J. Cent. South Univ. (2020) 27: 1235-1246

DOI: https://doi.org/10.1007/s11771-020-4363-5

Tunable left-hand characteristics in multi-nested square-split-ring enabled metamaterials

ABDULKARIM Yadgar. I.^{1, 2}, DENG Lian-wen(邓联文)¹, YANG Jun-liang(阳军亮)¹,

COLAK Sule³, KARAASLAN Muharrem⁴, HUANG Sheng-xiang(黄生祥)¹,HE Long-hui(贺龙辉)¹, LUO Heng(罗衡)¹

1. School of Physics and Electronics, Central South University, Changsha 410083, China;

2. Physics Department, College of Science, University of Sulaimani, Sulaymaniyah 46001, Iraq;

3. Department of Electrical and Electronics Engineering, Adana Alparslan Turkes University,Adana 01140, Turkey;

4. Department of Electrical and Electronics Engineering, Iskenderun Technical University,Hatay 31200, Turkey

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: Left-hand materials have drawn increasing attention from many disciplines and found widespread application, especially in microwave engineering. A sandwiched metamaterial consisting of multi-nested square-split-ring resonators on the top side and a set of wires on the back side is proposed. Scattering parameters are retrieved by high-frequency structure simulator (HFSS) software based on the finite element method. Effects of square-split-ring number on the left-hand characteristics containing negative values of permittivity, permeability, and refractive index have been intensively investigated. Simulated results show that obvious resonant left-hand characteristics could be observed within 8-18 GHz, and the resonant frequency counts are inclined to be in direct proportion to the square-split-ring number over 8-18 GHz. Besides, the proposed sandwiched metamaterial with three square-split-ring resonators and three wires presents the widest frequency band of left-hand characteristics in a range of 8-18 GHz. Further, electromagnetic field distributions demonstrated that the induced magnetic dipole dominates the resonant absorption. The multi-peak resonance characteristics of square-split-ring resonant structure are considered to be a promising candidate for selective-frequency absorption or modulation toward microwave frequency band.

Key words: metamaterial; square-split-ring; negative permittivity; induced magnetic dipole

Cite this article as: ABDULKARIM Yadgar. I., DENG Lian-wen, YANG Jun-liang, COLAK Sule, KARAASLAN Muharrem, HUANG Sheng-xiang, HE Long-hui, LUO Heng. Tunable left-hand characteristics in multi-nested square-split-ring enabled metamaterials [J]. Journal of Central South University, 2020, 27(4): 1235-1246. DOI: https://doi.org/10.1007/s11771-020-4363-5.

1 Introduction

Electromagnetic metamaterials are artificially constructed and exhibit physical properties unattainable naturally, such as negative permittivity, negative permeability, and negative refractive index, which are defined as left-hand characteristics [1-11] As the first experimental demonstration of negative refraction in 1999 [12], split-ring resonator (SSR) on a printed circuit board by integrating arrays of copper strips and split-ring resonators was fabricated by AYDIN et al [13]. They also established a dual-split-ring resonator with two rings placed along with opposite directions, accompanied with simultaneously negative permeability and permittivity. From then onwards, metamaterials (MMT) have drawn enthusiasm from many disciplines and are found widespread applications towards sub-wavelength imaging super-lens [14-16], microwave absorbers [17-23], antennas [24], cloaks [25, 26], etc. Furthermore, researches on left hand metamaterials in the Tera Hertz (THz) frequencies [27-31], infrared and microwave [32-34] and optical ranges [16, 35] have been widely carried out.

Due to the fast development of flexible portable devices such as mobile phones, laptops, wearable devices, etc., antennas with different tunable functions, based on variable structures, are still in urgent demand, especially in microwave band [33]. It is well established that the extraction method of negative parameters including negative permittivity and negative permeability is a crucial strategy for effective design of practically available meta materials [1, 16, 28, 36-39]. Some groups were ambidextrous to design negative-parameter material with index of refraction equal to minus one [40-42]. HINDY et al [42] developed a circular split-ring resonator with negative permittivity and permeability. It is found that, by using an array of conducting SRR and conducting continuous wires, negative permittivity and negative permeability could be achieved with this simple structure. However, the operating frequency band is quite limited. The metamaterials are of artificial composite structures that exhibit a homogeneous effective permittivity ε and permeability μ, which become negative over an operating frequency range. At this specific frequency, direction of propagation is reversed and the unit cells of the MMT are ordered in geometric arrangements with dimensions that are fractions of the wavelength of the radiated electromagnetic wave. As a result, the electromagnetic response of metamaterials strongly depends on the characteristic geometric parameters (i.e. patterns and dimensions). Therefore, transmission can be altered by adjusting the shape, size, and configurations of the unit cells. This results in control over permittivity and magnetic permeability, which determines the propagation of electromagnetic waves. Driven by the demand of broaden operation frequency band and tunable negative characteristics, it is quite essential to intensively explore the evolution of microwave scattering behaviors with number of this novel split-ring structure.

Herein, a new design, multi-ring square split ring resonator (SSRR), is introduced for multi-band meta-material applications both by numerical simulation and experiment. High-frequency structure simulator (HFSS) software is employed to analyze the scattering parameters (S₁₁ and S₂₁) of the metamaterial structure. Besides, the negative characteristics including negative permittivity, permeability and refractive index, are retrieved from S-parameters. Effects of split-ring number on scattering parameters are intensively investigated. Electromagnetic field distributions are also presented to explain the negative electromagnetic parameters as left-hand characteristics.

2 Method

The designed metamaterial structure has five nested square-split-ring resonators of copper with different lengths (L₁-L₅), but the same width (w) and gap (g) on one side of the substrate. Then five rectangular wires with the same length and width are printed on the other side of the substrate. The substrate is epoxy glass cloth (Grade, FR4) with the dielectric constant of 4.3 and the thickness of 1 mm. The designed metamaterial with five rings between two waveguide ports, front view (SSRR) and back view (wires), are shown in Figures 1(a)-(c), respectively. The simulations have been carried out using the HFSS software based on finite element method. The dimensions have been determined by using genetic algorithm approach and parametric study. The optimized structural parameters of the square split ring resonators, wires and substrates are listed in Table 1.

Retrieving dielectric is important because it can provide the electrical or magnetic characteristics of the materials. Dielectric coefficient and magnetic permeability value are directly calculated by using Nicolson-Ross-Weir (NRW) method in this study. This method separates the frequencies corresponding to half the wavelength of the materials with low loss values due to the phase mismatch.

Besides, electromagnetic parameters such as refractive index, effective dielectric coefficient, and effective magnetic permeability were extracted by using the idea of SMITH et al [43]. This method is presented as the most advantageous method in order to obtain the mentioned parameters directly and also to calculate the effective magnetic permeability value. In order to investigate the electromagnetic characteristics of the proposed structures with numerical simulation, complex μ and ε values of the material are obtained from S parameters at microwave frequency. From the resultant S parameters, unit cells refractive index (n) and wave impedance (Z) can be calculated as [43]:

                                  (1)

                                 (2)

              (3)

                       (4)

where k is the wave vector (i.e. k=2π/λ); and d is the unit cell dimension (i.e. W_s in Figure 1).

Figure 1 Simulation model of proposed structure between two waveguide ports in HFSS (a), top view of square-split-ring (b) and back view of wires (c)

Table 1 Structural parameters of nested square-split-ring resonators

3 Results and discussion

Figure 2 shows the simulated parameters of the designed structure with one square-split-ring resonator on one side of the dielectric substrate and one couple of wires on the other side. It can be seen from Figure 2(a) that the resonant frequency of the SRR is around 12 GHz where S₂₁ presents the minimum value, indicating the negative index in a certain frequency band. It is apparent that the complex permeability and permittivity have negative values simultaneously near 13.3 GHz as shown in Figures 2(b) and (c). The complex impedance shows resonance near 13.3 GHz, and the refractive index becomes negative in the range of 13.3-15 GHz.

When the number of square-split-ring resonators and a couple of wires doubled, as shown in Figure 3, it is obvious that S₂₁ has two minimum values located at 11.6 and 13.8 GHz, respectively. Permeability and permittivity have negative values near two frequencies of 10.5 and 14.0 GHz. Impedance and refractive index also present resonant tendency and negative values around the two frequency points. Besides, the first negative region of refractive index has been conserved, while the second region at a lower frequency region has arisen due to the higher dimensions of the SRR structure [44-46].

Figure 2 Simulated results of sandwiched metamaterial of one ring with different parameters:

When the number of square-split-ring increases to three, S₂₁ in Figure 4 shows three minimum values as predicted. The permeability, permittivity, impedance and refractive index all have negative values in three frequency points, near 10.5, 13.6 and 16.5 GHz, respectively.

Here, it is clear that the left hand characteristics can be tuned by changing the square-split-ring number. Negative refractive index value at medium frequency which is due to the center SRR+wire component has still been conserved. In addition, the resonance frequency of negative refractive index at 11.6 GHz attributed to the biggest SRR+wire component, shifted to 10.5 GHz for the increment of mutual interaction between the added SRR+wire. The newly negative refractive index at 16.5 GHz stems from the assigned SRR+wire with lower dimensions is observed.

Figure 3 Simulated results of sandwiched metamaterial of two rings with different parameters:

As shown in Figure 5(a), S₂₁ presents the four minimum values located in four different frequencies when the number of square-split-ring increases to four. But the frequency ranges with negative values for permeability, permittivity, impedance and refractive index, are not as synergistic as the structure with three rings. Unexpectedly, the frequency band with negative parameters is narrower than that of the structure with three rings. This disturbance of negative refractive index response can arise from the minimization of magnetic dipole moment induction occurring on square-split-ring due to reduction of opposite current flow [12, 25].

Figure 4 Simulated results sandwiched metamaterial of three rings with different parameters:

As shown in Figure 6(a), the number of split rings is increased to five and S₂₁ presents multiple minimum value. The frequency ranges of negative parameters are inconsistent and scattered, which are similar to the structure of four rings. Thus, the metamaterial structure, with three square-split-ring resonators and opposite wires, has the widest frequency band with left hand characteristics in the frequency range of 8-18 GHz.

The induced surface current and electric field distributions for the metamaterial with three rings at the frequencies of 10.5, 13.6 and 16.5 GHz are shown in Figure 7. The induced surface current forms a loop which starts and ends at the gap boundary. As it can be seen in Figure 7(d), the circulating currents on the first ring region concentrate on the center cross point rather than the outbound ring region at 10.5 GHz. It is observed in Figure 7(a) that, the highly concentrated electric field distributes around the outer sides of the rings. The electric field is powerfully coupled with the rings and responses like the electric dipole moment. Hence, the charges of the outer surface excite along the external electric field. As a result, magnetic dipole is induced, and magnetic response results in resonant absorption. There are similar variations at 13.6 and 16.5 GHz.

Figure 5 Simulated results of sandwiched metamaterial of four rings with different parameters:

4 Experimental validations

In order to verify the accuracy of simulated properties of this novel structure, experimental investigations are also carried out. The as-proposed structure is fabricated using the LPKF ProtoMAT E33 prototyping machine computerized numerical control (CNC). Five nested square-split-rings of copper are printed on the upper-side of the FR4 dielectric substrate, whereas five rectangular copper wires are on the back-side.

Figure 6 Simulated results of sandwiched metamaterial of five rings with different parameters:

Reflection and transmission coefficients are obtained based on waveguide method. The fabricated unit cell is placed between the waveguide ports (port 1 and port 2), which work as transmission and receiving terminals. A waveguide to coaxial adapters is connected to the Agilent PNA-L N5234A vector network analyzer via a semi-rigid cable for measuring the S-parameters of the operating desired frequency. The waveguide experiment is performed in an open-space environment, and the measurement is performed accurately calibrated and an Agilent PNA-L N5234A as a vector network analyzer.

Figure 9 shows the comparison between measured and simulated values for S-parameter obtained by experiment and by simulated model in HFSS. In addition to the agreement between experimental and simulation results, some important features should be noticed. It can be seen from Figure 9(a) that the reflection curve (S₁₁) has two intensive peaks at 2.80 and 5.5 GHz, suggesting a broad-band and enhanced left-hand behavior. In the same condition and the same way, the transmission curve (S₂₁) has been monitored within the frequency range of 2-7 GHz, which is as shown in Figure 9(b). Also noted that, curves with multi-peak value below -20 dB for both S₁₁ and S₂₁ could be achieved. This superior property makes SSRR a fascinating candidate for selective frequency absorption or modulation toward microwave frequency band.

Figure 7 Proposed three split-ring meta material with electric field distributions (E) at 10.5 GHz (a), 13.6 GHz (b), and 16.5 GHz (c) and surface current distributions (I) at 10.5 GHz (d), 13.6 GHz (e) and 16.5 GHz (f)

Figure 8 Photographs of fabricated structure of 180 mm×180 mm (18×18 unit cells left-hand material) LHM cell:

Figure 9 Magnitude of measured and simulated value for S-parameters of SSRR structure:

5 Conclusions

A sandwiched metamaterial containing multiple square-split-ring resonators and a set of wires, which exhibited left-hand characteristic in the microwave frequency range, was proposed. The left-hand characteristics, such as negative values of permittivity, permeability, impedance and refractive index are retrieved by high frequency structure simulator, and verified by experiments. These left-hand characteristics are demonstrated to be in direct proportion to the number of square-split-ring resonators in frequency range of 8-18 GHz. Besides, the metamaterial structure with three square-split-ring resonators and opposite wires has the widest frequency band of left-hand characteristics. The electric field and surface current distributions have clarified the physical mechanism of the negative characterization parameters for the designed sandwiched meta- material with three square-split-ring resonators and three wires. To support simulated results, the proposed structure has been fabricated and measured. The test results show good agreement with simulations. The operation band for both reflection coefficient (S₁₁) and transmission coefficient (S₂₁) is greatly improved. Multi-peak curves with optimal value below -20 dB for both S₁₁ and S₂₁ could be achieved. The tunable microwave scattering properties of multi-nested square-split-ring resonate structure would promote the wide application for selective-frequency absorption or modulation toward microwave frequency band.

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(Edited by ZHENG Yu-tong)

中文导读

基于多重嵌套方形开口环超材料的可调谐左手特性研究

摘要：具有左手特性的超材料因具有超常物理特性近年来倍受关注，在微波工程领域也具有重要应用价值。本文设计了一种由多重嵌套方形开口环和一组平行金属线构成的夹芯结构超材料，采用有限元全波仿真软件HFSS系统研究了多重嵌套方形开口环数量对介电常数、磁导率和折射率的影响规律。结果表明，该超材料在8~18 GHz范围内的散射参数(S₁₁和S₂₁)具有显著的谐振特性，其内禀电磁参量也呈现出典型的双负左手特性，并得到了实验验证；且随着多重嵌套方形开口环数量的增加，其谐振峰数量也增加，当开口环数量为3时具有最大的有效频率带宽；进一步分析电磁场分布发现感应磁偶极子是导致强吸收的主要机制。这种结构简单、频率可调谐的超材料在选择性微波吸收材料和微波调制器件中具有广阔的应用前景。

关键词：超材料；方形开口环；负介电常数；感应磁偶极子

Foundation item: Project(2017YFA0204600) supported by the National Key Research and Development Program of China; Project(51802352) supported by the National Natural Science Foundation of China; Project(2019JJ50768) supported by the Natural Science Foundation of Hunan Province of China

Received date: 2019-11-19; Accepted date: 2020-03-23

Corresponding author: LUO Heng, PhD, Lecturer; Tel: +86-731-88836457; E-mail: luohengcsu@csu.edu.cn; ORCID: 0000-0001-8805- 9813