodes to provide resistive tuning of the absorber reflectivity characteristics. Zhu et al. [22] demonstrated a switchable absorber with diodes connecting to the structure units, where the absorbers can be switched between the status of total reflection and total absorption for incidence waves by turning the diodes. Zhao et al [23] designed a polarization-insensitive tunable metamaterial absorber with varactor diodes, and found that the absorption frequency can be controlled by regulating the reverse bias voltage on the varactor diode. Another approach to achieving a variable impedance is to use the ferrite slabs or vanadium dioxides (VO₂). Yang et al. [24] introduced a broadband metamaterial absorber made of ferrite slabs and copper wire, in which the absorption band can be shifted linearly by adjusting the magnetic bias. Wen et al. [25] presented a switchable metamaterial absorber by VO₂ thin film between the electronic split ring resonator and the dielectric layer, and found that can be tuned thermally, electrically and optically.

However, tunable metamaterial absorbers reported previously are mainly at microwave frequencies. In this paper, a terahertz metamaterial absorber have been designed by using electric controlled diodes, results found that the absorption can be obtained by regulating the voltage-controlled diode resistors. In our design, it is very convenient to allow a control voltage to be applied to the diodes through the metal lines without incorporated an extra direct current bias line to each unit, which will reduce the machining difficulty greatly in the terahertz region.

2. Results and Discussions

The meander-line absorber is actually a sandwich structure concluding three parts: two metal meander-lines, a dielectric substrate, and a metal film with the thickness h₁=0.01mm, h₂=0.04mm and h₃=0.01mm, respectively. The front view of the unit cell is illustrated in Fig. 1, the metal lines consist of two identical meander-lines with the opposite orientation, and are connected by an active Schottky diode, the distance between them is d=0.025mm. For the metal meander-lines, it is very convenient to allow a voltage to be applied to the diodes without incorporated an extra bias line to each unit. Metallic patterns is the copper whose electric conductivity is 5.8×10⁷S/m, the dielectric substrate is polyimide whose relative dielectric constant is ε_r=3.9 and loss angle tangent tgδ=0.002. Other parameter settings for the calculation are: a=0.25, a₁=0.0125, a₂=0.175, b₁=0.0875, b2=0.025, g=0.025, all the unit of parameters is mm.

Figure 1. Front view of the meander-line absorber

To demonstrate the microwave absorption properties of our design, a full wave electromagnetic simulation has been performed based on the standard finite-difference time domain (FDTD) method by CST Microwave Studio software. For a plane wave normal incidence with the electric field parallel to the y-axis, no transmission has been examined, as it is blocked off by the metal film. Frequency characteristic of the absorption can be calculated using A(ω)=1-|S₁₁|². Fig. 2(a) shows the reflectivity magnitude S₁₁ over the frequency range of 0.2–0.6 THz, where the dotted, dot-dashed, dashed, and solid lines mark values R=200, 350, 800 and 1500 Ω, respectively. The corresponding absorption is given in Fig. 2(b). For R=200 Ω, the structure has a small refection and the smallest reflection magnitude is 0.25 at 0.45 THz. As R increases to 350 Ω, the reflectivity level reduces to 0.05 at 0.42 THz. Increasing resistors from 800 to 1500 Ω makes reflection stronger with the central frequency has little change. In Fig.2 (b), the maximum absorption values at 0.42THz are 1, 0.89 and 0.67 for R=350, 500 and 1500 Ω, respectively, and the relative absorption bandwidth over 90% reaches to 15% for R=350 Ω.

Figure 2. Simulated reflectance and absorption under different resistors

To clarify the mechanism underlying operation of the tunable absorber, the transmission-line equivalent circuit of the structure is shown in Fig. 3 [26, 27]. In this model, the metal lines are equivalent to be inductance L, the dielectric gap between metallic surfaces is equivalent to be capacitance C, ohmic losses can be taken into account by an additional resistor R_o, and the diode is modeled as a variable resistor R_s to represent the impedance of diode for varying bias voltage. Then, as the resistors changes, the whole impedance of the absorber can be varied in response to an applied electrical signal, the absorption of the basic unit will experience a high or low variation correspondingly. Furthermore, according to the equivalent circuit method, the resonant frequency ω_o is dependent on the effective capacitance C and inductance L, i.e., ω₀ ∝ (LC)^-1/2. Then, the absorption frequency has little change with varying bias voltage.

Figure 3. Transmission line equivalent circuit of the active absorber

On the other hand, to better understand the mechanism of the high absorption, the relative impedance z can be retrieved from the simulated S parameters [28, 29], where

(1)

Fig. 4 shows the real part and imagery part of the relative impedances, where the dotted, dot-dashed, dashed, and solid lines mark values R=200, 350, 800 and 1500 Ω, respectively. At the absorbance peak frequency of 0.42 THz, the real parts of the relative impedances are 0.63, 0.99, 0.99 and 0.73, and the imagery parts are 0.4, 0.09, -0.68 and -1.17 for R=200, 350, 800, and 1500Ω, respectively. It is clear that the calculated relative impedance is more close to 1 for R=350Ω, which means the absorber achieves near perfect impedance matched to the free space.

Figure 4. The real and imaginary parts of the relative wave impedances under different resistors

Fig. 5 shows the absorptions as a function of dielectric material for R=350Ω. The dot-dashed, solid and dashed lines represent ε_r=3, 3.9 and 5, respectively. As dielectric constant increases, the absorption peak shifts to the lower frequency with bandwidth decreasing. The effect of dielectric material on absorption frequencies can be explained from the equivalent circuit model. In fact, the resonant frequency ω₀ is inversely proportional to the effective capacitance C and inductance L, i.e., ω₀ ∝ (LC)^-1/2, and C is directly proportional to the dielectric constant ε_r of the dielectric material. As a result, the absorption frequency shifts to the lower frequency with increasing ε_r.

Figure 5. Absorption under different dielectric material

3. Conclusions

In conclusion, a tunable terahertz absorber based on voltage-controlled diodes is designed. The behavior of the active absorber can be described by the transmission-line equivalent circuit, in which, the reactance can be represented by a series combination of inductance and capacitance, and the diode is modeled as a variable resistor to represent the impedance of diode for varying bias voltages. By investing the real and imagery parts of the relative impedances under different resistors, it is found that the highest absorption is achieved when the relative impedance is more close to 1. When set the resistor to the largest absorption, the absorption frequency shifts to downward with increasing dielectric constant of dielectric material.

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China under grant Nos. 11174280, 60990323, 60990320, and 61107030, and China Postdoctoral Science Foundation.