Multiple-band terahertz metamaterial filter using coupling effect of U-type resonator and two same sizes of metallic split rings

This paper presents the multiple-band terahertz metamaterial filter consisting of an U-type resonator surrounded by two same sizes of metallic split rings. Four resonance dips with near zero transmission rates are obtained, of which three dips have narrow line-widths, about one-quarter of the other dip. The physical mechanism of the four resonance dips can be attributed to near field coupling between the three sub-resonators. Influence of structure parameters on the performance of the device is discussed. It is revealed that the frequencies of the four resonance dips can be effectively controlled by adjusting the dimensions of the two surrounded rings, while the number of resonance dips show the significant dependence on the parameters of the U-type resonator. These results indicate that the proposed structure can provide more ideas for multiple-band or broadband metamaterial resonance effects in absorption, filtering, imaging and other related applications.


Introduction
Metamaterials, usually referred to artificial composites, have attracted extensive interest from researchers because their peculiar electromagnetic properties that natural materials cannot directly obtain. Many types of structures have been proposed to verify the concept of metamaterials, such as nanorods [1,2], cut-wire pairs [3,4], fishnets [5], split ring resonators [6][7][8] and other stereo-structures [9,10]. These metamaterial structures are typically composed of metallic frequency selective surfaces arranged in periodic patterns placed on a very thin dielectric substrate. These structures have the ability to control their effective electromagnetic parameters and are often capable of scattering light, microwaves, and radio waves in a specific manner. In recent years, many applications based on the resonance effect of metamaterials have attracted a lot of interest, such as antennas [11,12], superlens [13], cloaking [14][15][16], absorbers [17][18][19], imaging [20,21], filters [22,23] and so on.
So far, many metamaterial structures have been proposed for exhibiting different properties. For example, Hu et al achieved the single channel resonance device with an absorption rate of 70% using composite structure of electric split ring and cut-wire [24]. Zhao et al proposed a dual-channel resonator using the structure of two split rings and nanorod, which can manipulate group delay and spectral configuration using modes of darkbright-bright and bright-dark-dark [25]. A dual-band resonator based on electromagnetically induced transparency effect was proposed by Pan et al [26], which is composed of a circular split ring and a square split ring, and can realize sensing with a refractive index sensitivity of 96.2 GHz/RIU. Unfortunately, these efforts have common shortcomings that it is difficult to further increase the number of frequency bands, which greatly hampers their practical applications.
Compared with single-band resonance devices, multiple-band resonators offer more selectivity for absorbers, filters and other related devices due to their ability to achieve multiple-band transmission at a fixed frequency. An effective way to expand the amounts of channels is to increase the number of resonators in the unit structure. For example, unit structure composed of four square metallic rings was designed to obtain quadband resonance response, and the number of channels can be further increased by using more metallic rings [19]. Metamaterial structure consisted of three different sizes of metallic resonators provides the ability to achieve triple-band resonance effect [27]. Multiple-band resonance device constructed by a double-channel Mie resonator in a unique configuration was demonstrated [28]. Although these metamaterial designs have been proven to produce multiple-band resonances, these efforts have the common characteristics that each metallic resonator or sub-unit corresponds to only one resonant mode and the coupling effect of the sub-units is neglected (almost independent of each other). In particular, there are very few papers on increasing the number of resonant bands using the coupling effects of sub-units or metallic resonators.
Herein, we demonstrate a four-band terahertz meta-device that utilizes the coupling effect of three sub-units of metamaterial formed by two same sizes of split rings embedded by an U-type resonator. Four resonance dips are obtained, of which one resonance dip has broad line-widths, about 4 times of the other three narrow-band dips. The formation of these bands can be attributed to the electric field coupling effect between different parts of the metamaterial. The number of the resonance bands are tunable by the coupling distances and the gap sizes. Meanwhile, the bandwidth of the four resonance dips and the transparent windows can also be tunable by varying the geometrical dimensions of the three sub-units. These results show that we can use a coupling effect between sub-units to achieve multiple-band resonance effect, thus providing more ideas for absorption, filtering, imaging, and other related applications for multiple-band resonance.

Materials and method
Figures 1(a) and (b) respectively show the cross section and top view of the four-band resonator, which is consisted of an U-type resonator surrounded by two same sizes of metallic split rings placed on an appropriate thickness of dielectric layer. The lengths of the two same sizes of split rings and the U-type resonator are respectively a=60 μm, b=40 μm, and the wire width of them is fixed at l 1 =5 μm. The width of their gaps are set to l 2 =5 μm and c=30 μm. The thickness of the dielectric layer (sio 2 ) is set to 200 μm with a refractive index of 1.5, and the thickness of the Au is 0.4 μm with a frequency independent conductivity of σ=4.09×10 7 Sm −1 . The repeat period is P=P x =P y =100 μm. The calculation results are carried out using finite-difference timedomain method (FDTD Solutions, Canada), where the period structures are incident perpendicular by a normally incident plane wave with the electric field polarized along the x direction. The periodic boundary conditions are in both directions of X and Y directions and perfectly matched layers are applied along the Z direction. Due to the shortage of experimental instruments, we are very sorry that further experimental verification is hard to implement. However, metallic gold could be deposited on the selected substrate by thermal spin coating, and then the metallic structure of the top layer could be processed by photolithography, so that the structure designed in the text may be fabricated.

Results and discussion
Figure 2(a) shows the transmission spectra of the proposed structure, it can be seen that there are three obvious dips with narrow bandwidths (of less than 0.13 THz) and a wide dip of the 0.5 THz bandwidth, the resonance bandwidth was defined as the full width at half maximum (FWHM). The four resonance dips are labeled as resonance modes D 1 , D 2 , D 3 and D 4 , and the resonance frequencies of them are 1.00, 1.20, 2.29 and 2.65 THz, respectively. The transmission amplitudes of these four resonance dips are very low (close to the zero). The reasons for these resonance dips are the interaction of different parts of metamaterial. The electric field distribution shown in figure 3 below reveals their physical mechanism. According to the definition of Q factor [29], the bandwidth of the full width at half maximum (FWHM) and the corresponding frequency point f 0 are taken, and the Q factor is calculated by the formula Q=f 0 /√2 FWHM because the figure 2(a) is the transmission, not the transmittance, and the Q factor of the three narrowband resonance dips (D 1 , D 2 , D 4 ) are 25, 15 and 42, respectively. These results show that the proposed structure has strong frequency selectivity in some related applications due to three narrow bands and the broad dip.
To better analyze the spectral characteristics of the proposed resonator, the transmission spectra of the reduced structure consisted of two same sizes of split rings, and the U-type resonator are respectively given, as the red and blue curves of figure 2(b) shown. What can be observed in the red curve are two narrow-band dips and one broad resonance peak, the bandwidth of the two narrow bands (amplitude of the resonance close to zero) is approximately 0.19 and 0.08 THz, while the bandwidth of the broad resonance peak with the transmission intensity of more than 90% even reaches 1.5 THz or more. The transmission spectrum (blue curve) of the reduced structure formed by U-type resonator is represented by a resonance dip with a bandwidth of 0.5 THz. By comparing these transmission curves, we found that the resonance dips of two split rings and the U-type ring correspond to the D 2 , D 4 and D 3 of the proposed structure, respectively, so it can be inferred that two split rings and the U-type ring are not simply superimposed.  In order to elucidate the physical mechanisms of these resonance dips and the origin of this difference, the calculated electric field (|E| and E z ) distributions corresponding to the four lowest transmission minimum (D 1 , D 2 , D 3 , and D 4 ) are given, as shown in figures 3 and 4. At 1.00 THz, the incident electromagnetic radiation is mainly localized in the upper and lower arms of two split rings, especially at the two gaps, and the coupling of electric field at the upper gap is stronger than that at the lower gap, thereby explaining the cause of D 1 , seeing figures 3(a) and 4(a). It can be seen from figure 2(a) that the resonance dips D 1 and D 2 are very similar, but can be observed from figures 3(b) and 4(b) that the D 2 is mainly due to the coupling between the left and right arms of the U-type ring and two split rings. Some incident terahertz radiation is trapped at the lower gap of two split rings. The electric field diagram of D 3 is shown in figures 3(c) and 4(c), a little electric field is localized at the left and right arms of two split rings, however, the coupling between the two gaps plays a major role in the formation of D 3 , as we see that the electric field is mainly concentrated at the gaps of the split rings. By analyzing the electric field distribution of D 4 , at f=2.65 THz the electromagnetic radiation is localized at the four corners of two split rings and the U-type ring, while a strong coupling effect is also observed at the two gaps. Coupling is also observed between the bottom of the U-type ring and the split rings. The formation of D 4 is due to the interaction of electric fields at these sections of the proposed structure, as shown in the figures 3(d) and 4(d).
Through the analysis of figures 3 and 4, we found that these resonance dips are mainly formed by the coupling effect between the different parts of two split rings and the U-type ring. Firstly, the influence of the size of two split rings on the performance of the proposed structure is discussed. Figure 5(a) shows the transmission when the length a of two split rings has been changed from 50 to 70 μm (keeping the U-type ring constant). With the increase of the length a, the coupling intensity between the split rings and the U-type ring gradually decreases, it can be seen that each resonance dip has a significant shift in the corresponding frequency, and there are more obvious changes in the resonance dips (D 1 and D 4 ). As the length of a increases, the transmission intensity of the two dips gradually increases, and the bandwidth of them decreases, by calculating, the Q factor of the D 1 increase to 65, while the Q factor of D 4 even increased to more than three times of the proposed structure, and its value is 147. When the length of a is reduced to 55 μm, the frequency shift phenomenon can also be observed, as shown by the blue curve in figure 5(a). Specifically, the resonant dips D 3 and D 4 are gradually merged into a wide band with the bandwidth of 0.4 THz.
Different from the figure 5(a), when we reduce the width b of the U-type ring from 40 μm to 25 μm, as shown in the figure 5(b), as the width b decreases, the transmission spectrum shows a significant blue shift. When the width b is reduced to 35 μm, the bandwidths of D 1 and D 4 are narrowed and the transmission intensities are increased, while the bandwidths of the D 2 and D 3 are obviously increased. The resonance dips (D 1 and D 4 ) become very weak, when the width b of the U-type ring is 30 μm, see the pink curve in the figure 5(b). Four-band resonance can be converted to dual-band resonance by using a U-type ring with a width of 25 μm. These results indicate that adjusting the size of the proposed can change the number of multiple bands and the bandwidth of the broadband, which is more potentials in related fields such as multiple-channel resonance devices As can be seen from figure 3, the coupling effect of the two gaps in the two split ring plays an indispensable role in the process of the formation of the four band resonator. In order to figure out the impact of the gaps on the performance of the transmission spectrum, two cases of just adjusting the number and the size of the gaps are discussed, as shown in the figure 6. First, when we close the upper gap, there is a significant red shift in the spectrum, and it can be observed that the bandwidth of the resonance dip D 3 is increased to 0.6 THz, which can be seen the pink curve in the figure 6(a). However, when we close the lower gap, the resulting transmission spectrum is very different from the proposed structure. It can be seen that there are five bands in one and half terahertz, seeing the red curve in the figure 6(a). When the closed-ring (no gaps) and the U-type ring are combined, the obtained transmission spectrum is shown in the black curve of figure 6(a), resonance dips D 2 and D 3 merge into a new broadband with a bandwidth of 1 THz.
The odd properties of metamaterials stem from their precise geometry and size, therefore changing the geometry of the proposed structure will inevitably lead to changes in the transmission spectrum, however, this change is hard to predict in advance. Therefore, it is easier to adjust the performance of the transmission spectrum by changing the size of the gaps, as shown in figure 6(b), the coupling effect between the gaps becomes weak due to the increase of the width l 2 of the gaps, when we enlarge the width l 2 of the gaps from 5 μm to 10 μm, by comparing the spectrum of the proposed structure, the whole spectrum appear an obvious blue phenomenon and it is worth noting that the bandwidth of D 1 increases and the bandwidths of D 2 and D 3 decreases, while the bandwidth of D 4 does not change significantly, seeing the pink curve in the figure 6(b).
A similar phenomenon can also be observed in the black and red curves of figure 6(b), but the differences are that when we increase the width l 2 of two gaps to 20 μm, the resonance dip D 4 disappears, which indicate that the transition of the four-band to three-band can be regulated by adjusting the width l 2 of the gaps. In figure 6(b), an interesting phenomenon can be found that the bandwidth of the peak between the D 2 and D 3 gradually becomes large with the increase of the width of two gaps, when the width l 1 =30 μm, as the black curve of the figure 6(b) shown, it can be seen that there is a transparent peak with a transmittance of approximately 95% and a bandwidth of approximately 1.2 THz. These results show that the proposed structure can not only achieve ultralow transmission four-band resonance, but also achieve the transparent peak with ultra-high transmission and ultra-bandwidth, which will provide more possibilities for multiple-channel and broad band resonators in related fields.
It should be noted that the so-called near-field coupling usually has two types: the near-field electric field coupling and near-field magnetic field coupling. This manuscript mainly uses the near-field electric field coupling to analyze the observed resonance phenomenon. Although this method can explain most of the observed phenomena, it is not perfect and clear. The authors hope to use the near-field magnetic field coupling or the combining ways of the near-field electric field coupling and near-field magnetic field coupling to explain the observed resonance performance more systematically and clearly. Because we don't fully grasp the method of the near-field magnetic field coupling, we also look forward to the following readers or more professional researchers to give the better analysis.

Conclusion
A four-band tunable terahertz metamaterial resonator is proposed herein, which is placed on a dielectric substrate of SiO 2 and consists of two metallic split rings and an U-shaped resonator. These four resonant dips are three narrow bands and one broadband with the transmission intensities are very close to zero, respectively, and their formation mechanism can be attributed to the electric field coupling effect between different parts of the sub-resonators. In particular, by adjusting the size of the two split rings and the U-shaped resonator, the resonant frequencies of the dips and the transition from the four-band to the dual-band resonance can be effectively tunable, while the three-band and ultra-bandwidth transparency peak can be obtained by changing the number and size of the gaps. These results indicate that the proposed structure can provide more ideas for multiple-band or broadband metamaterial resonance devices in absorption, filtering, imaging, and other related applications.