Research Article  Open Access
Si Li, Atef Z. Elsherbeni, Wenhua Yu, Wenxing Li, Yunlong Mao, "A Novel Tunable TripleBand LeftHanded Metamaterial", International Journal of Antennas and Propagation, vol. 2017, Article ID 7583736, 10 pages, 2017. https://doi.org/10.1155/2017/7583736
A Novel Tunable TripleBand LeftHanded Metamaterial
Abstract
A novel tunable tripleband lefthanded metamaterial (LHM) composed of a singleloop resonator (SLR) and a variable capacitorloaded short wire pair (CLSWP) printed on both sides of a substrate is presented in this paper. The CLSWPbased metamaterial (MTM) is a novel singlesided LHM. It is theoretically analyzed capable of extracting tunable negative permeability and a wideband negative permittivity. We ran simulations for the CLSWPbased MTM, the SLRbased MTM, and the proposed LHM. Together with the measured results, it is identified that this novel LHM exhibits a tunable tripleband lefthanded (LH) property. With the increase of the loaded capacitance, one LH band is relatively stable, while the other two are moving towards lower frequencies with their bandwidth getting wider and narrower, respectively. The surface current density distributions indicate that the first LH band is mainly decided by the SLR, one of the rest 2 LH bands is mainly decided by the CLSWP, and the other one is decided by the SLR and CLSWP together.
1. Introduction
Lefthanded metamaterials (LHMs) are a kind of engineering material which have negative permittivity and permeability in the same frequency ranges hence exhibiting special properties such as negative refractive index, the reversal of Snell’s Law, the Doppler effect, and the VavilovCerenkov effect and backward waves [1]. Because of the intrinsic and narrow resonant frequency band of most LHMs, however, it cannot be used in some wide operating frequency areas [2, 3].
Some tunable LHMs have been proposed by using various additional materials or structures, such as the ferrites [4–9], liquid crystals [10–12], varactors [13–16], and tunable structures [17–19]. Ferrites or liquid crystals can be easily added to conventional LHMs to achieve tunability. For instance, in [8], a ferrite rod is simply added to a LHM composed of split ring resonators (SRRs) and metallic wires, and in [10], the liquid crystal is simply inserted between two omegatype resonators. Such kinds of LHMs are easy to design but have disadvantages such that ferritebased tunability requires big magnetic bias and liquid crystalbased tunability has a finite tunable range [2]. Tunable structures can be implemented with the methods such as the displacement between layers [19] and the change of the thickness of the substrate [18]. This kind of tunability is not as convenient or flexible as the previous ones but is much easier to be implemented in practice. Varactorloaded tunability has been used in microwave engineering applications since they can be easily integrated into microwave circuits. However, the insertion requires a proper gap region, which increases the design difficulties.
There is also another increasing requirement of multiband property for LHMs in microwave applications. Multiband LHMs could be implemented with simply arranging multiple LHM units together [20, 21] or with particular elements that contain multiple resonances [22–26]. Such kinds of LHMs are well designed and usually have complex metallic structures for the purpose of making the μnegative and the ɛnegative frequency ranges overlapped.
However, tunable multiband LHMs are merely reported. In this paper, we present a novel tunable tripleband LHM. This LHM is a combination of a variable capacitorloaded short wire pair (CLSWP) and circular singleloop resonator (SLR) structures printed on both sides of a substrate. The CLSWPbased metamaterial (MTM) is singlesided, and it is a novel kind LHM. We theoretically analyzed the CLSWPbased MTM. The SLRbased MTM [25, 27, 28] is also singlesided and is capable of extracting dualband negative permeability. In our design, we print the circular SLR on the other side of the CLSWPbased MTM to build a novel LHM. Additionally, we also studied the connections among the CLSWP, the SLR, and the novel tunable tripleband LHMs with simulations and the help of “S parameter retrieval” method [29].
2. Model and Theoretical Analysis
The geometry of the SLRbased MTM and the CLSWPbased MTM is shown in Figures 1(a) and 1(b), respectively, where the yellow lines represent metallic wires with a thickness of 0.018 mm. The incidence is as illustrated, where k is the incident direction and E and H refer to the directions of the electric field and magnetic field, respectively. Both the structures are printed on a 15 mm × 15 mm × 0.8 mm Rogers 6006 substrate whose relative permittivity is 6.15. Here, a = 15 mm, b = 15 mm, R1 = 6.6 mm, w = 0.45 mm, g = 0.25 mm, ws = 4 mm, and gs = 1 mm.
(a)
(b)
The SLRbased MTM have previously been discussed and identified capable of extracting multiband negative permeability [25, 27, 28]. In this paper, we designed a circular SLR for the purpose of restraining electric coupling in the design of the tunable tripleband LHM.
Since the CLSWPbased MTM is a novel structure, it is important to explain why it is capable of extracting tunable negative permeability and a wideband negative permeability. Depending on the theoretical analysis of the SRRs proposed in [30, 31], magnetic resonance is motivated by the electromotive force around the circumference of the split rings. Considering an infinite array of such SRRs arranged in three orthogonal directions with a spatial period of d and an incident magnetic field polarized along the y direction, that is, perpendicular to the SRRs, there would be an electromotive force and an induced current I along the rings, satisfying the following: where H_{0} is the external magnetic field, R, L, and C are the parasitic resistance, inductance, and capacitance of each ring, respectively, and FL is the mutual inductance between different rings. With , and , the current I is given as follows:
Based on the magnetic moment per unit volume, and , where B is the corresponding external magnetic flux; then we can obtain the final effective permeability as follows:
From the analysis above, it is obvious that the effective permeability is completely irrelevant to the shape of the magnetic resonators. The real part of can be negative with proper selections of F, R, L, and C, while the imaginary part will always be positive.
For the CLSWPbased MTM, the loaded capacitance reversed the current flux on both open ends in the middle. Then the external magnetic field will motive the magnetic resonance around the middle gap. For this given structure, “L” and “R” are relatively unchangeable, while “C” is mainly decided by the loaded capacitance and “F” may be affected by other electromagnetic interference as we will discuss in the following sections. Hence, with proper values of “C” or “F,” the CLSWPbased MTM is capable of extracting tunable negative permeability as we can draw from (3). If we have , , and , then the change of the real part of with F changing from 0.5 to 0.9 is displayed in Figure 2, where “Real ()” represents the real part of the effective permeability. As can be drawn from Figure 2, the increase of F not only increased the maximum absolute value of the real part of μ but also widened the μnegative bandwidth.
On the other hand, the connected short wires are serving as arrayed metallic wires; hence, they are capable of extracting negative permittivity, as analyzed in [32]. However, this connection also brings an electric resonance. Since the domain size is much smaller than the wavelength of the incidence, the external electric field across a unit can be approximated as U = E_{z}b = RI + (−jωL)I + I/(−jωC), where E_{z} is the external electric field per length. Then, the volume current density J_{v} in each unit can be homogenized as follows:
While in [31], Hence,
From (6), at the resonant frequency, the real part of the effective permittivity is 1. With the increase of the frequency, the real part of the effective permittivity is getting smaller and it may be negative at frequencies higher than the resonant frequency. Therefore, the effective permittivity of CLSWP is a gaming result of its plasma frequency and the electric resonance. It can be negative in a wide frequency band if the electric resonance is not strong enough.
3. Simulations and Analysis
Based on the foregoing analysis, we print the circular SLR structure on the other side of the CLSWPbased LHM, for the purpose of building a novel tunable tripleband LHM. In this section, we ran simulations for the CLSWPbased MTM, the circular SLRbased MTM, and the combined LHM, respectively, with fullwave simulator HFSS. The loaded capacitance are chosen ranging from 12 pF to 18 pF, as an example. The effective parameters are retrieved through the “S parameter retrieval” method.
3.1. CLSWPBased MTM
The simulated S parameters for the CLSWPbased MTM with the loaded capacitance ranging from 12 pF to 18 pF is displayed in Figure 3, where the solid lines represent S_{11} (dB), while the dashed lines represent S_{21} (dB). The corresponding retrieved effective parameters are exhibited in Figures 4(a)–4(d), where all the solid lines represent the real part while the dashed lines represent the imaginary part of the parameters. The same rule is applied in the following figures for effective parameters.
(a)
(b)
(c)
(d)
In Figure 3, the resonant frequency is shifting from 2.456 GHz to 1.976 GHz, with the loaded capacitance ranging from 12 pF to 18 pF. However, the transmission character is not good. In Figure 4(a), negative permittivity is achieved at frequencies lower than the plasma frequency [33] of the arrayed wires. With the change of the loaded capacitance, electric resonances can be observed; however, they are not strong enough to make the permittivity positive. In Figure 4(b), negative permeability is achieved, and it is tunable with the change of the loaded capacitance. Negative refractive index is also observed tunable with the change of the loaded capacitance, as illustrated in Figure 4(d). Hence, the CLSWPbased MTM exhibit a tunable lefthanded (LH) property.
3.2. SLRBased MTM
Figure 5(a) displays the simulated S parameter of the SLRbased MTM, and Figure 5(b) displays the real part of the corresponding retrieved effective parameters. In Figure 5(a), the solid black line represents S_{11}, while the dashed red line represents S_{21}. There are two transmission valleys and the corresponding minimum S_{21} are observed at 1.759 GHz and 2.235 GHz, respectively, which indicates that around these frequencies, the MTM may exhibit a singlenegative (SNG) property. Accordingly, in Figure 5(b), negative permeability can be observed from 1.743 GHz to 1.816 GHz and 2.208 GHz to 2.305 GHz, while the permittivity are all positive at these frequencies. The minimum value of permeability is observed at 1.759 GHz in the first SNG frequency range and is at 2.235 GHz in the second SNG frequency range. Therefore, this SLRbased MTM is a dualband μnegative MTM.
(a)
(b)
We also displayed the surface current density at these 2 resonant frequencies, f_{1} = 1.759 GHz and f_{2} = 2.235 GHz, respectively, in Figures 6(a) and 6(b). The results imply that f_{1} is related to the bottom gap, while f_{2} is related to the top gap.
(a)
(b)
3.3. Tunable TripleBand LHM
Finally, we come to the simulations for the combined novel tunable tripleband LHM. The simulated S parameters with the change of loaded capacitance are displayed in Figure 7, where the solid lines represent S_{11} and the dashed lines represent S_{21}.
In Figure 7, there are 3 passband (S_{11} < −10 dB). Despite the increase of the loaded capacitance, the first passband is almost unchanged and its resonant frequency is approximately 1.75 GHz. The second passband is moving towards lower frequencies, and its minimum S_{11} is getting larger and its bandwidth is getting narrower with the increase of the loaded capacitance. For the third passband, when the loaded capacitance is 12 pF and 13 pF, its resonant frequency is 2.407 GHz and 2.336 GHz, respectively. For other capacitance, its resonant frequency is approximately 2.3 GHz.
The retrieved effective parameters are shown in Figures 8(a)–8(d). In Figure 8(a), the real part of permittivity is negative at frequencies lower than 2.45 GHz. In Figure 8(b), negative permeability is observed tunable at 3 different frequency ranges. These corresponding μnegative frequency ranges at different loaded capacitance are also listed in Table 1 which provides us with a more direct vision of their tunability. The “1st μNG,” “2nd μNG,” and “3rd μNG” represent the μnegative frequency ranges, “BW” represent the bandwidth of the frequency range in the previous column in Table 1, and they are all measured with “GHz.” The first μnegative frequency range is relatively stable around 1.7 GHz, and its bandwidth is around 0.08 GHz. The second μnegative range is moving towards lower frequencies, and its bandwidth is getting narrower with the increase of the loaded capacitance. The third μnegative range is also moving towards lower frequencies with the increase of the loaded capacitance, but its bandwidth is getting wider until the loaded capacitance is larger than 16 pF. The refractive index show a corresponding tunable tendency, as illustrated in Figure 8(d).
(a)
(b)
(c)
(d)

For a better comparison to explore the contributions the CLSWP and the SLR made to the novel tunable tripleband LHM, we displayed the surface current density distributions at the 3 resonant frequencies: 1.745 GHz, 2.169 GHz, and 2.407 GHz when the loaded capacitance is 12 pF in Figures 9(a), 9(c), and 9(e), respectively, and 1.749 GHz, 2.03 GHz, and 2.306 GHz when the loaded capacitance is 15 pF in Figures 9(b), 9(d), and 9(f), respectively. The current distribution in Figures 9(a) and 9(b) are all almost focused on the bottom gap of the SLR, which are similar to that displayed in Figure 6(a); hence, the first LH band is mainly decided by the first magnetic resonance of the SLR. In Figure 9(c), surface currents are observed focused on the mid gap of the CLSWP, and the top gap of the SLR, while in Figure 9(e), they are mainly distributed on the mid gap of the CLSWP. Hence, when the loaded capacitance is 12 pF, the second LH band is decided by the CLSWP and the SLR together, while the third LH band is mainly decided by the CLSWP. In Figure 9(d), surface currents are observed almost all around the mid gap of the CLSWP, while in Figure 9(f), they are observed both around the gaps of CLSWP and the SLR. Hence, when the loaded capacitance is 15 pF, the second LH band is mainly decided by the CLSWP, while the third LH band is decided by the CLSWP and the SLR together. Therefore, we can now come to a conclusion that the CLSWPrelated LH band has wider tuning frequency ranges than the SLRrelated ones. Except for that, the existence of the magnetic resonances of the SLR enhanced the mutual coupling coefficient “F” of the CLSWP, and hence the LH performance of the CLSWPrelated LH band in the novel LHM is much better than that displayed in Figure 4.
(a)
(b)
(c)
(d)
(e)
(f)
Finally, we use the standard rectangular waveguide method to experimentally characterize the effective parameters of the fabricated metamaterial [34]. The measurement setup is displayed in Figure 10(a), where a standard BJ22 waveguide is available at 1.72 GHz to 2.61 GHz. A singlelayer sample consisting of 7 pieces of 3 × 1 units is used. The S parameters are measured using Agilent’s E8361C vector network analyzer. The loaded capacitance is 15 pF for simplicity, as an example. The retrieved effective parameters from the simulations and the measurements, tagged with “Sim.” and “Mea.,” respectively, are displayed in Figure 10(b) with the frequencies ranging from 1.72 GHz to 2.5 GHz.
(a)
(b)
In Figure 10(b), there are two frequency bands where the proposed sample exhibits doublenegative properties. Compared to the simulated results, it is figured out that they correspond to the second and the third LH bands that are illustrated in Figure 8 while a little shifted to lower frequencies. The first LH band is not observed, as it is beyond the operating frequencies of the waveguide.
4. Conclusion
In this paper, we present a novel tunable tripleband LHM. This LHM is composed of a pair of short wires connected through a variable capacitor printed on one side of the substrate and a circular singleloop resonator printed on the other side of the substrate. The CLSWPbased MTM have been theoretically analyzed. Simulations are operated with HFSS, for the CLSWPbased MTM, the SLRbased MTM, and their combined novel LHM, respectively. Together with the measured results, the novel LHM is identified to have 3 tunable LH bands. It is also pointed out that the first LH band is mainly decided by the first magnetic resonance of SLR, and one of the rest two LH bands is mainly decided by the CLSWP, and the other one is decided by the SLR and the CLSWP together.
Conflicts of Interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This paper was supported by National Defense “973” Basic Research Development Program of China (no. 6131380101), by preresearch fund of the 12th FiveYear Plan (nos. 4010403020102 and 4010103020103), and the Fundamental Research Funds for the Central Universities (nos. HEUCFD1433 and HEUCF1508).
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Copyright © 2017 Si Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.