A Combined WU-shaped NRI Metamaterial for Dual Band Microwave Application

In the field of electromagnetism, artificially constructed metamaterial has opened a new hope for the researchers. Metamaterial is developed artificially and not found available in nature. This composite material shows more irregular properties than the natural materials. Negative refractive index (NRI) is one of the exceptional properties of it. Therefore, many researchers have started investigation with this material. Some metamaterials found in literature have NRI properties but very few of them are found operating simultaneously in C-and X-band. In this study, a new combined WU-shaped NRI metamaterial unit cell is presented. Here, three different substrate materials have been adopted for sensitivity analysis. The used substrate materials are FR-4, Rogers RT6006 and Rogers RT6010 and their permittivity are 4.3, 6.15 and 10.2 respectively. Finite integration technique based numerical tool is adopted for all analyses. The electromagnetic properties are determined by Nicolson-Ross-Weir (NRW) method. Perfect electric-magnetic boundary condition is applied for simulation. The metamaterial unit cell exhibits negative refractive index (NRI) within C-band and X-band for all these substrate materials. C-and X-band are widely used for satellite and long distance communication. Moreover, the proposed material shows better effective medium ratio with increasing relative permittivity which ensures the materials proper operation and sensitivity for any applications.


Introduction
The metamaterial (MTM) is an artificial material which is first introduced by the scientist V. G. Veselago in 1967. He proposed that this type of materials show the simultaneously negative permeability (μ) and negative permittivity (ε). The metamaterials are not found in naturally [1]. If a material shows simultaneously negative permeability and negative permittivity then the metamaterial is denoted as double negative (DNG) material or negative-reflective material. A double negative metamaterial is shown in [2] [3]. A metamaterial presents the negative of either epsilon (ε) or mu (μ) that is called single negative (SNG) metamaterials. These types of metamaterials are epsilon negative metamaterial (ENG) and mu negative metamaterial (MNG). An epsilon (ε) negative metamaterial and a Mu (μ) negative metamaterial are introduced in [4] and [5] respectively. After a long time of Veselago's suggestion, in 1996 J. B. Pendry was the first who showed a design of Thin-Wire which exhibits the negative permittivity [6]. The difficulty is to find a material which shows negative permeability (μ) naturally. For this reason, there are no experimental prove. At first, in 2000 Smith et al. reported experimental result of a new artificial metamaterials, which shows double negative property (both negative permeability and negative permittivity) [7]. In 2001, Shelby et al. determined the effective refractive index (η) by using Snell's law where it is negative in a frequency where both permittivity (ε) and permeability (μ) are simultaneously negative [8]. There are several shapes of metamaterials like spiral-shape [9], Triangular [10], S-shape [11], U-shape [12], V-shape [13] are introduced which exhibit their metamaterial properties at a certain frequency. However, all of them do not exhibit negative refractive index in C and X band. But the new proposed combined WU-shaped design shows a negative refractive index in C and X band.

Design
The proposed combined-WU shaped metamaterial unit cell design is displayed in the Figure 1. FR-4 is used as the substrate material which is popular substrate material. In which, dielectric constant (ε) and loss-tangent (δ) of FR-4 are 4.3 and 0.025 respectively. The current density of the unit cell at 3.145 GHz is given in Figure 2.  Both the substrate length and width of the proposed design is x = 10 mm. The thickness of the substrate material is 1.6 mm. The structure of proposed combined-WU shaped metamaterial has been designed with two metal (copper) split square resonator, in which the shape of one strip is W-like and another is opposite U-like. All of the copper thickness is kept 0.035mm. Table 1. enlists the structural parameters of unit cell. The substrate material FR-4 of this design is replaced by another two substrate materials Rogers RT6006 and Rogers RT6010 where the dielectric constants are 6.15 and 10.2 respectively, and the loss-tangents of those substrate materials are 0.0027 and 0.0023 respectively. The proposed design's dimensions of the metamaterials using Rogers RT6010 and Rogers RT6006 as substrate materials are fixed which dimensions are used in the metamaterial using substrate material FR-4.
However, according to the resonance frequency, the effective medium ratio of the proposed combined-WU shaped negative refractive index metamaterial unit cell using substrate material FR-4 is λ/x = 9.53895, where λ is the wavelength. Other two proposed same designed metamaterial unit cells using Rogers RT6010 and Rogers RT6006 as substrate materials maintain an effective medium ratio approximately 13 and 11 respectively.

Methodology
For numerical investigation of the mentioned unit cell, the Computer Simulation Technology Microwave Studio (CST MWS) software is used for electromagnetic simulation. Using CST MWS and placing mentioned cell, transverse electromagnetic wave is propagated through proposed unit cell between two waveguide ports along z-axis from +z to -z direction. On the x-axis and y-axis, perfect electric conductor (PEC) and perfect magnetic conductor (PMC) are applied respectively as boundary condition on waveguide. The S-parameters are S11 (reflection coefficient) and S21 (transmission coefficient) which are obtained after the simulator using the arrangement shown in Figure 3. Simulation arrangement for calculating S-parameters by wave propagating through the z-axis The same designed unit cells are fabricated on substrate materials FR-4, Rogers RT6010 and Rogers RT6006. The unit cell is simulated between the frequencies 1 to 12 GHz, which covers L, S, C, X band. In this paper, electromagnetic properties effective permeability (μr) and permittivity (εr) are determined by Nicolson-Ross-Weir (NRW) method and refractive index (η) is measured by the Direct-Refractive Index (DRI) method using simulated result of S11 and S21 of the proposed unit cell [14]. For analysis, the real values of all three parameters (εr, μr and η) are discussed. Equation (3) and (4) are used for extraction of effective permeability and effective permittivity respectively by using NRW method. V1 = S21 + S11 (1) Where d and k˳ are the thickness of substrate and wave number in the free space respectively, Where (k˳ = ω/c), the angular frequency is expressed as ω and the light speed in free space, c = 3×10 8 m/s.
Here, the refractive index η is obtained by using the direct refractive index (DRI) using (5).
Here, S21 and S11 are the S-parameters.

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A Combined WU-shaped NRI Metamaterial for Dual Band Microwave Application The results of effective permeability (μ), effective permittivity (ε) are found by using NRW method and refractive index (η) is found by using the DRI method for each same designed unit cell using FR-4, Rogers RT6006 and Rogers RT6010 as substrate material.
The simulated result of transmission coefficient, S21 for unit cell using FR-4 as substrate material is given in Fig.  4(a). The results of effective permeability, effective permittivity and refractive index are depicted in the Fig.  4(b), Fig. 4(c) and Fig. 4(d) respectively for the unit cell structure using FR-4.    Fig. 4(b) shows the negative permeability from 6.456 to 12 GHz. Fig. 4 10.328 GHz where all the parameters are negative. Actually when the unit cell exists in a charging magnetic field, the structure gap acts like a capacitor and a charge is created in the gap. In the high frequency the created current in the gap lags the driving field and the negative permeability is formed for this reason. However, Negative refraction is achieved when energy and phase of wave flow oppositely due to the structure.
The simulated result of transmission coefficient S21 for unit cell using Rogers RT6006 as substrate material is given in Fig. 5(a). The results of the effective permeability, effective permittivity and the refractive index are depicted in the Fig. 5(b), Fig. 5(c) and Fig. 5(d) respectively for that same unit cell structure using Rogers RT6006.    Fig. 5(c) shows the negative permittivity from 2.364 to 2.837 GHz, 3.519 to 5.466 GHz, 6.555 to 7.501 GHz and 7.655 to 9.503 GHz. Fig. 5(d) shows the negative refractive index from 2.276 to 2.419 GHz, 3.42 to 3.662 GHz, 4.157 to 4.377 GHz, 5.653 to 9.393 GHz, 9.767 to 10.57 GHz and 10.944 to 11.802 GHz. Hence the proposed unit cell acts as a negative refractive index metamaterials from 6.555 to 7.501 GHz and 7.655 to 9.393 GHz where all the parameters are negative.
The simulated result of transmission coefficient S21 for unit cell using Rogers RT6010 as substrate material is given in Fig. 6(a). The Fig. 6(b), Fig. 6(c) and Fig. 6(d) represent the result of effective permeability, effective permittivity and refractive index respectively for proposed unit cell structure using Rogers RT6010.   Fig. 6(c) Table 3, it is shown that the frequency ranges at which the effective permittivity, effective permeability and refractive index all three parameters are negative. The electric field and magnetic field of the material oscillate like sinusoidal shape when electromagnetic wave propagates through that material and its velocity depends on the electrical conductivity of the material which depends on the internal structure of that material. The relative speed of the electric signal passing through the material is changed according to the type of the interaction with internal structure. The transmission characteristics result depends on the changing of the electrical signal.
It is seen from the Table 3 that the proposed metamaterial shows NRI property in C-and X-band with different dielectric materials. It also holds the frequency band with increasing permittivity. Moreover, increasing bandwidth of NRI is found with increasing permittivity of dielectric materials.

Conclusions
The new designed metamaterial unit cell using different substrate materials exhibits the index of negative refraction (η) in certain area of C and X-band. This proposed NRI metamaterial unit cells using substrate materials FR-4, Rogers RT6006 and Rogers RT6010 cover C-band which band is used in far range radio communications and also covers X-band which is used in satellite communications, radar system and radio communication also. However, the material unit cell also reveals better effective medium ratio with increasing relative permittivity which ensures the materials proper operation and sensitivity for any applications. These properties make this new metamaterial unique and potential for electromagnetic paradigm.