In 1968, Victor Veselago proposed engineered materials with relative negative permittivity (ε less than 0) and permeability (μ less than 0). These different properties as compared to conventional materials with positive permittivity (ε greater than 0) and permeability (μ greater than 0), namely, negative group velocity and negative refractive index. Meta-atom is typically arranged periodically, at scales that maintain sub-wavelength phenomena. Due to non-appearance of properties of regular materials, this matter was less important until 1999. Negative permittivity properties of materials could be found, but to create engineered material with negative permeability was challenging work. Smith et al. developed a new engineered material with unusual properties such as negative permeability and permittivity in 2000 . Different types of unit-cell configuration have been introduced to obtain metamaterial properties. For instance, dual band electric atom and double split ring resonator are found in literature [2–4]. On the other hand, most of the traditional unit-cell depicts single band response. It is important to utilize metamaterial in multiband antenna applications to achieve gain enhancement in all operating bandwidths . However, metamaterials were broadly utilized to develop many antennas. In [6–8], the performance of the antennas was improved by embedding metamaterials.
Due to specific applications, various types of alphabetic structures of metamaterials were proposed. “Z” shaped metamaterial was proposed by Abdallah Dhouibi et al. in  that was found working in single band only with single negative property. The ratio between the wavelengths to unit-cell size is called an effective medium ratio which is important in the design of miniaturized meta-atom. The unit-cell can reveal negative permeability and/ or permittivity in the region of effective medium, whether it is greater than 4. Usually better EMR refers to better sub-wavelength operation of the meta-atom. In , a new two-orthogonal Z-shaped negative index metamaterial was analysed and suggested for multi band operation. Moreover, the design of unit-cell of metamaterial was very large in size and the effective medium ratio was 4.83. Theodosius et al. in  depicted a double negative (DNG) metamaterial of compact size with EMR of 6.9, but they utilized two different resonators at the two opposite sides of the substrate. Various analyses were performed for tri-band operation with a split-H-shaped metamaterial by Islam et al. , resulting in large metamaterial size and small EMR. In microwave imaging applications, negative index metamaterial embedded miniaturized antenna was utilized for ultra-wideband operation , whereas the metamaterial size was big and the effective medium ratio was 6.38. A new dual band metamaterial unit-cell construction was proposed in  with EMR 7.14 but they argumented single negative property for their dual band operation. Hossain et al. in  depicted a double negative (DNG) metamaterial of compact size with 7.44 EMR, but they utilised normal incidence of electromagnetic wave propagation for their analysis.
In this study, a new meta-atom is presented for microwave regime. The proposed meta-atom demonstrates negative permittivity in S-band and negative index meta-atom (NIM) properties for C- and X-band applications for the parallel incidence of electromagnetic wave. The structure of the meta-atom size is miniaturized and follows the good EMR. Moreover, a few parametric studies have been completed for a meta-atom structure that has followed above mentioned properties.
2.1 Geometry of the meta-atom
The proposed meta-atom unit-cell and structural parameters are shown in Figure 1(a). The proposed structure is established by two square-split C-shaped ringslinked to each other. The meta-atom’s thickness was 0.035 mm and FR4 lossy material is utilised as a substrate material. FR4 substrate material having a thickness of 1.6 mm, with a relative permittivity of 4.3 and loss tangent of 0.025 is utilised in the design. In Table 1, the meta-atom’s design specification are reported.
In this paper, the EM simulation solver based on finite-integrationtechnique is adopted to investigate this design. A linearly polarized incident electromagnetic wave parallel to the proposed design is used to provide excitation to the array of the meta-atom. The boundary conditions of PMC and PEC is considered along the z-axis and y-axis, respectively, while open add space boundary is applied tothe x-axis. The fabricated prototype of the suggested design is shown in Figure 1(b). The scattering parameters are determined using frequency domain solver at simulation. The range of frequencyconsidered is 1–15 GHz to simulate the design of meta-atom.
A fabricated prototype is displayed in Figure 2(a). The prototype contains 14 × 12 arrays of unit-cell of copper materials and the size of the prototype is 16.8 × 14.4 cm2. The measurement was performed with two waveguide in the free-space. To allow thepropagation of electromagnetic wave over the prototype, the prototype has been placed between two waveguide port that is similar to the simulation setup. In addition, the transmission coefficient was determined from the PNA network analyzer (N5227). The experimental setup of the proposed meta-atom characteristics measurement is shown in Figure 2(b).
2.2 Effective S-parameters calculation
The transmission coefficient (S21) and reflection coefficient (S11) are utilised to determine the characteristics of the meta-atom such as relative permeability (μ) and relative permittivity (ε). The superiority geometrical approximation can be achieved in the design using FIT based meshing scheme. By using EM simulation solver, S-parameters of the reported meta-atom and array are calculated. The NRW method  was used to excerpt the effective permeability (μ)and permittivity (ε) from the Scattering parameters. To extract effective refractive index (η) from the Scattering parameters, the direct refractive index method  was utilised. The simplified equation for the effective permeability, permittivity and refractive index are as follows: (1) (2) (3) Where c is the velocity of light, d is slab thickness and ω is angular frequency.
3 Results and discussion
In this segment, numerical and experimental result of the compact meta-atom are presented. The characteristics of numerous geometrical parameters and scattering parameters of the structure are also examined. The scattering parameters (S11 and S21) of the meta-atom are shown in Figure 3, which demonstrates the numerical values of three frequency span of resonance frequencies namely 2.13–2.92 GHz, 5.30–5.72 GHz, and 11.17–14.36 GHz that indicates the S -band, C-band and X-band applications.
The values of the transmission coefficient (S21) at the three resonance frequencies 2.60 GHz, 5.55 GHz, and 11.55 GHz are -23.43 dB, −19.73 dB, −22.19 dB, respectively. From Figure 3, it is observed that simulation and experimental results are in good agreement with each other. Figure 4 shows the surface current distributions and the electric field of the unit-cell at 2.60 GHz, 5.55 GHz, and 11.55 GHz respectively, where it reveals effective negative characteristics. Moreover, in Figure 4(a), it is shown that the distribution of surface current at lower frequencies is higher than at higher resonance frequencies of the unit-cell. According to the current distribution results, the current in the upper section is opposite to the lower section of the resonant frequency at 2.60 GHz. It is for this reason, the related magnetic fields nullify each other.
It is also seen that weak local electric field exist at the same time in Figure 4(b). At resonance frequency 5.55 GHz, the current flow in the upper section is same as the direction of the lower section. That is why; the related magnetic fields amplify each other and a strong electric field is observed as shown in Figure 4(c, d). Hence, it is concluded that electric and magnetic resonances exist at these frequencies, and negative refractive index is seen at that frequency which is shown in Figure 6. From Figure 4(e), it is seen that the behaviour of the current distribution is asymmetrical. Thus, the related magnetic fields nullify each other and make weak local electric field (Figure 4(f)). Frequency span of relative permittivity (ε), relative permeability (μ) and relative refractive index (η) of the unit-cell are 1.49–2.68 GHz, 2.946–5.158 GHz, 5.788–7.188 GHz, 9.806–11.08 GHz, 13.474–13.586 GHz, 13.852–14.622 GHz; 2.75–2.848 GHz, 4.528–6.334 GHz, 8.546–13.894 GHz, and 3.604–6.81 GHz, 9.736–11.08 GHz, 11.794–13.124 GHz, 13.32–14.02 GHz, respectively. Frequency span of the double Negative region of the unit-cell are 4.528-5.158 GHz, 5.788–6.334 GHz, 9.806–11.08 GHz, 13.474–13.586 GHz, and 13.852–13.894 GHz. It can be observed that the meta-atom has a negative refractive index at different resonance frequencies.
The retrieval effective permittivity, ε = ε/ + iε//, and effective permeability, μ = μ/ + iμ// are illustrated in Figure 5(a) and 5(b), respectively. Figure 6 illustrates the retrieval effective refractive index, n = n/ + in//. The relative negative refractive indices have been found to be negative for frequency span 3.604–6.81 GHz, 9.736–11.08 GHz, 11.794–13.124 GHz, and 13.32–14.02 GHz. The double negative (ε & μ) region has been found at the frequency regime 4.528–5.158 GHz, 5.788–6.334 GHz, 9.806–11.08 GHz, 13.474–13.586 GHz, and 13.852–13.894 GHz. The double negative region proves the unit-cell and array of meta-atom act as a left handed meta-atom (LHM). This has uses in many sophisticated areas, namely antenna performance enhancers, electromagnetic cloaking operation, design of filters, sensors and detectors, electromagnetic absorber, imaging, noise reduction, and energy harvester etc.
3.1 Role of the middle line width (b) of meta-atom
It is seen from Figure 7 that the reduction of the middle line of unit-cell leads to increase in electrical resonance and reduction of magnetic resonance at 2.60 GHz and 11.55 GHz, respectively.
The decrease in width caused by the reduction in capacitance between the mid-line and the resonator eventually shifts the permittivity curve to lower frequencies. Figures 8(a) and 8(b) show the real and imaginary curves of relative permittivity and relative permeability of unit-cell with a middle line width b = 0.7 mm, simultaneously. Figure 9 also demonstrates the relative negative refractive index curve verses frequency of unit-cell. The relative negative refractive index originated to be negative for frequency span 3.422–6.852 GHz, 9.694–10.87 GHz, 11.038–12.858 GHz, and 13.096–14.006 GHz. The double negative (ε & μ) region has been found at the frequency span 4.57–5.214 GHz, 5.844–6.362 GHz, 9.708–10.646 GHz, 13.278–13.544 GHz and 13.838–13.908 GHz from Figures 8 and 9.
3.2 Role of the resonator width (c) of meta-atom
The width of the square resonator (c) of the unit-cell has been reduced from 1.0 mm to 0.5 mm and investigations of the scattering parameters and effective medium parameters are shown in Figures 10, 11 and 12.
It is seen from Figure 10, the reduction of square resonator on the inner side of unit-cell leads to decrease of electrical resonance at 3.36 GHz and 11.57 GHz, respectively. It is also seen from Figure 10 that resonance points were shifted by a tiny amount at the left side compared to the reported unit-cell. This is due to increase in capacitance between the resonator and the mid-line. Similarly, the increment of the width of the resonator at the outer side would shift the transmittance toward the right side.
Figures 11(a) and (b) demonstrate the Real and imaginary curves of the relative permittivity and relative permeability of unit-cell with resonator width c = 0.5 mm, simultaneously. It is seen from the Figure 11(a) and (b) that the magnitude of the real and imaginary curves of relative permittivity has shifted negligibly and amplitude of the real part turned negative near 3 GHz. The relative permeability of this unit-cell was found constant. On the other hand, the magnitude of the permittivity curves is stronger than reported unit-cell. Figure 12 also illustrates the relative negative refractive index curve verses frequency of unit-cell. The relative negative refractive indices originated to be negative for frequency span 3.632–6.796 GHz, 9.61–10.912 GHz, and 12.13–14.104 GHz. The double negative (ε & μ) region has been obtained at frequency span 4.5–5.158 GHz, 5.774–6.32 GHz, 9.652–10.674 GHz, and 13.11–13.474 GHz. The magnitude of the relative refractive indices is stronger than reported unit-cell because of reduction in inductive path.
The comparison between the proposed meta-atom and other metamaterials are listed in Table 2. The comparison parameters of the metamaterial have been considered here are the size of the unit cell and effective medium ratio. The miniaturization of the metamaterials has been shown in [12, 14], and . Additionally, the mentioned metamaterials cannot preserve higher EMR. Consequently, the proposed meta-atom can achieve better miniaturization while maintaining better EMR than the mentioned designs that were utilised using parallel or normal incidence of electromagnetic wave propagation. In conclusion, the proposed meta-atom has been attained simple and miniaturize design comparing all mentioned references that are suitable for microwave regime.
A new design of miniaturized meta-atom structure was reported for tri-band applications in this paper. The transmission and reflection coefficient as well as EMR of the reported meta-atom were analyzed. The result exhibits negative refractive index properties of the unit-cell structure in tri-band frequency range as well. A comparative analysis also was carried out according to the size of the meta-atom and EMR for tri-band applications. The free-space measurement method was used to verify the results of the prototype of the meta-atom that was fabricated and tested. The proposed meta-atom size and effective medium ratio were 12.0 × 12.0 × 1.6 mm3 and 9.62, respectively. Hence, the meta-atom structure was miniaturized in size and obeys better EMR which were more appropriate in microwave bands.
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About the article
Published Online: 2017-07-03
Citation Information: Open Physics, Volume 15, Issue 1, Pages 464–471, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2017-0052.
© 2017 Mohammad Jakir Hossain et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0