1. Introduction

Metamaterials provide a flexible and effective way to manipulate electromagnetic waves and to develop novel photonic devices. However, narrow bandwidth resulting from their resonant nature has raised doubts concerning their usefulness. To solve the problem, various methods have been suggested to make broadband metamaterial devices, including the integration of multiple resonances [1–5], of multi-order diffractions [6–8], of multiple anisotropic metamaterial waveguides [9-10], frequency dispersion engineering [11-12], as well as two-dimensional material plasmonic engineering [13-14]. Recently, sectional asymmetric structure has been proposed to broaden metamaterial devices’ bandwidth [15]. This structure is equivalent to the parallel connection of four RLC resonant circuits, thus achieving the superposition of four LC resonances. Its advantages include small unit-cell, ultra-thinness, and insensitivity of broadband absorption to polarization and incident angle. However, compared to the traditional mono-ring resonance structure, it can only broaden the bandwidth to about 2.8 times [15].

To further broaden the bandwidth, we studied the structure’s high-order resonances and found that the position of the resonances could be tuned by changing the width of the sectional asymmetric brackets. This means that the frequency position of high-order resonances can be controlled by changing the size of the new structure, so that the high-order resonances and the low-order resonances are close to overlap, then realizing a quasi-continuous absorption band. Therefore, it is possible to draw the metamaterial structure’s high-order resonances closer to the structure’s low-order resonances, thus further broaden the absorption bandwidth. This method makes a simple modification to the structure without increasing fabrication difficulty. For verification, we simulated the positional tunability of the sectional asymmetric metamaterial, and fabricated a structure using semiconductor fabrication technology. After that, we built a fiber coupled reflective terahertz time-domain spectroscopy system to measure the spectra of the structure with He-Ne laser assisted alignment. Results show that the new method matches our expectations and can further broaden bandwidth to about 7 times. We believe that this method can be used in the designing of THz broadband devices, and that the said devices can have great application in terahertz imaging and communication.

2. Principle and simulation

Metamaterials’ unit size is much smaller than their wavelength, therefore they can be regarded as an effective artificial material characterized by a complex electric permittivity ε(ω) and a complex magnetic permeability µ(ω). Their complicated structure making it difficult to use the analytical calculation method, their reflectance and transmission are usually acquired by simulating the frequency dependent S parameters, i.e., S₁₁ and S₂₁ [7]. Then, the absorptivity A of a given metamaterial is represented as:

Here, R = |S₁₁|² and T = |S₂₁|² stand for reflectance and transmission respectively. The structural design and the tunability of the metamaterial are simulated by the electromagnetic simulation software CST 2014 (Computer Simulation Technology 2014), which can be used to calculate the S parameters.

Figure 1(a) shows the unit-cell structure of the metamaterial. It includes three layers: the top layer is the resonators; the middle layer is the SiO₂ dielectric film; the bottom layer is the Au ground. The resonators are composed of four sectional Au brackets: 1, 2, 3, and 4. They are based on four square rings and the outer lengths (one side) of the square rings are L₁ = 27 µm, L₂ = 26 µm, L₃ = 25 µm, and L₄ = 24 µm, respectively. The gaps between the brackets are g = 4 µm and the period of the unit cells is P = 30 µm. Because the terahertz cannot penetrate the Au ground, the transmission T is zero. Therefore, the absorptivity of the metamaterial is calculated by A = 1-R.

 

Fig. 1 (a) 3D structure of the metamaterials’ unit-cell; and the simulated absorption spectra: (b) Au bracket resonators’ width w = 4.5µm; (c) w = 6µm; (d) w = 8µm.

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According to the simulation and the calculation of Eq. (1), not only the metamaterial structure’s low-order resonances can form broadband absorption bands, the high-order resonances can form broadband absorption bands as well. In addition, the distance between the low-order resonances absorption and the high-order resonances absorption can be tuned by changing the Au bracket resonators’ width w.

Figure 1 shows an interesting phenomenon: Fig. 1(b) is the absorption spectrum when Au brackets’ width w = 4.5 µm. Figure 1(c) shows the corresponding absorption spectrum when w = 6 µm. It can be seen that as the width w increases, the low-order resonances absorption peaks and the high-order resonances absorption peaks get closer to each other. With the further increase of the brackets’ width w, the two can be combined to form a quasi-continuous ultra-broad absorption area. Figure 1(d) shows the combined broadband absorption spectrum when the brackets’ width w = 8µm. Compared with the single bracket metamaterial structure, the bandwidth is further broadened to about 7 times. The simulated results provide us with a simple method to tune metamaterial’s resonances and further broaden the bandwidth of devices.

To further discuss the physical mechanism of bandwidth broadening, we simulate the resonant current distribution at 4.89THz and 7.42THz when the bracket resonators’ width w = 4.5µm. As can be seen from Fig. 1(b), 4.89THz and 7.42THz are the frequencies corresponding to the first absorption peak of the low-order resonances and the first absorption peak of the high-order resonances, respectively. Moreover, it can be seen from Fig. 2 that these two absorption peaks are generated by bracket1’s resonances, but the distributions of resonant current generated by bracket1’s low-order and high-order resonances are quite different. With the increase of w, the brackets’ structure changes, resulting in the absorption peaks of low-order and high-order resonances close to each other and overlap, so as to form the quasi-continuous broadband absorption region. It should be noted that the parameter ‘w’ can tune the positions of the lower-order and high-order resonances, but the relative positions of the four lower-order (or high-order) resonance peaks are almost unchanged. The reasons can be summarized as follows: 1) no matter the high-order resonances and low-order resonances, according to the design principle of the metamaterials, four asymmetric brackets will produce four corresponding absorption peaks close to each other, and the relative positions of the absorption peaks are mainly determined by the outer lengths of brackets [15]; 2) because the outer lengths L₁, L₂, L₃, and L₄ of brackets are unchanged, the relative positions of the four low-order (high-order) resonance peaks remain almost unchanged.

 

Fig. 2 The resonant current distribution at 4.89THz and 7.42THz when the Au bracket resonators’ width w = 4.5µm.

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3. Fabrication and measurement

The metamaterial described above mainly works in the 4 THz to 9 THz frequency range. Outside this frequency range, the proposed structure can also be applied to other frequency ranges. Considering that most of the terahertz time-domain spectroscopy (THz-TDS) systems’ measurement range is from 0.1 THz to 2 THz, we have designed and fabricated a sectional asymmetric metamaterial absorber whose working frequency range is below 2THz. Figure 3(a) shows the top-view of one unit-cell of the designed structure. Its top layer is four sectional asymmetric Au brackets (0.1 µm thick); the middle layer is the SiO₂ dielectric film (4 µm thick); the bottom layer is the Au ground (0.1µm thick). The Au brackets are based on four square rings whose outer lengths (one side) are L₁ = 140 µm, L₂ = 136 µm, L₃ = 132 µm, and L₄ = 128 µm, respectively. The gaps between the brackets are g = 10 µm, while the Au brackets’ width w = 46 µm and the period of the unit cells is P = 160 µm.

 

Fig. 3 (a) A unit cell of the designed structure; (b) fabrication process of the metamaterial; (c) a photo of the fabricated sample.

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Figure 3(b) presents the fabrication process, starting with a polished silicon wafer of 400µm thickness. The detailed steps are as follows: (I) Sputter 10 nm chromium film and 100 nm Au film on the surface of silicon by high vacuum magnetron sputtering coating machine; (II) Deposit 4 µm SiO₂ dielectric film on the Au film layer with plasma chemical vapor deposition (PECVD) method; (III) Sputter Cr/Au films of 10nm/100nm thickness on the surface of dielectric film after the lithography, then pattern to form the sectional asymmetric structures by the lift-off method. Finally, clean the wafer using deionized water and dry by nitrogen. Figure 3(c) shows a photo of the fabricated metamaterial sample.

Next, a fiber coupled reflective terahertz time-domain spectroscopy system is set up to measure the spectrum of the structure with He-Ne laser assisted alignment. Figure 4(a) is the schematic of the measurement system and Fig. 4(b) is the corresponding photograph of the system. The THz transmission antenna Tx emits radiation, which is then reflected to the sample by an off-axis parabolic mirror, and finally reflected to the THz receiving antenna Rx by a second off-axis parabolic mirror. In order to measure absorption, there are two steps to follow. The first is to measure an object with near 100% reflectivity (Gold plane reflector) as the reference spectrum R_ref. The second is to measure the metamaterial sample as the signal spectrum R_sam. The absorption of the sample can be calculated by

 

Fig. 4 (a) Schematic of the reflective THz-TDS measurement system; (b) corresponding photograph of the system.

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It should be noted that since we need to measure two target objects, their spatial position (horizontal position, vertical position, as well as angle) should be kept the same to ensure that the radiation energy received by the THz antenna does not deviate from the focal point after we change the measured objects. However, we cannot observe whether or not deviation has occurred because terahertz wave is invisible and this could lead to serious errors each time we change measured objects after measurement. To solve this problem, we have developed a He-Ne laser assisted alignment module. As is shown in Fig. 4(a), we drill a small hole in the center of the first off-axis parabolic mirror; then, the collimated He-Ne laser passes through the hole and is reflected by the sample and then by the second off-axis parabolic mirror to the THz receiving antenna. Because the He-Ne laser is visible, we can observe whether the reflected He-Ne laser irradiates the center of the terahertz antenna Rx when we change the sample to measure the spectrum each time. This ensures that the terahertz radiation received by the antenna will not deviate from the focal point.

Figure 5 shows the simulation and the measured results. It can be seen that the absorptivity of the fabricated metamaterial is above 50% at the broadband frequency range of 0.97 THz to 1.25 THz. Compared with the measured results, the simulation results shown in Fig. 5(b) provide broader bandwidth. There are two main reasons for this: one, the error between the reflective measurement and theoretical simulation; and two, the dimensional inaccuracy of the metamaterial structure made during fabrication. The aforementioned discrepancy notwithstanding, the simulation results agree with the experiment results, especially in the broadband characteristics. This proves the validity of the proposed metamaterial and method.

 

Fig. 5 The simulation and measured results: (a) photograph of the fabricated structure; (b) the simulation results; (c) the measured results.

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4. Conclusion

This paper presents a simple method to broaden the working bandwidth of the sectional asymmetric metamaterials. Taking advantage of the tunability of the higher order resonances, a quasi-continuous and ultra-wide absorption band is realized by drawing the resonant frequency bands closer to each other. This method is simple and easy, with no increase in fabrication difficulty. In order to verify this method, we have fabricated a sectional asymmetric metamaterial absorbing structure which works in the 0.9-1.3THz frequency range. Then, a fiber coupled reflective terahertz time-domain spectroscopy system based on He-Ne laser alignment is built to measure the spectra of the structure. The simulation results agree with the measured results. We believe that this method can make broadband metamaterial designing more flexible, and may bring more novel applications in terahertz imaging and communication.