Abstract
The design and absorption analysis of a unit cell of a new multiband split-S-shaped metamaterial is presented in this paper. The computer simulation technology (CST) software based on finite-difference time-domain method was used for the design of the unit cell and its S-parameter calculations. The proposed design shows the resonance frequency within the S-band, X-band, and Ku-band of the microwave spectra. In addition, the proposed material can be used in ε-negative, μ-negative, near-zero refractive index, and double-negative applications as well. The measured result is presented, which shows good conformity with the simulated result. The material shows nearly the same characteristics with bit shifted transmittance at the higher frequency side after reducing the coupling capacitance in the y- or z-axis of the proposed metamaterial. Moreover, it is evident from the investigation that, for shifting the lower ring in the z-axis, 15% more absorption can be achieved for the proposed metamaterial. The simple design, multipurpose applications, and compact size have made the design novel in the electromagnetic paradigm.
1 Introduction
In 1968, Veselago proposed artificial materials that are naturally unavailable and exhibit some extraordinary electromagnetic properties, such as negative refractive index (NRI), Cherenkov radiation, and inverted Doppler effect [1]. Against the natural materials, these artificial materials also may exhibit negative permittivity and permeability simultaneously. The materials that show such type of negative characteristics are called metamaterials, left-handed materials (LHM), NRI materials, and backward wave media. Metamaterials with simultaneous negative permittivity and permeability are called double-negative (DNG) metamaterials. Metamaterials with either negative permittivity or permeability are called single-negative (SNG) metamaterials. Until 1999, this issue was not much interesting to the scientists, as these materials are naturally impossible. Smith and colleagues in 2000 effectively demonstrated such material of DNG property (i.e. both permittivity and permeability are negative), where natural optical or electromagnetic properties are inverted [2]. Due to these extraordinary properties, these materials have been used recently in many important applications, such as antenna design [3, 4], electromagnetic cloaking [5], electromagnetic absorption reduction, and absorber [6, 7]. The near-zero refractive index (NZRI) property of a metamaterial was used to develop a high gain antenna [3, 4]. A μ-negative (MNG) property of a metamaterial was used to develop an electromagnetic cloak [5], and an ε-negative (ENG) metamaterial was used to reduce the SAR effect in human tissues [6]. A multiband metamaterial absorber can be used for the detection of bolometers and explosives as well [7]. According to the applications, different types of metamaterial unit cell designs have been projected in the literature, such as spiral, U-shape, Z-shape, and H-shape [8–12]. However, only a few of them operate in the multiband region of microwave spectra. For example, Benosman and Hacene proposed an S-shaped metamaterial that shows DNG characteristics at the Ku-band only [13]. Turkmen et al. presented a nested U-ring-type metamaterial for the C-band and X-band applications, which does not show DNG characteristics [14]. Mallik et al. suggested a U-shaped DNG metamaterial, which was applicable for the X-band only [15]. In addition, a multiband metamaterial was developed recently but was applicable for DNG and NZRI applications only [11]. However, none of the above authors did an analysis of the absorption properties of their metamaterial in detail.
This paper introduces a unit cell of a new multiband metamaterial that holds two split-ring resonators. These resonators are placed in such a way that it looks like a split-S-shaped structure. It shows resonance within the S-band, X-band, and Ku-band of the microwave region. The proposed metamaterial can be used for multipurpose applications, such as ENG, MNG, DNG, and NZRI. It also shows an SNG property in the S-band, X-band, and DNG properties in the Ku-band. In all the cases, absorption properties are investigated. A further study was done by shifting the lower ring of the unit cell structure a certain distance in the z- and y-axis to see the metamaterial characteristics.
1.1 Structure of the unit cell
The schematic view and the design parameter of the proposed unit cell structure are seen in Figure 1A. The current distribution at 10 GHz and the equivalent circuit of the unit cell are presented in Figure 1B and C, where L, C, and Cp are the inductance, capacitance, and coupling capacitance, respectively. In this structure, two copper-made split-ring resonators are placed in such a way that it forms a split-S-shaped structure. The thickness of each ring is 0.035 mm. The structure was designed over a 20×20 mm2 rectangular FR-4 substrate material with a dielectric constant of 4.5, dielectric loss tangent of 0.002, and thickness of 1.6 mm. The unit cell parameters are seen in Table 1.
(A) Proposed unit cell structure, (B) current distribution, (C) equivalent circuit of the unit cell, and (D) fabricated metamaterial prototype on FR-4 substrate material for measurement.
Design specifications of the unit structure.
| Unit cell parameters | Value (mm) |
|---|---|
| g | 0.25 |
| h | 7 |
| l | 12 |
| s | 1 |
| t | 1 |
| w | 10 |
2 Materials and methods
The metamaterials are characterized by the effective permittivity and permeability that are dependent on S-parameters. There are some commercially available simulation software that are used to calculate these parameters, and each of them uses a different method, such as finite-element method and finite-difference time-domain (FDTD) method. In this study, FDTD-based CST Microwave Studio software (Thomas Weiland; Darmstadt, Germany) has been used to compute complex scattering parameters of the proposed unit cell structure.
The transverse electromagnetic wave was allowed to flow through the structure that was placed between two waveguide ports of positive and negative of z-axis. The perfect electric and perfect magnetic boundary conditions were applied in the x- and y-axis, respectively. The normalized impedance has been set to 50 ohms. The simulation was done in the frequency range of 2–16 GHz. The effective medium parameters permeability and permittivity were extracted from the simulated complex S21 and S11 parameters using the method mentioned in Ref. [16]. The simplified formulas have been given below:
where εr is the effective permittivity, μr is the effective permeability, d is the thickness of the substrate, k0 is the wave number, and η is the refractive index.
For the measurement purpose, the method mentioned in Ref. [17] was followed. A 180×160 mm2 prototype of 9×8 unit cell was fabricated for the measurement, as shown in Figure 1D. The prototype was then placed between two horn antennas that were 1.5 m apart in the same plane. The measurement arrangement is displayed in Figure 2A, where the metamaterial is faced in the z-axis of the antenna. An Agilent E8363D vector network analyzer was used to calculate the transmission coefficient. For calibration purposes, measurements without metamaterial and with metamaterial were done.
(A) Measurement setup (top view) and (B) simulated and measured magnitude of transmission coefficient (S21) in dB.
Further investigation was done after shifting the lower ring 1.6 mm back of the substrate and absorption spectra were observed. For the calculation of the absorbance, the equation mentioned in Ref. [14] was used as mentioned below:
3 Results and discussion
The simulated and experimental results of the transmission coefficient (S21) for the proposed unit cell structure are shown in Figure 2B. Here, the simulated spectra of the transmission coefficient (S21) show the major resonances (that are approximately -10 dB) at 3.47, 8.54, 9.85, 10.73, 13.78, and 14.95 GHz. The resonance frequency of 3.47 GHz is in the range of the S-band, 8.54, 9.85, and 10.73 GHz are in the range of the X-band, and 13.76 and 14.95 GHz are in the range of the Ku-band of the microwave spectra. The experimental result of the transmission coefficient that is seen in the Figure 2B almost agrees well with the simulated result. The measured transmittance shows a slight right-shifted spectra, and at 3.47 and 10.73 GHz, bit extended resonance is visible in the measured result. This shift most likely occurs due to fabrication error.
The effective permeability is shown in Figure 3A and the effective permittivity is shown in Figure 3B against frequency. In Figure 3A and B, it is obvious that, at the maximum point of resonance frequency of 3.47 GHz, both curves of permeability show positive value and permittivity curve shows a negative magnitude: μ=152.65 (real) and ε=-15.31 (real). Therefore, the structure can be characterized as an SNG metamaterial. In the X-band, at 8.54, 9.85, and 10.73 GHz, the permittivity curve is found to be negative and permeability is positive. Therefore, at these points of resonance frequency, the material was also characterized as SNG or ENG. Similarly, at the frequency of 13.78 GHz, the permeability and permittivity show negative values: ε=-1.05 (real) and μ=-2.37 (real). As a result, the structure can be described as a DNG metamaterial. In the same way, at the frequency of 14.95 GHz, the real value of permeability and permittivity is found as ε=-2.96 (real) and μ=-0.15 (real). Therefore, at this point, the structure displays DNG characteristics as well. Normally in the charging magnetic field, the gap of the split ring builds up a charge and produces capacitance. At low frequency, the current of the oscillator remains in the phase of the driving field; at higher frequency, the current starts lagging, which produces negative permeability at that frequency.
(A) Real value of effective permeability (μ) versus frequency and (B) real value of effective permittivity (ε) versus frequency.
In Figure 4A, the real part of the refractive index curve is seen against the frequency, where, at the frequency of 3.47 GHz, the refractive index is η=22.7. At 8.54, 9.85, and 10.73 GHz, the refractive index is also positive (η=1.5, 0.29, and 4.07, respectively). Therefore, the NZRI property is found at 9.85 GHz in conjunction with the ENG property as well. Similarly, at the frequency of 13.78 and 14.95 GHz, the refractive indices are η=-3.60 and -1.62, respectively. Therefore, at 13.76 and 14.95 GHz, the material acts as a DNG metamaterial. The DNG material is also called NRI material, backward media, and LHM.
(A) Real value of refractive index versus frequency and (B) absorption spectra versus frequency.
Moreover in the Figure 4A, the material shows maximum NRI property in the lower frequency region. It covers more than 2 GHz (3.74–5.78 GHz) bandwidth that is better than the characteristics of the material in Ref. [11]. Therefore, the material can be characterized as “wide-band NRI” material as well. In this type of material, the energy flow of waves and phase moves in the opposite direction, which produces this negative refractive media. The overall material characteristics are presented in Table 2. Figure 4B shows the absorption spectra for the proposed metamaterial, where a maximum 45% absorption is achieved.
Basic unit cell characteristics.
| Frequency (GHz) | ε (Re) | μ (Re) | η (Re) | Metamaterial | Absorption |
|---|---|---|---|---|---|
| 3.47 | -5.31 | 152.65 | 22.77 | ENG | 39% |
| 8.54 | -15.32 | 3.31 | 1.5 | ENG | 19% |
| 9.85 | -4.05 | 9.12 | 0.29 | NZRI | 6% |
| 10.73 | -0.4 | 24.82 | 4.07 | ENG | 27% |
| 13.78 | -1.05 | -2.37 | -3.6 | DNG | 25% |
| 14.95 | -2.96 | -0.05 | -1.62 | DNG | 25% |
3.1 Analysis after reducing the coupling capacitance in the z-axis
A further analysis was done by shifting the lower end ring 1.6 mm in the z-axis of the unit cell structure to reduce the coupling capacitance between the two rings. The same methodology is used for simulation. The simulation arrangement, equivalent circuit, and transmittance are seen in Figure 5A–C.
After shifting the lower ring 1.6 mm in the z-axis on the FR-4 substrate: (A) simulation geometry, (B) equivalent circuit, and (C) simulated magnitude of transmission coefficient (S21) in dB.
Figure 6A shows the absorption spectra and Figure 6B shows the real magnitude of permittivity after shifting the lower ring back of the substrate of the unit cell structure. The absorption spectra in Figure 6A show more absorption picks and extended magnitude, especially in the higher-frequency side. The maximum absorbance is gained at 15.58 GHz. In Figure 6B, it is evident that the real magnitude of permittivity at 3.70, 8.35, 8.57, 10.02, and 13.81 GHz is negative, and at 11.00 GHz, a positive magnitude is obtained. Figure 7A and B depicts the real magnitude of permeability and refractive index for shifting the lower ring 1.6 mm in the z-axis. It is seen from Figure 7A that the permeability at 3.70 GHz is negative, and at 8.35, 8.57, and 10.02 GHz, it is positive. The permittivity is also found negative at 11.00 and 13.81 GHz. Therefore, it is apparent that, after shifting the lower ring 1.6 mm in the z-axis of the unit cell, the material acts as an SNG material at the four resonances of X-bands and it displays DNG characteristics at 3.70 and 13.81 GHz in a row. Accordingly, the real value of the refractive index is presented in Figure 7B. It reveals that the material shows DNG characteristics at 3.70 and 13.81 GHz, ENG characteristics at the frequency of 8.35, 8.57, and 10.03 GHz and MNG characteristics in the 11.00 GHz of the X-band. Moreover, the material also exhibits NZRI property in the frequency of 10.03 and 11 GHz besides the consecutive ENG and MNG properties.
After shifting the lower ring in the z-axis: (A) absorption spectra versus frequency and (B) real magnitude of permittivity (ε) material.
(A) Real magnitude of permeability (μ) and (B) real magnitude of refractive index (η) after shifting the lower ring in the z-axis.
Actually, the two metal rings are responsible for creating the inductance and the split of the rings is responsible for creating the capacitance. By increasing the side, the length of the rings the inductance can be increased, which leads to the decrease of the LC resonance frequency. On the contrary, by increasing the gap, the capacitance can be reduced, which leads to increase the LC resonance frequency. The gap “g” in Figure 1A refers to the coupling capacitance. When two conductors are separated by a slit in a changing field, it results in a coupling capacitance. Usually, when the changing field is applied to the two metal rings, they enjoy currents in two opposite directions. Due to the eddy current effect, the propagating current through the coupling conductor produces a magnetic field that makes hindrance for the main flow and results in a negative transmittance. When the gap between the conductors (rings) is increased, the coupling capacitance decreases, which leads to a higher resonance frequency that is evident in Figure 5C if it is compared with the transmittance of Figure 2B. In addition, it is also seen from Figure 6A that, after reducing the coupling capacitance, maximum absorbance has reached up to 55% of the proposed structure. Therefore, approximately 10% absorbance can be increased by reducing the coupling capacitance after shifting the lower ring only 1.6 mm back. The overall results from shifting the lower ring in the z-axis are summarized in Table 3.
Characteristics for shifting in the z-axis.
| Frequency (GHz) | ε (Re) | μ (Re) | η (Re) | Metamaterial | Absorption |
|---|---|---|---|---|---|
| 3.7 | -5.93 | -7089.81 | -314.95 | DNG | 47% |
| 8.35 | -20.81 | 3.08 | 1.32 | ENG | 13% |
| 8.57 | -13.3 | 4.22 | 1.4 | ENG | 18% |
| 10.03 | -2.29 | 14.89 | 0.34 | ENG/NZRI | 9% |
| 11 | 1.66 | -94.17 | 0.45 | MNG/NZRI | 37% |
| 13.81 | -2.92 | -1.52 | -3.15 | DNG | 49% |
3.2 Analysis after reducing the coupling capacitance in the y-axis
A further investigation was done by shifting the lower end ring horizontally 1.6 mm in the downward direction in the y-axis (i.e. on the same plane of the upper ring) of the unit cell structure to reduce the coupling capacitance between the two rings. The same methodology is used for simulation. The simulation arrangement, equivalent circuit, and transmittance are seen in Figure 8A–C, respectively. In Figure 8C, the major resonances are seen at 3.52 GHz in the S-band, at 8.74, 10.03, 10.87, 11.29, and 11.66 GHz in the range of the X-band, and at 14.96 GHz in the Ku-band.
After shifting the lower ring 1.6 mm downward from the upper ring: (A) simulation geometry, (B) equivalent circuit, and (C) simulated magnitude of transmission coefficient (S21) in dB.
The transmission characteristics are likely the same as the basic unit cell transmittance. At the low-frequency side, bit right-shifted resonances are seen compared to the basic unit cell. Moreover, all the resonances have bit reduced magnitude in this case. Figure 9A shows the absorption spectra and Figure 9B shows the real magnitude of permittivity after shifting the lower ring 1.6 mm in the y-axis (i.e. on the same plane of the upper ring) of the unit cell structure. In Figure 9A, the maximum absorption is achieved at 3.47 GHz. In addition, at the relevant frequencies (resonant frequencies), the percentage of absorption follows a nearly identical behavior of the basic unit cell. In Figure 9B, the real magnitude of permittivity at 3.52, 8.74, 10.03, 10.87, 11.29, and 14.96 GHz is negative but at 11.66 GHz is positive. The permittivity curve looks like quite similar to the curve for the basic unit cell. Figure 10A and B displays the real magnitude of permeability and refractive index for shifting the lower ring 1.6 mm downward from the upper ring. The permeability curve in Figure 10A shows nearly the same characteristics as in the basic unit cell permeability curve. It is visible from Figure 10A that the permeability at 3.52, 8.74, 10.03, 10.87, and 11.29 GHz is positive and the permeability at 11.66 and 14.96 GHz is negative.
(A) Absorption spectra versus frequency and (B) real magnitude of permittivity (ε) for the unit cell shifting the lower ring 1.6 mm downward from the upper ring.
(A) Real magnitude of permeability (μ) and (B) real magnitude of refractive index (η) after shifting the lower ring 1.6 mm downward from the upper ring.
As a result, the material can be characterized as an ENG metamaterial at the frequency of 3.52, 8.74, 10.03, 10.87, and 11.29 GHz, and at the 11.66 and 14.96 GHz, the material can be characterized as MNG and DNG metamaterials, respectively. The material can be also characterized as NZRI at the frequency of 8.74 and 10.03 GHz. The refractive index curve in Figure 10B also demonstrates these properties. All the corresponding values are given in Table 4. In addition, Figure 9A clearly shows that, after reducing the coupling capacitance by shifting the lower ring down from the upper ring, maximum absorbance has reached up to 47% for the proposed structure.
Unit cell characteristics for shifting in the y-axis.
| Frequency (GHz) | ε (Re) | μ (Re) | η (Re) | Metamaterial | Absorption |
|---|---|---|---|---|---|
| 3.52 | -9.29 | 179.9 | 24.4 | ENG | 43% |
| 8.74 | -12.22 | 3.93 | 0.99 | ENG/NZRI | 16% |
| 10.03 | -3.37 | 10.63 | 0.35 | ENG/NZRI | 7% |
| 10.87 | -1.18 | 35.8 | 1.86 | ENG | 15% |
| 11.29 | -0.42 | 111.61 | 13.26 | ENG | 27% |
| 11.66 | 1.55 | -29.02 | 3 | MNG | 22% |
| 14.96 | -7.3 | -0.09 | -1.73 | DNG | 17% |
3.3 Comparison for reducing the coupling capacitance in two different directions
There are some certain effects clearly visible from the study. It is apparent from the above investigation that, for the changes of coupling capacitance in either direction, the proposed unit cell is still maintaining SNG characteristics in the X-band and DNG characteristics in the Ku-band. However, the varying characteristic is seen in the S-band region, as it has switched to DNG from SNG for shifting the lower ring in the z-axis of the basic unit cell. The transmittance characteristics are compared with the basic unit cell characteristics. It was seen that, in the X-band, the resonance at 8.57 GHz for z-axis shifting of the lower ring was very close to the resonance at 8.54 GHz for the basic unit cell and the resonance at 10.87 GHz for the y-axis shifting was very close to the resonance position at 10.73 GHz for the basic unit cell structure. The resonance has slight shifted towards the high-frequency side from the basic resonance point of the unit cell for the vertical shift (in the z-direction) of the lower ring.
On the contrary, in the Ku-band, there were two resonance points (13.78 and 14.95 GHz) for the basic unit cell. The resonance at 13.78 GHz was very close to the single resonance point at 13.81 GHz that has been achieved for z-axis shifting. Similarly, the resonance at 14.95 GHz was very close to the single resonance point at 14.96 GHz that has been achieved for y-axis shifting. Therefore, it is evident from the study that the reduction of coupling capacitance in the z-axis has a very nominal effect on the resonance at 8.54 and 13.78 GHz for the basic unit cell. Equally, the decrease of coupling capacitance in the y-axis has a very trivial effect on the resonance at 14.95 GHz for the unit cell. That is why these points of resonance are still unchanged after changing the coupling capacitances. Moreover, another noticeable thing is that, for the changes of coupling capacitance in either direction, the resonance at 10.03 GHz is certain that was at 9.45 GHz for the original unit cell. Therefore, it is evident that the resonance at 10.03 GHz has occurred due to the fixed difference between the rings in the other direction.
Figure 11 displays the comparative scenario of absorption characteristics for the reduction of coupling capacitance in different directions. It is seen from Figure 11 that the maximum absorption is achieved for the shifting in the z-axis, and for the rest of the cases, the absorption is nearly same. Similarly, from the resonance point of view, a significant difference is visible in Figure 12 for the shifting of the lower ring. Figure 12A shows the maximum absorption position for shifting the lower ring in the different direction against the frequency in the S-band only. In the same way, Figure 12B and C displays the maximum absorption point against the frequency in the X-band and Ku-band, respectively. The curve pattern in Figure 12A and B looks similar. In the S-band and X-band, the maximum absorption points are shifting the high-frequency side for shifting the lower ring at different directions. In the case of the Ku-band, the maximum absorption occurs at the high-frequency side for the z-axis shifting, but for y-axis shifting the maximum absorption occurs at an earlier frequency point.
Maximum absorption comparison for the reduction of coupling capacitances.
(A) Maximum absorption comparison against frequency in the S-band, (B) maximum absorption comparison against frequency in the X-band, and (C) maximum absorption comparison against frequency in the Ku-band.
4 Conclusion
This paper presents a new DNG metamaterial structure designed on the FR-4 substrate. It resonates at the S-band, X-band, and Ku-band of microwave spectra. The measured result shows good conformity with the numerical result. The S-band, X-band, and Ku-band are widely used in satellite and radar communications. This metamaterial can be a useful one for cloaking satellite as well. A further investigation was done after shifting the lower ring in the y- and z-axis to see the effect of reduced coupling capacitance. It shows that the reduced coupling capacitance increases the absorbance approximately 2% in the y-axis and 15% in the z-axis of this material. Therefore, this structure can be effectively used besides other metamaterials, especially in the S-band, X-band, and Ku-band applications.
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